TECHNICAL FIELD

The present invention generally relates to fluidic systems and methods, and in particular to such systems and methods for mixing fluid flows.

BACKGROUND

There is a trend in replacing traditional batch chemistry processes with miniaturized continuous systems, such as in flow chemistry, as it allows for systems with a high degree of automatization while also allowing for increased control of key variables, such as residence time, temperature, pressure, and transfer rates. Meanwhile, novel pressurized solvents with high fluidity, like supercritical CO2, allow for an increased efficiency for both chemical reaction and chromatography, and are applied in many different fields of chemistry. However, to fully benefit from such solvents in miniaturized continuous systems, added flow control is needed.

To create fluids with a high solvent power for more polar compounds while maintaining a low viscosity, one option is to use moderately pressurized organic solvents with an addition of a gas, resulting in a gas- expanded liquid. Often, single phase, two-component C02-expanded liquids (CXLs) are used. CXLs have shown to be very efficient in separation systems, increasing extraction rates up to a factor of ten when switching the extraction solvent from supercritical CO2 to C02-expanded methanol or ethanol. CXLs are also tuneable solvents, where changes in pressure, temperature, and composition allow the solvent power to be set, which in turn allows both for the tuning of reaction parameters and for the use of efficient methods to separate and purify products. In supercritical fluid chromatography, the tunable eluent strength of CO2 - methanol/ethanol mixtures provides a route for method optimizations. Waste and energy intensive methods, such as distillation, can be avoided and a reduction of the environmental footprint is also possible by the substantial replacement of organic solvents with reusable and benign CO2.

The use of CXLs in microfluidic systems have so far only seen a mild interest, mainly because it is hard to accurately control polarity and composition of the compressible fluids.

Journal of Micromechanics and Microengineering 2017, 27(1 ): 015018 discloses thin film Pt sensors embedded in shallow etched trenches in a glass wafer that was bonded with another glass wafer having microfluidic channels. The devices having sensors integrated into the flow channels sustained pressures up to 220 bar, typical for the operation of supercritical CO2. Integrated temperature sensors were capable of measuring local decompression cooling effects and integrated calorimetric sensors measured flow velocities over the range 0.5-13.8 mm/s. SUMMARY

It is a general objective to provide an improved mixing microfluidic system and method.

It is a particular objective to provide such a mixing microfluidic system and method capable of handling high-pressure fluids.

These and other objectives are met by the invention as disclosed herein.

The invention relates to a mixing microfluidic system and a method of mixing fluid flows as defined in the independent claims. Further embodiments of the invention are defined in dependent claims.

A mixing microfluidic system of the invention comprises a mixing device configured to mix a first fluid flow and a second fluid flow into a mixed fluid flow. A sensor determines a value of a parameter representative of a composition of the mixed fluid flow. The system also comprises a heating device connected to a microfluidic conduit in fluid connection with the mixing device. The heating device is configured to apply, to a fluid flow passing through the microfluidic conduit, heat based on a control signal generated at least partly based on the value of the parameter.

The invention can be used for control of flow and composition of mixed fluids. Actuation of flow in terms of application of heat can be controlled to affect viscosity and/or density. Accordingly, the mixing microfluidic system can control and tune both the composition of mixed fluids and the total flow rate of different fluid streams with a shared pressure. The mixing microfluidic system has a large rangeability over the entire compositional scale and can be fine-tuned to various levels. Furthermore, the mixing microfluidic system is stable and can operated with low drift and fluctuation. BRIEF DESCRIPTION OF THE DRAWINGS

The embodiments, together with further objects and advantages thereof, may best be understood by making reference to the following description taken together with the accompanying drawings, in which:

Fig. 1 is a schematic illustration of a mixing microfluidic system according to an embodiment; Fig. 2 is a schematic illustration of a mixing microfluidic system according to another embodiment;

Fig. 3 is a schematic illustration of a mixing microfluidic system according to a further embodiment;

Fig. 4 is a schematic illustration of a mixing microfluidic system according to yet another embodiment;

Fig. 5 is a schematic illustration of a mixing microfluidic system according to a further embodiment; Fig. 6 is a schematic illustration of a mixing microfluidic system according to an embodiment;

Fig. 7 is schematic illustrations of three different fluid delivery setups for a binary component fluid flow.

The two fluids, CO2 (1.) and a co-solvent (CS) (2.), are driven to a point where they are mixed (Mixing) and subsequently used in an application (Application). After the application, regulation of the back- pressure (BPR) may be performed. In Fig. 7A, two piston pumps deliver the two fluids separately. In Fig. 7B, the two fluids are delivered by a single CO2 pump and a piston separated chamber with preloaded co-solvent. The CO2 is pumped towards the application but is also connected to a piston separated chamber. On the opposite side of the piston in the chamber, preloaded co-solvent is driven forward. In Fig. 7C, a closed compressed CO2 container is used and no pumps are used as the force required to drive the flow is generated from a compressed fluid, like CO2, in a container of fixed volume. Co-solvent is delivered as in Fig. 7B. For Figs. 7A and 7B, the pumps operate by either maintaining a constant pressure (at the pumps) or a constant piston movement. For Fig. 7C, pressure will decrease over time. Rr is a defined restriction along the flow path. Fig. 8 illustrates the flow regulating board (FRB), having actuators chips (hCS, hC02) connected to their respective fluid sources at pressure P2 and Pi (Fig. 8a). As fluids flow, they reach the mixing chip (MIX) where they mix. Thereafter, the mixed fluid passes a relative permittivity sensor (SEN). Schematic of the actuator chip from top (Fig. 8b) and side view (Fig. 8c), showing the two glass wafers. The thin film conductors, made from 15 nm Ta and 100 nm Pt thin film conductors, can be seen with its 20 connection pads at the sides of the chip, heating resistors placed over the fluid restrictor and, two temperature sensors in the ends of the fluid restrictor. The fluid path consists of an inlet leading to a fluid restrictor, which is a 77.6 mm long meander, and an outlet. The inlet and outlet are etched deeper than the restrictor, allowing capillaries to be mounted in them. At each end of the restrictor, a temperature sensor is placed. Fig. 8d illustrates a cross section of the fluid meander showing the dimensions and positions of the heater in mm. The dimensions of the narrow and wide restrictor channel with heater were shown in pm. Fig. 8e is a close-up of the restrictor channel outlet showing the end of a heating resistor (H) as well as the outlet temperature sensor giving the temperature Tf. The direction of flow is indicated by an arrow. Fig. 9 illustrates diagrams of the control systems I and J. Fig. 9 left, system I was applied to regulate both sr and Qtot using PI2 and PI1 , respectively, by comparing the input variables to w _er and wotot. The actuators, i.e., hCS and hC02, are shown as valves together with the manipulated variable, i.e., the duty cycles, yco2 and yes. Fig. 9 right, system J was applied to regulate only s _r . w _er was compared with the input variable s _r at the controllers PI4 and PI5. For hC02, cascade control of two regulators where used. The output of PI4 was the reference variable for PI3, which regulated Ti to a constant temperature higher than WTmin. The signal conversion from the scattering parameter sn to s _r is also shown.

Fig. 10 illustrates operation of either hCS (top-left) or hC02 (bottom-left) using application of power in a square wave (light grey line) between zero and full power. As power was applied, both the outlet temperature of each actuator and the relative permittivity (marked with arrow) increased and reached a steady state value. When power was off, s _r assumed a value of 11 ± 2, while the total flow rate was 95 pL/min. It can be noted that the falling edge curve of hCS was convex downwards, but for hC02, the curve had a local minimum before reaching the plateau. The axis of s _r is set between the limits 1.44 and 35.7, corresponding to the pure components at the temperature of the sensor. Fig. 10 right, the relative permittivity as a function X2. Data points (dots) over the region 0.344 to 0.773 are shown together with the sigmoid fitting curve (black line) and the measurements of the pure components (black diamonds).

Fig. 1 1 illustrates operation of either hCS (Figs. 1 1 a, 11 c) or hC02 (Figs. 1 1 b, 1 1 d). During operation, only one actuator was powered, having the other actuator turned off. (Figs. 1 1 a, 1 1 b) s _r (dots), X2 (triangles) and x ₂ (dashed lines) as a function of Tf for each powered actuator. Tf of the unpowered actuator was 4.7-7.4°C (Fig. 1 1 a) and 4.8-6.1 °C (Fig. 1 1 b), respectively. (Figs. 1 1 c, 1 1 d) s _r as a function of the volumetric flow rates Q2 (triangles), Q1 (squares) and Qtot (diamonds). During the operation of hCS, Qtot varied around an average flow rate of 69 pL/min. For hC02, Qtot decreased with -3.4 pL/min per unit of sr. Fluid setup in Fig. 7A was used with P2, Pi and Pb of 92.8 ± 0.02, 78.5 ± 0.02 and 70.2 ± 0.2 bar, respectively. The baseline relative permittivity was 10.5 ± 2.

Fig. 12 illustrates total volumetric flow rate (top) and relative permittivity (bottom) as a function of time. Flow is delivered at constant pressure using a single pump (fluid setup in Fig. 7B). When the FRB was not activated (marked by dotted ellipse), s _r was 2.90 ± 0.30 and Qtot was 79 ± 13 L/min. When control system I of the FBR was activated to wotot = 50 pL/min and ws _r = 6, the flow and relative permittivity reaches 49 ± 6 pL/min and 5.99 ± 0.05. Two replicate measurements at both activated and deactivated mode are shown. Pb = 64.5 ± 0.05 bar.

Fig. 13 illustrates estimated molar fraction, x ₂ , as a function of time while running gradients of x ₂ using control system J. Flow was driven by operating a single pump (fluid setup in Fig. 7B) at a constant flow rate of 25 pL/min. After 2 min, four different gradients were initiated by increasing w _er from 16 to 26, corresponding to x ₂ of 0.49 to 0.74, over 4, 8.5, 14, and 19.5 min. During the gradient, Pi varied between 72 and 75 bar. Pb = 64.5 ± 0.05 bar.

Fig. 14 top, s _r (marked with black arrow) as a function of time when activating control system J and allowing P to vary. Before the system was activated, the baseline had a relative permittivity of 16.4 ± 0.65. From 0-220 s, flow was delivered from a single pump at a constant pressure P _op , then, at 220 s, (dotted line) pressure regulation of Pco2 from the piston pump was turned off allowing the pressure to drop from 74 bar to 68 bar over 1 1.5 min, thus replicating conditions of fluid setup Fig. 7C. w _er = 20 (dashed line). Fig. 14 bottom, duty ratio as a function of time for the two actuators hCS (marked with black arrow) and hC02 while using the control system. After 220 s, the duty ratio rose to compensate for the falling pressure.

Fig. 15 m2Ό2 (squares) and miui (circles) as a function of temperature. Values were calculated from Tf and the average pressures over the FRB using Journal of Physical and Chemical Reference Data, 1996, 25(6): 1509-1596; J. Phys. Chem. Ref Data, 1998, 27(1 ): 31-44; Int. J. Thermophys., 1987, 8(2): 147- 163; J. Chem. Thermodyn., 2008, 40(9): 1386-1401 and the measured P and T. A local minimum of miui was seen at 30.9 °C.

Fig. 16 illustrates the layout of the fluid system, composed of the two piston pumps, fluid lines, valves, filters, the two chips and back pressure sensor and regulator (BPR) (Fig. 16a). The one-port connection between the sensor chip and the network analyzer (NA) is also outlined. The locations (grey arrows) of pumps, restrictions, t-junction and backpressure sensor is indexed by p, r, t and b, respectively. Fig. 16b illustrates a model circuit diagram of the microfluidic system with its restrictions and flow direction (black arrows). Variables are indexed on the form fl where f and I denotes the fluid type and location type, respectively. From each inlet, molar flow, m, of either CO2 (f = 1 ) or ethanol (f = 2) first reaches the restrictions Rir and R2r (having the inlet pressures Pip and P2 _P ) and are then mixed at the T-junction. The mixed flow (f = m) then passes the restriction R _mr , attaining the backpressure Pfb. At the T-junction, all 3 restrictors shared the pressure Pmt. Fig. 17 is a sketch of the ring-shaped flow channel with the two ring shaped plate electrodes, forming a capacitor. One of the conductor paths, following from the bottom of the etched channel to the bond plane, is seen in the close-up (dashed rectangle). The center diameter of the ring channel, the width of its cross- section and the distance between the plates is also shown. Fig. 18 illustrates the thin film conductor following the etch wall, showing the bond interface plane to the left and the etched channel to the right (Fig. 18a). The image was taken before wafer bonding. Fig. 18b shows an image of the sensor chip showing the electrodes in black, forming a ring-shaped plate capacitor. Perpendicular to the direction of the electrical conductors and connection pads, the fluid interfaces and channels can be seen connecting to the central ring.

Fig. 19 shows reference s _r as a function of measured capacitance. The linear calibration curve, r ² = 0.9999, was made using six different reference fluids. s _r as a function of time (bottom right box) when the fluid in the sensor was changed from ethanol to methanol, showing each data point as circles. Pumping at 300 pL/min was started at 37 s (dotted line). T = 21 ± 1 °C.

Fig. 20 shows s _r as a function of Pfb for CO2 under a gradual pressure build-up from 50 to 65 bar. The change corresponded to the phase transition when crossing the vapor-liquid equilibrium (dotted line) at 58.5 bar and 21 °C. T = 21 ± 1 °C. Fig. 21 shows how ethanol entered the T-junction of the mixing chip from the left, and contacted CO2 flowing in from the top. At the mixing point of the T-junction, a phase interface was formed between ethanol and CO2. As the flow ratio was changed, corresponding to an X2P of 0.5 (Fig. 21 a) and 0.8 (Fig. 21 b), the position of this phase interface across the channel changed. Pfb = 82 ± 0.6 bar, T = 21 ± 1 °C. Fig. 22 shows s _r as a function of molar fraction ethanol in CO2. Measurement points of s _r (solid circles) are shown as a function of either X2Q (Fig. 22a) or x2P (Fig. 22b). Measurements of the pure components (Black diamonds) as well as fitting curves (Black lines) are also shown. In Fig. 22a, s _r deviates from the fitting curve (ky = -0.41 ± 0.26) at high X2Q. In Fig. 22b, the correlation to the fitting curve (ky = -0.63 ± 0.02) is higher, and values of X2P range from 0.06 to 0.90. The relative uncertainties of X2Q and X2P are also shown. R¾ = 82 ± 0.6 bar, T = 21 ± 1 °C.

Fig. 23 shows feedback control of s _r when flowing the C02-ethanol. The measured (full line marked with arrow) and set point (dotted line) values are shown as a function of time. P2 _P is the manipulated variable. Pip = 102 bar, R¾ = 79.3 ± 0.2 bar, T = 21 ± 1 °C, The total flow rate were 80-90 pL/min and 56-68 pL/min at s _r of 10 and 15, respectively.

Fig. 24 is a flow chart illustrating a method of mixing fluidic flows according to an embodiment;

Fig. 25 is a flow chart illustrating an additional step of the method shown in Fig. 24 according to an embodiment;

Fig. 26 is a flow chart illustrating an additional step of the method shown in Fig. 25 according to an embodiment; and

Fig. 27 is a flow chart illustrating an additional step of the method shown in Fig. 25 according to an embodiment. DETAILED DESCRIPTION

Throughout the drawings, the same reference numbers are used for similar or corresponding elements.

The present invention generally relates to microfluidic systems and methods, and in particular to such systems and methods for mixing fluid flows.

Miniaturized flow systems for chemical analysis create more accessible analytics, which have potential for today’s data driven society where more information is a key advantage. Yet, common high performance equipment for these purposes, such as high pressure liquid chromatography (HPLC), have difficulties when it comes to downscaling due to their reliance on moving parts, such as motors, valves and pumps. To achieve miniaturizations of flow systems, many areas and processes must be addressed, but one is to regulate fluid flow and composition of the fluid flows.

For instance, a binary fluid mixture, such as using CO2 and a co-solvent, for instance an alcohol, such as methanol or ethanol, is often used as a mobile phase in supercritical fluid chromatography and enriched fluidity chromatography due to its low viscosity and tunable solvent power. By using such a mobile phase, a very high performance can be achieved in chromatography. There is, thus, a need to accurately produce such binary fluid mixtures. CO2 is compressible and can by pressurization have a density comparable to alcohols, but with a lower viscosity. Due to its low critical point, it has a variable density with pressure and temperature. Generally, this is a problem for people working with C02-containing binary fluid mixtures, as it makes handling and control very difficult. This property of CO2 and other compounds can, however, be exploited to control mixing of fluid flows in a mixing microfluidic system of the present invention.

Further, compressed CO2 can be used as a pressure source instead of pumps, which is useful for miniaturized systems, such as a mixing microfluidic system of the present invention. Generally, driving flow with compressed CO2 is limiting as it becomes even more difficult to control flow rate and additions of co-solvents to the mobile phase. The mixing microfluidic system of the invention solves such problems and enables an efficient formation of controllable binary fluid mixtures.

Generally, the mixing microfluidic system can operate on high pressure microflows of fluids, such as CO2 and a co-solvent, and uses heat to actuate and induce changes in fluid flows rather than relying on moving parts. Feedback information from at least one sensor, such as a relative permitivity sensor and optionally a total flow rate sensor, to the actuator(s) can then be used to control the composition and/or flow of the fluid mixture.

In an embodiment, the mixing microfluidic system can utilize the special density properties of CO2 and similar fluids to achieve the composition and/or flow control, where heat from the actuator(s) can be used to partly "stop" the CO2 flow. Furthermore, heating the co-solvent lowers its viscosity, thus, increasing its flow. The mixing microfluidic system can thereby be used to create a mobile phase, such as consisting of CO2 and a co-solvent.

An advantage of the mixing microfluidic system of the invention is that it can, over a given timescale, keep the flow and the composition constant, even if the fluid flows are driven from pumpless sources, such as pressure generated only from compressed CO2.

An aspect of the invention relates to a mixing microfluidic system 1 , see Fig. 1. The mixing microfluidic system 1 comprises a mixing device 10, a sensor 20 and a heating device 30. The mixing device 10 comprises a first fluid input 1 1 and a second fluid input 12 and a fluid output 13. This mixing device 10 is configured to mix a first fluid flow received in the first fluid input 11 and a second fluid flow received in the second fluid input 12 into a mixed fluid flow that is output at the fluid output 13.

The sensor 20 is configured to determine a value of a parameter representative of a composition of the mixed fluid flow.

The heating device 30 of the mixing microfluidic system 1 is connected to a microfluidic conduit 32 in fluid connection with the first fluid input 1 1 (as shown in Fig. 1 ) or the second fluid input 12. The heating device 30 is configured to apply heat to a fluid flow passing through the microfluidic conduit 32. In more detail, the heating device 30 is configured to apply heat to the fluid flow based on a control signal generated at least partly based on the value of the parameter. Thus, the mixing microfluidic system 1 includes a mixing device 10, in which at least two fluid flows are mixed into a mixed fluid flow. The at least two fluid flows enter the mixing device 10 in a respective fluid input 1 1 , 12 and the resulting mixed fluid flow leaves the mixing device 10 at a fluid output 13.

At least one of the fluid flows entering the mixing device 10 has passed through a heating device 30, also referred to as actuator herein. Fig. 1 illustrates a situation, in which only one of the fluid flows passes a heating device 30, such as the first fluid flow or the second fluid flow. Fig. 3 illustrates another embodiment of the mixing microfluidic system 1 having two heating devices 30, 31 , one for each of the first and second fluid flows. The at least one heating device 30 of the mixing microfluidic system 1 applies heat to the fluid flow passing through the microfluidic conduit 32 in the heating device 30. The amount of heat applied by the heating device 30 to the fluid flow is in turn based on and thereby controlled by a control signal. This control signal is generated at least partly based on the value of the parameter representative of a composition of the mixed fluid flow exiting the mixing device 10 and determined or measured by the sensor 20. As a consequence, the heat application by the heating device 30 is dependent on and controlled at least partly based on this parameter value.

“Composition of the mixed fluid flow” or, simply,“composition” as used herein relates to the composition of the mixed fluid flow, i.e., the composition of the fluid flow exiting, and thereby downstream of, the mixing device 10 in the mixing microfluidic system 1. The sensor 20 of the mixing microfluidic system 1 is configured to determine a value of the parameter representative of such a composition of the mixed fluid flow. As is shown in Fig. 1 , the heating device 30 is arranged upstream, with the regard to the flows of the fluids through the mixing fluidic system 1 , of the mixing device 10, which is in turn arranged upstream of the sensor 20. Hence, an output of the heating device 30 is in fluid connection with the first fluid input 1 1 or the second fluid input 12 of the mixing device 10. Correspondingly, the fluid output 13 of the mixing device 10 is in fluid connection with the input to the sensor 20. The mixed fluid flow exits the mixing microfluidic system 1 downstream of the sensor 20.

The heating device 30 is, in an embodiment, configured to apply, based on the control signal, heat to the fluid flow to adjust a flow rate of the fluid through the microfluidic conduit 32. As is further shown in the Examples presented herein, an (individual) adjustment of fluid flows by control of heat application to the fluid flows can be used to control and adjust the composition of the mixed fluid flow.

Usage of heat from the heating device 30 to control fluid flows and thereby the composition of the mixed fluid flow has advantages as compared to traditional solutions involving controllable pumps and valves. Such controllable pumps and valves are very hard to miniaturize, in particular when used in connection with high pressure fluids. Hence, they are not suitable to be included in a mixing microfluidic system 1 operating on small fluid volumes, such as in the form of a mixing microfluidic system 1 or in handheld or portable devices where the space and weight should be minimized.

In addition, the small volume of the components 10, 20, 30 of the mixing microfluidic system 1 implies that they can be arranged close to each other, thereby reducing the time required for fluid flows to pass through the mixing microfluidic system 1. This in turn implies that changes in the composition of the mixed fluid flow can be detected by the sensor 20 at an earlier stage and thereby corrected for by controlling the heat applied by the heating device 30. As a consequence, the performance of the mixing microfluidic system 1 will increase.

Furthermore, the low total fluid volume of the mixing microfluidic system 1 reduces flow variations and thereby makes the mixing microfluidic system 1 very stable. If a given volume of a compressible fluid, such as CO2, is exposed to changes in pressure and/or temperature, the fluid flow and composition will be affected. Such variations increase if the fluid volume is larger. Hence, it is generally preferred to minimize the fluid volume in the mixing microfluidic system 1 , i.e., minimizing so-called dead volume. Mixing microfluidic systems 1 with low dead volumes are more efficient since less fluid volumes are needed and fluid variations are suppressed. The small total size that can be achieved with a mixing microfluidic system 1 according to the invention implies that the mixing microfluidic system 1 can be arranged in connection with the actual application or usage of the resulting mixed fluid flow, such as in connection with a chromatography column.

Hence, the fluid conduits of the mixing microfluidic system 1 , including the fluid conduit 32 connected to the heating device and a fluid conduit 15 of the mixing device, are microfluidic conduits 15, 32, i.e., having at least one cross-sectional dimension within the micrometer range. Thus, the diameter, width and/or height of the microfluidic conduits 15, 32, depending on the particular cross-sectional shape of the microfluidic conduits 15, 32, is within the micrometer range. This micrometer range is preferably from 1 m up to 1000 m but may also include sub-micrometer dimensions, i.e., below 1 pm. Correspondingly, the fluid flows in the mixing microfluidic system 1 , such as through the microfluidic conduits 15, 32, are fluid microflows, i.e., fluid flows of small volumes and typically within the microliter range, such as from about 1 mI up to 1000 mI but may also include sub-microliter volumes, i.e., below 1 mI.

The fluid flows through the mixing microfluidic system 1 and the microfluidic conduits 15, 32 therein are preferably microfluidic flows with a flow rate ranging from mI per hour up to mI per second, i.e., from mI/h up to mI/s, including within the range of mI/min, such as from 1 mI/min up to 1000 mI/min as illustrative, but non-limiting, examples.

In an embodiment, the heating device 30 is configured to apply, based on the control signal, heat to the fluid flow to adjust at least one of a viscosity and a density of the fluid flow through the microfluidic conduit 32.

Hence, the heating device 30 can adjust the fluid flow through the microfluidic conduit 32 by affecting the flow resistance that the fluid flow is exposed to when passing through the microfluidic conduit 32. A change in heat applied to the fluid flow affects the viscosity and/or density of the fluid, both of which affects flow resistance and thereby the flow rate of the fluid.

Generally, application of heat to a fluid reduces the viscosity of the fluid and thereby increases the flow rate of the fluid. This general effect applies for most fluids, such as co-solvents. However, for compressible fluids, such as dense CO2, the effect was surprisingly opposite. Hence, application of heat to a CO2 flow lowered the flow rate of the CO2 flow. A reason for this opposite effect may be related more to changes in density of the CO2 flow rather than to changes in viscosity of the CO2 flow. In an embodiment, the mixing microfluidic system 1 comprises a flow regulating board 2 comprising the mixing device 10, the sensor 20 and the heating device 30. This flow regulating board 2, or FRB for short, may, for instance, be in the form of a printed circuit board or chip acting as a support for the mixing device 10, the sensor 20 and the heating device 30. This in turn implies that these components 10, 20, 30 of the mixing fluidic system 1 can be handled as a single unit if arranged on the flow regulating board 2.

The microfluidic conduits 15, 32 of the mixing fluidic system 1 can then be implemented as microchannels in the printed circuit board or chip.

Fig. 6 illustrates another embodiment of the mixing microfluidic system 1 that does not comprise any flow regulating board 2. In such an embodiment, the microfluidic conduits 15, 32 of the mixing microfluidic system 1 could be in the form of thin pipes or tubes, such as capillaries, rather than microchannels in a printed circuit board or chip.

The mixing microfluidic system 1 preferably comprises, in an embodiment, a closed control system 5 connected to the heating device 30 and to the sensor 20. The closed control system 5 is configured to generate the control signal based on the value of the parameter. In this embodiment, the closed control system 5, also referred to as controller (CTRL) herein, receives the parameter value as determined by the sensor 20 and generates the control signal that is input to the heating device 30 and used therein to control the amount of heat to apply to the fluid flow through the microfluidic conduit 32. In other words, the closed control system 5 generates the control signal Sctri as a function f[ ) of the determined parameter value e, i.e., Sctri = f[ s ).

In a particular embodiment, the closed control system 5 is configured to generate the control signal based on the value of the parameter and a target value of the parameter. In such a particular embodiment, the closed control system 5 uses not only the determined parameter value but also a target value for the parameter when generating the control signal. For instance, the closed control system 5 could generate the control signal based on a difference between the determined parameter value and the target value ST, i.e., Sctri = f[ s - ST ), Sctri = f[ ST - s ) or Sctri = f[ |e - ST\ ), or a quotient between the determined parameter value and the target value, i.e., Sctri = f[ s I ST ) or Sctri = f[ s T I S ). In these embodiments comprising the closed control system 5, the target parameter value is representative of a target composition of the mixed fluid flow. This means that the above mentioned difference or quotient represents a current deviation of the actual composition of the mixed fluid flow from the desired target composition. The closed control system 5 can thereby control the heating device 30 to adjust the amount of applied heat to obtain a determined parameter value that is as close as possible to the target parameter value, and thereby obtain a composition of the mixed fluid flow that is as close as possible to the target composition. A difference equal to or close to zero and a quotient equal to or close to one represent a composition of the mixed fluid flow that is close to the target composition.

In an embodiment, the heating device 30 is an inline heating device 30 comprising a meander microfluidic conduit 32 in direct or indirect connection with at least one heat generating element 34.

In an implementation example, the heating device 30 comprises at least one pair of heat generating elements 34, preferably multiple, i.e., at least two, pairs of heat generating elements 34. In such a case, one heat generating element 34 in each pair is arranged at one side of the meander microfluidic conduit 32 with the other heat generating element 34 in each pair arranged at the other, opposite side of the meander microfluidic conduit 32 as shown in Fig. 1. This implementation solution provides an efficient heating of the fluid flow through the meander microfluidic conduit 32 with a rapid response time, i.e., can change the temperature of the fluid flow in the meander microfluidic conduit 32 very rapidly.

In the embodiment shown in Fig. 1 having a single heating device 30 one of the fluids will have a longer fluid path through the mixing microfluidic system 1 as compared to the other fluid since it has to pass through the meander microfluidic conduit 32 of the heating device 30.

In another embodiment shown in Fig. 2, the mixing microfluidic system 1 also comprises a single heating device 30 but in this embodiment both fluids have substantially the same fluid path lengths through the mixing microfluidic system 1. This is achieved by arranging a meander microfluidic conduit 42 for the fluid not passing through the heating device 30. In such a case, this meander microfluidic conduit 42 preferably has a same or similar length as the meander microfluidic conduit 32 of the heating device 30 as shown in Fig. 2. Flowever, in clear contrast to the meander microfluidic conduit 32 in the heating device 30 this meander microfluidic conduit 42 is not in direct or indirect connection with any heat generating elements 34. In a further embodiment, the mixing microfluidic device 1 comprises two heating devices 30, 31 as shown in Fig. 3. In such a case, a first heating device 30 is connected to a first microfluidic conduit 32 in fluid connection with the first fluid input 1 1 of the mixing device 10. The first heating device 30 is configured to apply heat to the first fluid flow passing through the first microfluidic conduit 32. The first heating device 30 is configured to apply this heat based on a first control signal generated at least partly based on the determined parameter value. A second heating device 31 of the mixing microfluidic system 1 is connected to a second microfluidic conduit 33 in fluid connection with the second fluid input 12 of the mixing device 10. The second heating device 31 is configured to apply heat to the second fluid flow passing through the second microfluidic conduit 33. The second heating device 31 is configured to apply this heat based on a second control signal generated at least partly based on the determined parameter value.

In an implementation example, the two heating devices 30, 31 are substantially the same and thereby have the same number of heating elements 34, 35 and substantially the same meander microfluidic conduit 32, 33. However, the two heating devices 30, 31 are preferably independently controlled using different control signals generated by the closed control system 5 based on the parameter value from the sensor 20. Such an individual control of the heating devices 30, 31 is preferred since it enables a more accurate control of the composition of the resulting mixed fluid flow.

In a less preferred embodiment, the two heating devices 30, 31 are instead controlled, such as by the closed control system 5, using a same control signal.

In the following, various additional embodiments of the mixing fluidic system 1 will be described with reference to Figs. 4 and 5 and comprising additional sensors 6, 7. In Figs. 4 and 5, a mixing microfluidic system 1 as schematically shown in Fig. 1 has been used. In other embodiments, a mixing microfluidic system 1 as shown in Fig. 2, 3 or 6 could instead be used together with the flow sensor (FS) 6 as shown in Fig. 4 and/or the temperature sensor (TS) 7 as shown in Fig. 5.

Hence, in an embodiment, the mixing microfluidic system 1 comprises a flow sensor 6 as shown in Fig. 4. This flow sensor 6 is configured to measure a flow rate of the mixed fluid flow. The heating device 30 is then configured to apply heat based on the control signal generated at least partly based on the determined parameter value and the measured flow rate.

In an embodiment, the mixing microfluidic system 1 also comprises the previously mentioned closed control system 5 that is connected to the heating device 30, the flow sensor 6 and the sensor 20. In this particular embodiment, the closed control system 5 is configured to generate the control signal based on the value of the parameter determined by the sensor 20 and the flow rate Qtot measured by the flow sensor 6, i.e., Sctri = f{ s, Qtot ). In a particular embodiment, the closed control system 5 is configured to generate the control signal based on the value of the parameter determined by the sensor 20, the flow rate measured by the flow sensor 6, a target value of the parameter and a target flow rate QT i.e., Sctri = f[ e, ST, Qtot , QT ). In such a particular embodiment, the closed control system 5 employs not only the determined parameter value and the measured flow rate but also corresponding target values when generating the control signal. For instance, the closed control system 5 could generate the control signal based on a difference or quotient between the determined or measured value and the target value, i.e., Sctri = f[ |e - ST\, \ Qtot - Qr| ), Sctri = f{ e / ST, | Qiof - Qr| ), Sctri = f{ ST I S, |Qfof - Qr| ), Sctri = f{ |e - et|, Qtot/ Qr ), Sctri = f{ |e - et|, Qr/ Qtot ), Sctri = f{ s l ST, Qtot/ QT ), Sctri = f{ s l et, QT/ Qtot ), Sctri = f{ sTl s, Qtot/ QT ) or Sctri = f{ sT I s, QT/ Qtot ). In the above exemplified functions, the absolute difference |-4 - AT\ can be replaced by ( A - AT), {AT - A) or {A -AT) ^m , wherein A represents e or Qtot and m is an integer equal to or larger than two, preferably equal to two.

In these embodiments comprising the closed control system 5 and the flow sensor 6, the target parameter value is representative of a target composition of the mixed fluid flow and the target flow rate is representative of a target rate of the mixed fluid flow. This means that the above mentioned differences and/or quotients represent current deviation of the actual composition of the mixed fluid flow from the desired target composition and the actual flow rate of the mixed fluid flow from the desired target rate. The closed control system 5 can thereby control the heating device 30 to adjust the amount of applied heat to obtain a determined parameter value that is as close as possible to the target parameter value, and thereby obtain a composition of the mixed fluid flow that is as close as possible to the target composition, and a measured flow rate that is as close as possible to the target flow rate.

The flow sensor 6 is arranged to measure a flow rate of the mixed fluid flow. In an embodiment, the flow sensor 6 is arranged downstream of the sensor 20 as shown in Fig. 4 to thereby perform the flow rate measurements of the mixed fluid flow leaving the sensor 20. In another embodiment, the flow sensor 6 is arranged downstream of the mixing device 10 but upstream of the sensor 20. In an embodiment, the mixing microfluidic system 1 comprises at least one temperature sensor 7 as shown in Fig. 5. In a preferred embodiment, the at least one temperature sensor 7 is arranged downstream of the heating device 30 and is configured to measure a temperature of the fluid flow exiting the heating device 30.

The mixing microfluidic system 1 could comprise at least two temperature sensors 7. In such a case, a first such temperature sensor 7 is preferably arranged as shown in Fig. 5, i.e., downstream of the heating device 30. A second temperature sensor 7 may then be arranged upstream of the heating device 30 to measure a temperature of the fluid flow entering the heating device 30. The at least one temperature sensor 7 is configured to measure a temperature of the fluid flow from the heating device 30. The heating device 30 is then configured to apply heat based on the control signal generated at least partly based on the determined parameter value and the measured temperature.

In an embodiment, the mixing fluidic system 1 also comprises the previously mentioned closed control system 5 that is connected to the heating device 30, the temperature sensor 7 and the sensor 20. In this particular embodiment, the closed control system 5 is configured to generate the control signal based on the value of the parameter determined by the sensor 20 and the temperature T measured by the temperature sensor 7, i.e., Sctri = f[ e, T ). In a further particular embodiment, the closed control system 5 is configured to generate the control signal based on the value of the parameter determined by the sensor 20, the temperature measured by the temperature sensor 7, a target value of the parameter and a minimum temperature Tmin I.e., Sctrl - f[ 8, ST, T , Tmin ). In such a particular embodiment, the closed control system 5 employs not only the determined parameter value and the measured temperature but also corresponding target or minimum value when generating the control signal. For instance, the closed control system 5 could generate the control signal based on a difference or quotient between the determined or measured value and the target or minimum value, i.e., Sctri = f( |e - si\, | T - Tmin\ ), Sctri =†( S I ST, \ T - Tmin\ ), Sctri =†( ST I S, \ T - Tmin\ ), Sctri— f[ |e 8 | , T / Tmin ), Sctri— f[ |e 8 | , Tmin / T ), Sctri— f[ 8 / ST, T / Tmin ), Sctri - f( S I ST, Tmin / T ), Sctri = f[ ST I e, T / Tmin ) or Sctri = f[ 8T / e, Tmin / T ). In the above exemplified functions, the absolute difference |A - Avmin\ can be replaced by ( A - At/mm), ( At/min - A) or {A - Avmin) ^m , wherein A represents e or T The inclusion of the measured temperature in the control of the mixing of the fluid flows in the mixing fluidic system 1 generally improves the control. As is shown in Fig. 15 and discussed in more detail in the Example section, the behavior of a fluid may change rapidly at a given temperature, in particular for compressible fluids, such as CO2. For instance, there may be a significant change in the viscosity and/or density of a fluid at given temperature or temperature range. The response of the fluid to applied heat may then differ at a first region with temperatures below this given temperature (range) as compared to the response of the fluid to applied heat at a second region with temperatures above the given temperature (range), which is clearly shown in Fig. 15. The minimum temperature used by the closed control system 5 in generating the control signal could then represent this given temperature. In such case, the heating device 30 is preferably controlled by the closed control system 5 to keep the temperature of the fluid above this minimum temperature as verified by temperature sensor 7. The fluid is then kept at the second region and its response in terms of viscosity and/or density dependency on temperature is more accurately controlled. In an embodiment of a mixing fluidic device 1 with a first heating device 30 and a second heating device 31 as shown in Fig. 3, then a first temperature sensor 7 could be arranged downstream of the first heating device 30 to measure the temperature of the first fluid flow exiting the first heating device 30 and a second temperature sensor is likewise preferably arranged downstream of the second heating device 31 to measure the temperature of the second fluid flow exiting the second heating device 31. In such an embodiment, additional temperature sensors may optionally be arranged upstream of the first heating device 30 and the second heating device 31 to measure the temperatures of the first and second fluid flows entering the first and second heating devices 31 , 32, respectively.

A temperature sensor may optionally also be used to measure the temperature of a fluid flow that does not pass through any heating device 30, such as the fluid flow entering the second fluid input 12 of the mixing device 10 in Fig. 5.

In the above presented embodiments, the closed control system 5 controls the heating device 30 based at least partly on the minimum temperature. In another embodiment, the closed control system 5 could instead control the heating device 30 based on the determined and target parameter value, the measured temperature and a maximum temperature Tmax. This embodiment could be useful if it is desired to keep the fluid in the first region, i.e., at temperatures below the given temperature (range) at which there is a rapid change in viscosity and/or density. In a further embodiment, the mixing microfluidic device 1 comprises both a flow sensor 6 as shown in Fig. 4 and a temperature sensor 7 as shown in Fig. 5. The closed control system 5 is then preferably configured to generate the control signal based on the value of the parameter determined by the sensor 20, the flow rate measured by the flow sensor 6 and the temperature measured by the temperature sensor 7, i.e., Sctri = f[ e, Qtot J ), and more preferably Sctri = f[ e, et, Qtot, QT, T , Tmn ) or Sctri = f[ e, et, Qtot, QT, T , Tmax ).

The sensor 20 of the mixing fluidic device 1 could be any sensor 20 capable of determining a value of a parameter representative of the composition of the mixed fluid flow. In an example, the sensor 20 is a relative permittivity sensor 20 configured to determine a value of a static relative permittivity of the mixed fluid flow. Relative permittivity is a material parameter related to the ability of a material to store energy when an external electric field is applied. Relative permittivity consists of a real part related to the energy from an external electric field stored within the material and a complex part related to the losses of energy in the material. The relative permittivity is preferably the relative permittivity at direct current (DC) and can, for instance, be determined by measuring the capacitance of a material contained between two parallel conducting plates. Various sensor technologies can be used to measure the static relative permittivity of the mixed fluid flow including, but not limited to, an inductance, capacitance and impedance (LCZ) meter, a C meter and a network analyzer, such as a radio frequency (RF) vector network analyzer designed to measure a scattering parameter or impedance Z.

In an embodiment, the relative permittivity sensor 20 comprises a parallel plate capacitor with a microfluidic channel between capacitor plates, see Fig. 17. The relative permittivity sensor 20 also comprises a RF vector network analyzer configured to measure a value of an impedance representing parameter and determine the stative relative permittivity based on the value of the impedance representing parameter.

In an embodiment, the impedance representing parameter is a scattering parameter, such as Sn for a RF vector network analyzer in a reflective one-port configuration, or Sn, S12, S21 and/or S22 for a RF vector network analyzer in a reflective two-port configuration, and so on.

Another example of a sensor 20 that can be used is a sensor 20 configured to measure refractive index of the mixed fluid flow. The refractive index describes how light propagates through the mixed fluid flow. The sensor 20 may then be an interferometer, such as a Mach-Zehnder interferometer. A sensor 20 that is based on optical measurements, such as an interferometer, is, though, less preferred when miniaturizing the mixing fluidic system 1. Thus, for mixing fluidic systems handling minute volumes of fluids, i.e., so called mixing microfluidic systems 1 , the optical path length in the sensor 20 decreases resulting in low signal to noise ratios. In an embodiment, the mixing device 10 comprises a T-junction 14 connected to the first fluid input 1 1 and the second fluid input 12. The mixing device 10 also comprises, in this embodiment, a meander microfluidic conduit 15 having a first end connected to the T-junction 14 and a second end connected to the fluid output 13. In this embodiment, the two fluid flows meet at the T-junction 14 and are mixed in the following meander microfluidic conduit 15 to form the mixed fluid flow at the fluid output 13. The two fluid flows can meet at the T-junction 14 in any angle, in particular any angle within a range of 0° and 180°.

In an embodiment, the mixing microfluidic system 1 comprises a first fluid source 3 and a second fluid source 4 configured to contain the two fluids. In a particular embodiment, one of the first fluid source 3 and the second fluid source 4 is configured to contain CO2, or another compressible fluid, and the other of the first fluid source 3 and the second fluid source 4 is configured to contain a co-solvent.

In an illustrative example, CO2 or the other compressible fluid is a supercritical fluid (SCF), such as supercritical CO2 (SCCO2). SCFs have properties of both gases and liquids most importantly compressibility, the ability to dissolve other materials due to high density, and high diffusivity. The combined temperature and pressure point at which this occurs is called the critical point and close to this critical point small changes in temperature and/or pressure cause large changes in the density and dissolving power of the SCF, thereby allowing for fine tuning of its properties. SCCO2 has a critical point of 304.2 K and 73.7 bar. SCCO2 is nonpolar and has a limited dissolving power for ionic and polar compounds. Accordingly, co-solvents, such as methanol, ethanol and other alcohols, can be added to further increase the range of materials that could be dissolved. SCCO2 with a co-solvent may therefore be useful in supercritical fluid extraction (SFE).

Thus, in order to create fluids with a high solvent power for more polar compounds, while maintaining a low viscosity, an option is to use moderately pressurized organic solvents with an addition of a gas, resulting in a gas-expanded liquid. An example thereof, is two-component C02-expanded liquids (CXLs) that may be efficiently used in separation system, increasing extraction rates up to a factor of ten when switching the extraction solvent from, for instance, supercritical CO2 to, for instance, C02-expanded ethanol. “Fluid” as used herein refers to a substance that continually deforms (flows) under an applied shear stress. Fluids are a subset of the phases of matter and include, among others, liquids and gases. Fluids are substances that have zero shear modulus, or, in simpler terms, a fluid is a substance, which cannot resist any shear force applied to it. Flence, fluid as used herein includes liquids, gases, mixtures of liquids and gases, including CXLs, supercritical and subcritical fluids.

The above described and in Figs. 1 to 6 illustrated embodiments of the mixing microfluidic system 1 have mainly been discussed in connection with mixing two fluid flows into a mixed fluid flow. The embodiments are, however, not limited thereto. In clear contrast, the mixing microfluidic system 1 could be used to mix multiple, such as two, three, or more, fluid flows into the mixed fluids. In such a case, one, all or a portion of the multiple fluid flows could pass through a respective heating device 30, 31 to thereby control the flow rate, viscosity and/or density of the fluid flow(s). For instance, in the case of three fluid flows, all three fluid flows could be mixed in one mixing device or first and second fluid flow are first mixed in a first mixing device to a obtain a first or initial mixed fluid flow. This first mixed fluid flow is then mixed with the third fluid flow in a second mixing device to obtain a second or final mixed fluid flow.

The mixing microfluidic system 1 of the invention can be used for control of flow and composition of mixed fluids. Actuation of flow in terms of application of heat can be controlled to affect viscosity and/or density. Accordingly, the mixing microfluidic system 1 can control and tune both the composition and the total flow rate of two different fluid streams with a shared pressure. The mixing microfluidic system 1 can further be operated to run concentration gradients. The mixing microfluidic system 1 has a large rangeability over the entire compositional scale and can be fine-tuned to various levels. Furthermore, the mixing microfluidic system 1 is stable and can operated with low drift and fluctuation. Another aspect of the invention relates to a method of mixing fluidic flows, see Figs. 1 -6 and 24. The method comprises mixing, in step S2 and in a mixing device 10 comprising a first fluid input 1 1 and a second fluid input 12 and a fluid output 13, a first fluid flow received in the first fluid input 11 and a second fluid flow received in the second fluid input 12 into a mixed fluid flow output at the fluid output 13. The method also comprises determining, in step S3, a value of a parameter representative of a composition of the mixed fluid flow. The method further comprises applying, in step S1 , to a fluid flow passing through a microfluidic conduit 32, 33 in fluid connection with the first fluid input 1 1 or the second fluid input 12, heat based on a control signal generated at least partly based on the value of the parameter. The method shown in Fig. 24 is preferably a closed control method as indicated by the line L1 in the figure. Hence, the parameter is preferably determined at multiple time instances to thereby adjust and control the heat application in step S1 based on at least the latest determined parameter value. The determination of the parameter value in step S3 can, thus, be conducted at multiple scheduled time instances, such as every X ^th second or every X ^th minute for some value of x. Alternatively, the parameter could be measured more or less continuously during operation of the mixing microfluidic system 1.

In these embodiments, the application of heat in step S1 could be based on the latest determined parameter value or based on N³ 2 determined parameter values, preferably the /V ^th latest determined parameter values, such as Sctri = f[ e _h , e _h -i, e _h -2, ..., e _h -N+i ). For instance, the average of the /V ^th latest determined parameter values, S _ctrl = f ^a weighted average of the /V ^th latest

determined parameter values, S _ctrl = could be used in the control of heat

application. In the latter case, larger weights are preferably used for more recently determined parameter values as compared to past parameter values, w _h > w _h-c > · ·· > w _h-N+1 .

In an embodiment, step S1 comprises applying, based on the control signal, heat to the fluid flow to adjust a flow rate of the fluid flow through the microfluidic conduit 32, 33. In an embodiment, step S1 comprises applying, based on the control signal, heatto the fluid flow to adjust at least one of a viscosity and a density of the fluid flow through the microfluidic conduit 32, 33.

Fig. 25 is a flow chart illustrating an additional, optional step of the method shown in Fig. 24. The method continues from step S3 in Fig. 24. A next step S10 comprises generating the control signal based on the value of the parameter and a target value of the parameter. The method then continues to step S1 in Fig. 24, where the heat is applied to the fluid flow passing through the microfluidic conduit 32, 33 based on the generated control signal.

Fig. 26 is a flow chart illustrating an additional, optional step of the method shown in Fig. 25. The method continues from step S3 in Fig. 24. A next step S20 comprises measuring a flow rate of the mixed fluid flow. The method then continues to step S10 in Fig. 25. In this embodiment, step S10 comprises generating the control signal based on the value of the parameter, the measured flow rate, a target value of the parameter and a target flow rate. Furthermore, Fig. 27 is also a flow chart illustrating an additional, optional step of the method shown in Fig. 24 or 25. The method continues from step S1 in Fig. 24 or step S10 in Fig. 25. A next step S30 comprises measuring a temperature of the fluid flow exiting the microfluidic conduit 32, 33. The method then continues to step S1 or S2 in Fig. 24. This embodiment preferably also comprises step S10 in Fig. 25. In such a case, step S10 preferably comprises generating the control signal based on the value of the parameter, a target value of the parameter, the measured temperature and a minimum temperature.

In an embodiment, step S3 in Fig. 24 comprises determining a value of a static relative permittivity of the mixed fluid flow.

In an embodiment, step S2 in Fig. 24 comprises mixing, in the mixing device 10, carbon dioxide fluid and a co-solvent flow into a binary fluid mixture. In an embodiment, step S1 in Fig. 24 comprises applying, to the first fluid flow passing through a first microfluidic conduit 32 in fluid connection with the first fluid input 1 1 , heat based on a first control signal generated at least partly based on the value of the parameter. Step S1 also comprises, in this embodiment, applying, to the second fluid flow passing through a second microfluidic conduit 33 in fluid connection with the second fluid input 12, heat based on a second control signal generated at least partly based on the value of the parameter.

EXAMPLES

EXAMPLE 1 - Integrated fluid delivery and control system

Fluid delivery setups

High pressure flow is typically generated using displacement pumps with pistons and, depending on the application, is either of reciprocating or a single-stroke type. Driving flow using reciprocating pumps allow for long continues operation but also introduces pulsing into the flow. Single-stroke piston pumps instead provide a close to pulseless flow, but require refilling. Containers, which hold a pressurized fluid also offer a way to deliver flow, but the pressure is both limited to that of the container and will decrease as fluid flows. A measurement of either the flow rate or pressure provide, together with some means to changing them, the basis for a flow control system. This allows fluid to be delivered at either a constant flow rate or at a constant pressure. In many cases, both the measurements and the change of flow rate are done at the pumps. In that case, a multicomponent flow requires one pump for each fluid component, which will be independently varied. An example of such a system is shown in Fig. 7A. In that case, two fluids meet at the mixing point (mixing box in Fig. 7) and create a single mixed fluid. To vary the composition of the mixed flow, the flow or pressure ratio can be changed. While ideal for many applications, it requires one pump and one flow control system for each fluid component. This limitation can, however, be circumvented. By using piston separated containers for each extra fluid component and driving the flow from one common source of pressure, a multicomponent fluid flow can be achieved. The common source of pressure can either be a piston pump, Fig. 7B, or a pressurized container, Fig. 7C. When a piston pump, which can deliver a constant flow rate or at a constant pressure is used, only the composition is controlled. To achieve flow control were the composition instead can be varied, an extra control element is need which can measure and change composition. In this Example 1 , such a control element in the form of a flow regulating board (FRB) is disclosed.

Flow model

To understand the mixing behavior in a microfluidic circuitry, static flow models can be used. For two flows, each having a volumetric flow rate, Q _f , with a corresponding molar volume, u _f , the molar flow rate n _f is n _f = Qf/u _f . To distinguish between the different flows, f is used as an index, being f = 1 for CO2, f = 2 for methanol, and f = m for a mixture. A combination of the two flows, ¾ and n ₂ , will result in a mixture which have a molar fraction, x ₂ , of methanol as,

For incompressible and laminar conditions, the flow rate can be expressed in terms of pressure drops and resistances using the Hagen-Poiseuille equation. While pressure fluctuations and instabilities can be modelled by transient models, the static conditions can also be investigated. For three fluid restrictions, which connect at a single point, i.e., a T-junction, a flow of both CO2 and methanol into the point result in a mixture emitted from the third. This can be described by the following equation system,

Pi Pt — Ri n _x (2)

P ₂ P _t — R ₂ n ₂ (3) p _t - Pb = R _m (ni + n ₂ ) (4)

R _f = k _f m _G u _G (5) where R _c , P ₂ , P _t and P _b are the pressures of CO2 or methanol flow before the restrictions; the pressure at the T-junction; and the backpressure, respectively. R _x , R ₂ and R _m are the fluid resistances of CO2, methanol, and the mixture, respectively, as it passes the restrictions. By (5), these fluid restrictions, R _f , are each related to the viscosities, m _G , molar volumes, u _f , and geometrical constants, k _f , at a given restriction. k _f describe the dimensions of the restriction and is expressed as k _f = 2LP ² /<A ³ , where L, and A are the length, perimeter and cross-sectional area of the restrictions, respectively. Using (1), (2), (3), (4) and (5), x ₂ can then be estimated with x ₂ as,

R ₂ ²

5

R _m Ri

In this Example 1 , tuning and control of x ₂ is achieved by manipulating R _x and R ₂ , affecting the products m _G u _G . For a given temperature and pressure, m ₁ u ₁ and m ₂ u ₂ can be estimated from literature data. m _ih u _ih is, however, not straightforward to estimate, as density, viscosity, and average molecular weight is a function of composition. In Example 1 , m _ih u _ih is approximated by a linear model of the pure components and the volumetric measurement of the molar fraction x ₂ .

Compositional measurements from the relative permittivity

The relative permittivity, e _t , of a fluid depends on its polarization per unit volume, f, where ά _m is the dipole moment of the fluid, N _A is the Avogadro constant, a is the molecular polarizability, k _B is the Boltzmann constant and g is a correction factor. From (7), it follows that the temperature and pressure dependence of e _r is determined by changes to v _f and the temperature dependent term d*g/3k _B T. Hence, for fluids with a significant dipole moment, e _r decreases with increasing temperature. For example, methanol has a dipole moment, ά _m , of 1.69 and at 1 1 °C e _r is 36.7, at 24 °C, e _t is less, 32.7. The polarization of CO2 is instead affected by pressure and temperature through the molar volume, as it has zero dipole moment and shows larger compressibility.

For fluid mixtures, e _r is dependent on the dielectric properties of the pure components and interactions between the components in the mixture. When components are of similar type, binary mixtures often have a linear dependency on the pure components. For mixtures of polar and non-polar components, the dependence is often non-linear and described using quadratic mixing rules. For methanol and CO2 mixtures, two studies [Fluid Phase Equilib., 1991 , 61 (3): 227-241 ; Fluid Phase Equilib., 1999, 158-160: 101 1-1019] have investigated the relative permittivity over a variety of temperatures, pressures and compositions. While neither study has explored the temperature region (~1 1 °C) used in this Example 1 , a sigmoid dependence on composition has been identified, showing resemblance with the methanol- methane system. Therefore, the e _G (c ₂ ) data presented in this Example 1 is described using a sigmoid function with four coefficients bi, b2, b3 and b4. Taking the inverse of the sigmoid function, a measurement of e _G by the sensor can then expressed in terms of molar fraction as, Variations of the temperature and pressure affect the molar volume and polarization, and therefore the sensor should be kept close to constant conditions.

Experimental setup

The three fluid setups shown in Figs. 7A-7C are used. The FRB is placed at the mixing point. For a full description of the different supporting equipment used, see Description of supporting equipment below.

The FRB, Fig. 8a, had chips for actuation, mixing and sensing. Two fluids passed the actuator chips (hCS and hCCte), where internal heaters heated the fluids to change the fluid resistance, and the fluids combined in a mixing chip. As the fluid was heated, the fluid resistance was changed. The two flows were then combined in a mixing chip. Downstream from the mixing, a relative permittivity sensor was placed and used to measure the relative permittivity. The measured e _G could be used directly or expressed as x ₂ using (8). The operational temperature limits were set by temperature sensors Ti, T2 and the components work together in a closed control system.

The four components of the FRB were mounted on a cooled printed circuit board, which acted as a support for the chips and allowed for fluid and electrical interfaces. The printed circuit board provided conductors for power and signal circuits, input and output pin headers for interacting with the actuator chips. The actuator chips, Fig. 8b, were surface mounted with their top open pads, Fig. 8c, to the pads of the printed circuit board. Openings through the printed circuit board allowed the actuator chips to be in direct thermal contact with the cooling fixture and kept at 5.7 ± 0.5 °C. The mixing chip and the relative permittivity sensor were mounted on top of the board and held at 10.7 ± 0.5 °C.

On the FRB, strain-relieved, 1/16” stainless steel tubing (T19C5D, VICI) acted as fluid connections from board. Silica capillaries (TSP040105, Polymicro Technologies) with an inner diameter of 40 m were connected into both the tubing and chip inlets, which then were epoxy glued (Araldite Rapid, Fluntsman advanced materials). The cooling fixture (EK-Thermosphere, EKWB) was connected to the water bath and thermal contact between the actuator chips and the cooling fixture was achieved by using thermal paste. The printed circuit board provided the following electrical features: conductors for power and signal circuits; input and output pin headers for interacting with the actuator chips; and had a SubMiniature version A (SMA) connector for the relative permittivity sensor. A board mounted 4-point Pt100 temperature sensor was used for calibrations. The board-to-chip electrical connections were made using electrically conductive epoxy (CW2400, Circuit works). The actuator chips were surface mounted and the relative permittivity sensor had its electrical connection pads on the side, having a copper-coated polyimide film as a conductive bridge between the board and the sensor. The actuator chips are disclosed in Fig. 8b. Each chip, which was made from borosilicate glass with embedded 15 nm Ta and 100 nm Pt thin film conductors, was essentially a long fluid restriction with an integrated heater running along it and a temperature sensor. The heater had direct contact with the fluid and cooling was applied from the opposite side of the heaters, Fig. 8d. The actuator chips were made in two different versions: one with a 16.7 m deep restrictor and the other with an 8.7 pm deep restrictor giving the geometrical constant, k _f, of either 5.3 - 10 ¹⁸ nr ³ or 4.4- 10 ¹⁹ nr ³ , respectively. The heater consisted of eleven, 12 pm wide, resistor elements powered in parallel, which each ran along a segment of the meander and were distributed to six pads on each side of the chips. The chips had two temperature sensors, Fig. 8e, which both consisted of 12 pm wide and 0.3 mm long resistor elements. The resistance varied with different chips but were in the range 30-35 ohm for the temperature sensors and 400-550 ohm for each resistor element. Details regarding the methods of fabrication can also be found elsewhere [J. Micromechanics Microengineering, 2017, 27(1)].

To drive the heaters in the actuator chips, a lab power supply (QL355P, TTi) was used to feed a dual full bridge driver (L298, STMicroelectronics) with 30 V and each actuator chip was connected to a separate driver output. The power output to the actuators were controlled from two 12-bit pulse-width-modulated signals generated by a microcontroller (Zero, Arduino). The relative permittivity sensor was connected to a network analyser (FieldFox N9923A, Agilent), measuring the reflective scattering parameter, sn, at 3 MFIz. The temperature sensors were connected to a data acquisition unit (34901 , Agilent). The microcontroller, network analyzer and data acquisition unit were connected to a computer running a custom control program developed using software (Matlab R2017, Mathworks).

Operation of system

Fluid setups A, B and C in Figs. 7A-7C all provide means of driving a flow of both CO2 and co-solvent (CS) to the FRB, where mixing and regulation of the composition can occur. When fluid flows, but not the FRB, were activated, x ₂ and the total flow rate, Qtot, stabilized to a static baseline, determined by the restrictions, e.g., k _± and k ₂ , which by (5) and (6) affect x ₂ , and inlet pressures. Equally sized restrictors favor a CO2 rich baseline composition and by having smaller restrictors on hC02 than on hCS, the baseline x ₂ was increased. External unheated restrictors, such as R _r , could also be used. Variations in temperatures, pressures and restrictions of these setups also affected this baseline, producing nonstable conditions and long term drift. Thus, the operation of the FRB had two important tasks: stabilization and dynamic tuning. By actively regulating x ₂ and Qtot to a level above their current baseline, drift and variations imposed by pressure changes could be stabilized to keep x ₂ and Qtot constant. By setting different degrees of actuation, a specific x ₂ and Qtot could be tuned.

The working principle of the FRB can be explained by its two parts forming a closed control system; the actuators and the sensors. For actuation, the flow resistors in hCS and hC02 were heated by their internal heaters, subsequently heating the fluids. This affected how easily the fluids could flow through the actuators as the temperature and pressure dependent products m ₁ u ₁ and m ₂ u ₂ changed that, by (5), affected x ₂ and Qtot. The other part of the FRB is its sensors. x ₂ was measured indirectly using a relative permittivity sensor placed downstream of the actuators, giving a measurement of e _r . e _r can either be used directly, or expressed in terms of x ₂ , in a closed control system. To express e _r as x ₂ , a function describing their relationship is used. In this Example 1 , (8) was used for the C02-methanol system. With the outlet temperature sensors, operational temperature limits could be set. The total flow rate was measured externally by the backpressure regulator.

Two different closed control systems were used, Fig. 9. Control system I was used to control both e _r and Qtot and control system J was used to control only e _r but could also keep a minimum temperature in hC02. For control system I, two setpoints, i.e., reference variables, were used, w _£r and w _Qtot , expressing the wanted value of the control variables e _r and Qtot. For control system J, a minimum temperature reference variable, w _Tmin , was also used and set to 40°C. The controllers, PI 1 , PI3, PI4 and PI5, defined the duty cycle ratio, i.e., manipulated variables, yes and yco2 by the error between the control and reference variables, e.g., e _r - w _£r , using one proportional term and one integral term. Different constants for these terms were used for each regulator.

Measurements

The system was demonstrated with CO2 and methanol as a co-solvent. The experiments were divided into two parts: one to examine the functionality of the FRB, the other to demonstrate its performance.

To investigate the basic functionality of the two actuators, fluid setup A (Fig. 7A) was used as it allowed separate flow rate measurements. The actuators, both having 16.7 m deep restrictors, were powered separately while the following parameters were recorded: the relative permittivity e _r ; the output temperatures T _x and T ₂ ; and volumetric flows Q _x and Q ₂ corresponding to both CO2 and methanol. Using Q _x , Q ₂ and (1 ), x ₂ was calculated. Power was applied by either a square-wave or step function of increasing magnitude. For the square-wave, which had a period of 400 s, the power was switched between zero and a maximum power output chosen so that T _f never exceeded 85°C. Eight periods of the square wave were used to measure the time constants t _eG and t _t (defined as the time required to reach 63.2% of the full response of either e _r or Tf, respectively) as well as the dead times Q _£T and q _t (defined as the time it takes before a response of e _r or Tf is initially seen). The step function had a step length of 200 s and a step height of 2.8 % of full duty cycle. For each step, a measurement point was taken using 142 s of data (centered over the step). A total of 35 and 27 measurement points were made while testing hCS and hC02, respectively. For both the square-wave and step function measurements, the measured pressures P ₁ P ₂ , and P _b were held constant by the pumps to 78.5, 92.8, and 70.5 bar, respectively. For the flow model, the pressure loss (less than 0.7 bar) between the pressure sensors and the FRB was compensated for by three separate extra R _f terms, describing the restrictions due to capillary connections. To demonstrate the FRB, three modes of operation were used together with fluid setup B in Fig. 7B. For the first mode, flow was driven by a single pump operating at a constant pressure of 75.0 ± 0.05 bar. Here, both hC02 and hCS had 16.7 m deep restrictors. Using control system I, both the e _G and the total flow rate was tuned and regulated. For the second mode, fluid setup B in Fig. 7B and control system J was used, while having the pump operating in a constant flow mode of 25 pL/min. Here, the FRB had 8.7 pm and 16.7 pm deep restrictors for hC02 and hCS, respectively. To achieve gradients, a slope function was applied to w _£r , which allowed the set point to change gradually from 16 to 26 over 4, 8.5, 14, or 19.5 min. For the third mode, operation was demonstrated when input pressure was varied and no pumping was enabled, mimicking the pumpless operation of fluid setup C in Fig. 7C, where instead a pressurized constant volume is used to drive a flow. This was demonstrated using control system J. Here, a capillary restriction R _r (Fig. 7C) was used together with two 16.7 pm deep restrictors. For the first 220 s, R _c was kept constant to 74.0 ± 0.05 bar and then regulation was turned off. For all measurements, the relative permittivity sensor was held at 10.7 ± 0.5 °C and the system operated at pressures ranging from 65 to 75 bar. The sensor was calibrated using measurements of two pure components, i.e., methanol and CO2.

Functionality of FRB

Using flow driven at a constant pressure from two separate pump (fluid setup A in Fig. 7A), the basic operation of the FRB was explored. In Fig. 10, the square wave powering resulted in temperature and relative permittivity responses, corresponding to an increase of methanol in the mixed flow. hCS responded over a larger relative permittivity range than hC02, covering 40% and 24% of the full scale, respectively. For hCS and hC02 respectively, the time constants for the response in relative permittivity, t _e , were 6.6 s and 5.9 s and for the response in temperature, t _T , 8.1 s and 4.2 s. For both hCS and hC02, the response in relative permittivity had a dead time, 0 _£r , of 2.9 s. This can be compared to the corresponding residence time between the T-junction and the sensor, which was 1.0 s. The sample loop time, i.e., the time between two measurement points, was 1.4 ± 0.2 s, the same as the temperature sensor dead time, q _t . By operation of the actuators and the step function, the composition of the mixed flow could be varied and a measurement of the relative permittivity as a function of molar fraction, x ₂ , Fig. 10 (right) was done. The molar fraction range was between 0.344 and 0.773. Sigmoidal fitting (r ² = 0.9998) gave the four coefficients 1.66, 2.58, 0.81 and 45.05 for bi, b2, b3 and b4 to (8), respectively. The residuals between the sigmoidal curve and the measurements were 0.45 ± 0.72. In Figs. 1 1 a and 1 1 b, measurements of both the molar fraction and the relative permittivity as a function of Tf are shown when using either hCS or hC02. The molar fraction and relative permittivity correlated strongly over the explored temperature range. The response was, however, very different for hCS and hC02. For hCS, a linear response was seen, with X2 increasing with 0.44 10 ² / °C. For hC02, the response was considerably more complex as it contained two regions or regimes: the first, from 8.0 to 26.6 °C, had a negative response with increased temperature. The second, from 26.6 °C and upwards, had instead a non-linear, but positive, response with temperature, increasing roughly by 0.40 10 ² / °C. The x ₂ estimate from the fluid model correlated with the measurement of x ₂ for hCS and first region of hC02, but not with the second hC02 region.

In Figs. 1 1 c and 1 1 d, while operating either hCS or hC02, the volumetric flow rate from each pump, Q ₂ and Qi, is shown together with the total flow rate, Qtot. For hCS, Qtot did not change with added heat, thus being constant, and as the methanol flow rate, Q ₂ , increased, the flow of CO2, Q ₁ decreased. For hC02, Q ₂ did not change, only Q _x was restricted, and therefore, Qtot increased with increased proportions of CO2. The different behaviours influenced the functionality. hCS could be used to tune composition without affecting the total flow rate and as hC02 acted on both composition and total flow, it could be used to tune either of these parameter at the cost of changing the other. By using both hCS and hC02 together, both composition and total flow could be controlled independently. Composition and flow rate control at constant pressure

In Fig. 12, control system I is demonstrated, showing how both e _r and the total flow rate Qtot were controlled independently and simultaneously, under a constant pressure driven flow by a single pump (fluid setup B in Fig. 7B). e _r and Qtot were set to be kept constant to a relative permittivity of 6 and a total flow rate of 50 mI/min. Before the system was turned on, the system fluctuated around its baseline which had a relative permittivity of 2.9 and a total flow rate of 79 pL/min. When the active system had tuned itself in, the relative permittivity reached 5.99 ± 0.05 and the total flow rate 49 ± 6 pL/min. This corresponded to offsets from the reference variables of 0.15% and 1.6 % for e _r and Qtot, respectively. Variations in e _r were lowered when the control system was used, being 84 % less when turned on compared to when turned off. For a e _r of 6, the estimate of the composition from the relative permittivity, x ₂ , was 23.7 ± 0.3 - 10 ² and when the system was turned off, 12.8 ± 2.8 - 10- ² .

Composition control at constant total flow

To create composition gradients, Fig. 12, a single pump (fluid setup B in Fig. 7B) was used at a constant flow rate. This represented conditions typical for chromatography, were Pi can vary and the pump keeps the total flow rate fixed. Using control system J, relative permittivities of up to 26 was possible to control, giving gradients over the composition range 0.49 to 0.74. The steepest gradient was 6.4 10 ² / min.

Composition control at variable pressure

In Fig. 14, the inlet pressure was allowed to change as no active pumping was used (fluid setup C in Fig. 7C). Using control system J, an increase in power to the actuators could compensate for the change in composition that the pressure loss would have. Beyond 220 s, the flow was being driven by the compressed CO2. No moving parts, except the piston of the dual chamber container and the BPR, were then used. The total flow rate dropped from 26 pL/min at 74 bar to 15 pL/min at 69 bar.

The viscosity and molar volume product of the fluids in the actuators chips were estimated, Fig. 15. For hCS actuator, the product m ₂ u ₂ decreased due to a large drop in the viscosity, from 699 to 279 Pa-s. This gave less restriction {R ₂ ) through the actuator, which resulted in a higher flow rate. For hC02, as the outlet temperature of CO2 increased, density and viscosity could be expected to drop from 91 1 to 155 kg/m ³ and 94.5 to 19.4 Pa-s, respectively. Over this range, m·^ formed a local minimum with two regimes or regions.

For the restrictor dimensions, flow rates, compressibilities and viscosities present for the measured response of hCS, Fig. 1 1 a, and the first regime or region of hC02, Fig. 1 1 b, the flow could be considered to be approximatively laminar and incompressible. This agrees with the fluid model, which correlates with the responses under those two conditions. When hC02 is off, Reynolds numbers are about 200. Flowever, close to the critical temperature (31 °C), Reynolds numbers are estimated to be 760. Between 8 °C and 72 °C, the compressibility increased from about 1.0 l O ⁸ Pa ¹ to 1.8 Ί 0- ⁷ Pa ¹ and, around the critical temperature, an even higher compressibility is expected. At such conditions, a more advanced fluid model should be used. By Fig. 15, some interpretation was however possible. In the first regime or region of m^ _! , the viscosity decreased more than the density and R _x decreased with temperature, resulting in decreasing e _r . In the second regime or region, the opposite was instead true, and and e _r increased. At the minimum, CO2 transformed from a liquid to a gas, or, at supercritical conditions, to a liquid-like to a gas-like supercritical fluid. As the local minimum of x ₂ occurred at 26 °C, i.e., 5 °C lower than for x ₂ , and as the model also underestimated x ₂ in the second regime or region, the temperature measurement might deviate beyond the critical point. Here, thermal properties, such as the Prandtl number, changed. The changing effect of m ₁ u ₁ can be handled and by temperature limits in hC02, e.g. w _Tmin , a single m^ regime or region can be chosen to keep a constant control direction. The pressure at the T-junction, P _t , was shared by all three restrictors and could be used for interpretation. The constant total flow rate of the system when only hCS was operated was a result of the increase, and countering decrease, of the methanol and CO2 respective flow rates. As hCS was heated, x ₂ increased and more high viscosity methanol passed the outlet restriction, which subsequently increased R _m . By looking at (4) and noting that both the backpressure, P _b , and the total flow rate, (r^ + n ₂ ), were constant, P _t must rise. Simultaneously, hC02 was unheated and therefore, its fluid resistance, R ₁ was constant, and as also the CO2 pressure, R _c , was kept constant, (2) suggests that the increase of P _t must be countered by a drop of flow in CO2, ¾. When hC02 instead was heated, heating also caused x ₂ to increase, which subsequently increased R _m . Yet here, R _m was countered by the decrease of (r^ + n ₂ ), leaving P _t constant. This agrees with the constant flow of Q ₂ , seen in Fig. 1 1 d.

For both the response of e _r and Tf, the time constants were larger than the dead times, i.e., t _eG > q _et and t _t > q _t , and the processes were therefore lag-dominant. Low dead times are advantageous for control and they can be kept low by using short sampling loop times as well as minimizing the time required for a change to be noticed by the sensors. In this type of system, the temperature was measured directly after the heater and the relative permittivity was measured 83 mm downstream of the fluid path. This agrees with q _t , which was not larger than the minimum dead time, i.e., the sampling loop time. It is reasonable to assume that q _et is flow rate dependent and that deadtime dominance would occur at low enough flow rates. This could be counteracted by further miniaturizing the FRB to keep residence times low enough to not create a dead-time dominated system. The sampling loop time could be reduced by using dedicated hardware and software. Use of robust transient control models could also be explored [Sci. Rep., 2016, 6: 1-12]

While being designed for flow control, the system was also effective for measuring the relationship between the composition and relative permittivity. The FRB allowed for incremental changes in flow, which was advantageous for mapping parameters. If the composition of flowing C02-alcohol mixtures was changed by alternating pump pressures, variations of the CO2 properties were also introduced into the fluid occupied in the pump and tubing. If composition was then determined by volumetric measurements, the compressibility could introduce deviation. Notably, when operating the FRB, composition could be varied while keeping the majority of CO2 at a fixed inlet pressure, hindering density variations in the pump to occur.

The rangeability of the system was demonstrated in Fig. 13, where 32% of the whole compositional range was used for control from a static baseline level of 0.49. The baseline was altered by the dimensions of the restrictions, which in this case were smaller for hC02 than for hCS. Therefore, the FRB could be configured for different operational ranges. In Fig. 12, equally sized restrictors were used, giving a baseline e _r of 2.9 (x ₂ « 0.12). The system was also effective for determining the relationship between the composition and the relative permittivity. As the actuator chips allowed for small incremental changes in flow, the system was advantageous for mapping parameters dependent on the composition. Methods, which change a CO2 flow by alternating pump pressures, are affected by compressibility effects leading to a deviation between the volumetric change of piston movements and actual flow. For determinations of the relationship between the relative permittivity and composition, using the piston movements of pumps, a large degree of scatter can occur, especially at low flow rates and minute-scale timelines, which requires the need of pressure derived estimations. Notably, the situation is very different when operating the FRB. The residuals of the measurement in Fig. 10 (right) were low. This can be attributed to that the majority of all fluid volumes in the system, i.e., in the fluid lines and pump, were kept at a constant pressure and did not need to change as the actuator is operated and the composition changes.

Example 1 therefore demonstrates an integrated microfluidic control system for control of flow, composition and relative permittivity. Temperature controlled actuation of flow could be created by changing both viscosity and density. The system could control and tune both the composition and total flow rate of two different fluids flows with a shared pressure. The system could further be operated to run concentration gradients, demonstrated here between 49% and 74% methanol in CO2. The span was 32% over the entire compositional scale (0 - 100 mol%) and the range could be positioned by changes to the static flow resistance of the system. Using the control system, drift could be removed and variation could be reduced by 84%.

An integrated high-pressure microfluidic control system for flow, composition and relative permittivity was demonstrated. Actuation of flow was achieved without movable parts, instead the fluid resistance was changed by temperature acting on both viscosity and density. With a span of 32% of the entire compositional scale (0 - 100 mol%), drift could be removed and variation could be reduced with 84%. Depending on how the static baseline of flow resistance was set, the range could be positioned. Within a set range, the system could control and tune both the composition and total flow rate of two different fluids, CO2 and methanol, with a single shared pressure source. EXAMPLE 2 - Microfluidic relative permittivity sensor for feedback control of carbon dioxide expanded liquid flows

Binary C02-alcohol mixtures, such as C02-expanded liquids (CXLs), are promising green solvents for reaching higher performance in flow chemistry and separation processing, but their compressibility and high working pressure make them challenging to handle as properties vary with pressure and temperature. A great advantage of CXLs is their tuneable polarity, but precise regulation of the composition is needed. Here, a microfluidic system consisting of a relative permittivity sensor and a mixing chip was used to actively regulate the relative permittivity of CXLs and indirectly composition. The sensor was a high pressure tolerant fluid-filled plate capacitor created using embedded 3D-structured thin films and had a linearity of 0.9999, a sensitivity of 4.88 pF, and a precision within 0.6% for a sampling volume of 0.3 mί. The relationship between composition and relative permittivity of C02-ethanol was measured at 82 bar and 21 °C under flow. By flow and dielectric models, this relationship was found to be described by the pure components and a quadratic mixing rule with an interaction parameter, ky, of - 0.63 ± 0.02. Microflows with a relative permittivity of 1.7 to 21.4 were generated, and using the models, this was found to correspond to compositions of 6 to 90 mol % ethanol in CO2. With the sensor, a closed loop control system was realised and C02-ethanol flows was tuned to set points of the relative permittivity in 30 s with increased stability. The complex relative dielectric permittivity is a frequency dependent number. For both polar fluids, and non-polar liquids, the real part of the relative permittivity, e _r , stays close to the static relative permittivity up to 10 MHz. For an ideal parallel plate capacitor, the capacitance, C, is related to e _G as follows, with e ₀ being the permittivity of vacuum and where the distance between plates and the area of each plate form the geometrical ratio Ag/d _g . In a circuit, parasitic elements from electrical paths and interfaces will add a constant background capacitance in parallel, Cb. Furthermore, the ratio Ag/d _g does not take into account variations in alignment, surface roughness, and edge effects, so by defining an effective ratio Ae/de, the following expression can be made, where C _b and the effective ratio AJde can be determined as the sensor is calibrated using fluids of known e _t . The scattering parameter, S , can be used in a reflection coefficient method to calculate the complex impedance, Z, around the reference impedance, Z ₀ , of 50 ohm. Using (3), C can then be calculated as follows, which by combining with (2) can be used to calculate e _r . e _r can further be used to relate the polarization per unit volume of the fluid being measured, p, by the following equation,

The polarization of polar-nonpolar fluid mixtures, p _m , can be estimated using parameters of the pure components and a quadratic mixing rule. For a specific binary fluid system, a parameter, can then be used to describe the deviation from linearity and non-ideal conditions. For a binary component system i-j, where the index f denotes the fluid type (either f= 1 for CO2 or f= 2 for ethanol),

where v _lt p , v ₂ and p ₂ are the molar volumes and polarisations of the pure components, i.e., CO2 and ethanol, respectively. x ₁ and x ₂ are the molar fractions of CO2 and ethanol, respectively. From (5), (6) and (7), a relationship between the relative permittivity and molar fraction, i.e. e _r (x), is possible if /c _i;· is determined. To measure the £ _r (x)-relationship and find the composition should be measured. This requires a description of the flow situation, Fig. 16b. Volumetric flows, Q _fl , can be expressed as a molar flow n _f by, where v _fl is T and P dependent. Using the measured the rate of piston movements in the pumps, a volumetric definition of the molar fraction, x _2Q , can then be stated together with the required variables as,

This volumetric definition, e.g., x _2Q , does, however, not take into account compressibility effects in the pumps, and for the more compressible fluid, CO2, this can give errors in estimating n Alternatively, can estimated from the pressures and restrictions by a flow restriction model. For laminar non- compressible flow, the Hagen— Poiseuille equation gives a linear relationship between pressure differences and flow. Therefore, the 3 restrictions can be represented by an equation system as,

Pip - P _mt = Ri^ _lr ^i _r ni (10)

P _2p ^— Pmt ^— ^2G^2G^2G^2 (1 1 ) P _mt - Pmb = Rim^mr^mrO _l + ¾) (12) where Rf _r is a fluid resistance constant dependent solely on geometrical contributions and m _G is the viscosity. Using this method, it is possible to define x without any volumetric flow measurements, but this requires knowledge of mr nr, e.g., the viscosity and average molar volume of the mixture x can instead be expressed with n ₂ (but without n . Using (9), (10) and (1 1 ), x _2P is then stated together with the required variables as, The viscosity and molar volume products of the pure component [m _1t u _1t and m _2G u _2G ) are T and P dependent. Rfr . which must be estimated, is the restrictions imposed by capillaries, filters and tubing between the T-junction and the pumps. The total geometrical fluid resistance, R _fpb , is the sum of all fluid resistances between either the CO2 or ethanol pump and the backpressure regulator, i.e., between Pip or Pip and ^P fb _' ^{lf R} mr is estimated from known dimensions of the capillaries leading to and from the sensor as well as the geometrical resistance of the sensor, where L _c and r _c is the length and inner radius of the capillaries. L _s , T and A is the length, perimeter and cross-sectional area of the narrowest part of the sensor. In this Example 2, the flow conditions in the restrictors indicate that the CO flow can be approximated as incompressible.

Relative permittivity sensor and mixing chip

The high-pressure tolerant borosilicate glass sensor chip (15x15x2.2 mm), consisted of a microfluidic channel with integrated 660 m wide 100 nm thick Pt electrodes on top of a 30 nm thick Ta adhesion layer. The microfluidic channel had deeper inlets on the side walls of the chip used to connect capillaries, a narrow fluid path leading to the sensing element, and a central ring-shaped channel containing the sensor element. The embedded conductors followed from the wafer bond plane down, along the etch wall, to the bottom or top of the etched channel, forming a non-planar geometry, Fig. 17. The high pressure tolerant mixing chip, Fig. 16a, also made from borosilicate glass wafers, consisted of a T-junction, where the fluids contact each other, and a 54 mm long meander. The main channel, forming the base of the T-junction and the meander, acted as the inlet of the organic solvent and had a channel depth of 120 m and a top width of 300 pm. The CO2 inlet of the T-junction had a depth of 8 m and a width of 76 pm. The main fabrication steps of the mixing and sensor chip are described elsewhere [J. Micromech. and Microeng., 2016, 26: 095009; J. Micromech. and Microeng., 2017, 27: 015018] but differ somewhat in the fabrication of the embedded non-planar electrodes, as described in Fabrication of the non-planar electrodes in the permittivity sensor below.

Measurements

The sensor was connected to a network analyzer (FieldFox N9923A, Agilent) in a reflective one-port configuration, measuring the S11 reflective parameter at 3 MFIz with a bandwidth of 1 kHz, resulting in a sweep time of roughly 0.6 s. A schematic drawing of the fluid system is shown in Fig. 16a and a full of the experimental setup is found in Experimental setup below. A linear calibration in order to determine C _b and the effective ratio Ae/de of the sensor was made using different reference solvents: CO2 (N55, Air Liquide), 2-propanol (99.0% Rectapur, VWR) ethanol (99.5% Ph. Eur., VWR), methanol (99.8% Ph. Eur., VWR) and acetonitrile (99.9% HPLC grade, VWR) under flow, complemented with a static measurement of air. The relative precision was calculated as 2 s _£r /e _r , where s _£r and e _r is the standard deviation and average of the relative permittivity. During the fabrication of the sensor, the thin film conductors leading to the plate electrodes were examined by scanning electron microscopy (SEM, 1550, Zeiss) and the distance between the two electrode plates was measured on a diced cross section of the sensor chip.

To demonstrate the basic operation of the sensor, the sensor was first filled with ethanol and then changing the solvent in the sensor to methanol by using a pump rate of 300 pL/min. This was followed by studying the change in e _G of CO2 over the vapour-liquid equilibrium. Having the backpressure regulator fully closed and setting the CO2 pump to 80 bar, the fluid system was slowly pressurized, a process that took 36 min. The pressure sensitivity of the sensor was checked by flowing 50 pL/min of ethanol through the sensor while Pf _b was changed in the range 53-91 bar.

The £ _r (x)-relationship of CO2 and ethanol was measured by generating a fluid flow of variable composition which was measured by the sensor. This was achieved using a constant backpressure Pf _b of 82 + 0.6 bar while setting P _2p and P _lp to 41 different levels of constant pressure, each corresponding to a measurement point, over the range 83-109 bar and 124-98 bar, respectively. After setting a new condition, the setup was equilibrated for 2 min before the next measurement was performed. Total flow rates varied over the range 54-174 pL/min. Meanwhile, the flow stability and fluid behaviour was studied by observing the T-junction and meander. For each measurement point (sampled by n = 100 data points), m _ΐG u _ΐG and P2r ^v 2r was calculated from viscosity and density data at representable pressures (estimated by the average between Pfp and P _fb ) and temperatures (measured as T _lr = 5 °C and T _2r = 21 °C). The measurement point variation was calculated as 2 s _£r /(n ^1/2 _r ). For u _1r , density was estimated from Pi _p and T _lp - 6 °C. Using a dielectric model based on (5), (6) and (7), the measured e _r was then fitted against the corresponding values of x _2Q and x _2P by a least squares method. was treated as a single fitting coefficient. R _fpb was determined by applying (8), (10), (1 1 ), (12) and measuring Pfp, Pf _b and Q _fl while pumping one fluid at a time at flow rates higher than 100 pL/min. The feedback control system of the C02-ethanol flow was set to alternate the set points of the relative permittivity, e _{r SP} , to either 10 or 15 in a square wave having a period of 40 s. To control e _r , P _lp was held constant while ¾P was as a manipulated variable in a closed control loop having e _G as the controlled variable. The regulator was of PI type (containing both a proportional and integral term). During operation, P _lp and Pf _b were held to 102 and 79.3 ± 0.2 bar, respectively. The temperature of the sensor chip was 21 + 1 °C.

Relative permittivity sensor

The thin film conductors crossing the etch wall can be seen in Fig. 18, showing a continuous metal layer leading from the bond interface plane to the bottom of the etched channel. The total height between the plates were 22.9 ± 0.2 m and the area of the plates were 12.7 ± 0.3 mm ² , giving an Ag/d _g ratio of 0.56 ± 0.02 m. The volume of the fluid channel in the chip was 0.3 pL, corresponding to a residence time of 6.3 ms for a 50 pL/min flow. In air, the capacitive signal of the sensor setup was 28.7 pF, having an RMS noise of 34.5 fF. A time- dependent drift of 7.1 fF/h was measured over 40 min and the time resolution of the system was 0.8 ± 0.2 s.

From the calibration of the sensor with the reference solvents, Fig. 19, the response was shown to be highly linear, r ² = 0.9999, giving an AJde ratio of 0.55 ± 0.008 m and a C _b of 24 + 1.6 pF. Over the calibrated range of e _r , 1 -36, the sensor sensitivity was 4.88 ± 0.007 pF and the relative precision was within 0.6%. Over the P _fb range 53-91 bar, a relative difference in response of less than 0.6% was seen when flowing ethanol, suggesting that the pressure sensitivity of the sensor was negligible. The basic operation of the sensor is demonstrated in the insert of Fig. 19, showing how e _G increases as the solvent in the system is changed from ethanol to methanol.

By gradually increasing the pressure of CO2, Fig. 20, the sensor could detect the crossing of the vapour- liquid equilibrium line at 58.5 bar and 21 °C. Mixing of ethanol and CO2

The C02-ethanol mixtures were made at conditions where only a single phase exists at equilibrium, and stable flow and mixing was possible over the range 0.06 ± 0.02 < x _2P < 0.90 ± 0.01. At the mixing point, Fig. 21 , the fluids initially had a phase interface which, over a distance of about 6-14 mm along the meander microchannel, became increasingly less visible and eventually disappeared completely. The position of the phase interface across the microchannel allowed both for an estimate of the flow ratio and as a marker for when unstable flow occurred. When mixing the fluid with a low amount of CO2, x _{2 P} > 0.90, fluctuations of the flow occurred, resulting in a pulsating behaviour with ethanol flowing into the CO2 inlet.

The measured e _G as a function of x _2Q and x _2P , Fig. 22, shows that CXLs having an e _G between 1.7 and 21.4 were possible to produce. For both e _r (x _2Q ) and e _G (x _2P ), a non-linear relationship between x and e _G is noted, as the measurement points follow a convex shape over the studied range. For the fitting model, such convex shape suggests a negative value of fc _/ — which also was determined. x _2Q and X ₂ P were notably different, and as e _r (x _2Q ) had significantly scattered points at high values, it was poorly explained (r ² = 0.545) by the fitting model. This could be attributed to Q _lp at low flow rates. While the pressures, P _lp> reached a constant level within the equilibrium time (~2 min), the volumetric flow (as measured in the CO2 pump) did not. Using e _r (x _2Q ), only an estimate of kij with a very high degree of uncertainty was possible to make, -0.41 ± 0.26. By instead using e _G (c _2R ), the fitting model agreed considerably better (r ² = 0.995) and kij could be determined with much lower uncertainty, i.e. -0.63 ± 0.02.

When measuring e _G of the CXL, more variation is seen than when measuring the pure reference solvents, resulting in a relative precision of up to 2.5% for CO2 rich flows. The measurement point variation was 0.3% or ± 0.01. The variations P _2p , P _lp and Q _2p result in relative uncertainties between 1 % and 30% at high and low values of x _2P , respectively, with Q _2p being the major source of the variation.

Operation of CXL control system

The average cycle time for each feedback loop was 0.9 ± 0.3 s. Both the set point and measured e _G are shown in Fig. 23, together with the used manipulated variable ^ _2p After changing between the set points and allowing the system to stabilise for about 30 s, e _G reached either 10 ± 0.2 or 15 + 0.2. With the control system activated, the fluid flow can be maintained with a constant e _G even when other variables in the system are changing. Not activated, increasing Pf _b affect the fluid composition and decreases the permittivity of about 0.18/bar over the range 75-87 bar. When the control loop was enabled, this effect was compensated for by an increase in Pi _p - A comparison between the experimental ratio AJde (0.55 ± 0.008 m) and geometrical ratio Ag/d _g (0.56 ± 0.02 m) showed only a small difference, about 1 %, with the uncertainties overlapping. This suggests that the sensor approximatively behaves as an ideal plate capacitor with misalignment, surface roughness and edge effects not having a noticeable effect on C. Using the reference solvents, rather than geometrical measurements, a lower uncertainty of the A/d ratio, i.e., 2% instead of 8%, was achieved. Using reference solvents is a more viable method, as it also removes possible sensor bias and allow for a method to remove parasitic elements, i.e., Cb. It is important for sensor signal that the response does not change with pressure due to deflection of the glass, affecting d _g . Over the range 53-91 bar, no such change was seen.

The sensor allowed for fast measurements of the £ _r (x)-relationship, as the microfluidic system could reach constant P, T and x _2P conditions within 2 min and the sampling time needed was about 80 s for each measurement point. Having short measurement times is highly interesting for detailed mapping of more complex fluid systems, e.g., ternary system with additives compounds. While this system is demonstrated on a two-component system at a fixed temperature, it could be easily expanded to contain both a heat stage and more fluid inlet restrictors, allowing for a fast and automated system capable of analysing the relative permittivity of multicomponent fluids over a wide P, T, x space.

For these faster measurements, the method relied on the flow restriction model, i.e., x _2P , as the volumetric conditions in the CO2 pump does not reach enough equilibrium fast enough to use x _2Q reliably. The flow restriction model relies on several estimations and, hence, the accuracy of x _2P is dependent on variables such as Tir, T _2r and R _mr . For example, the temperature for the CO2 restrictor can be affected by cooling as the pressure drops. Therefore, it is important to further validate the flow restriction model. Two other studies have measured e _r of C02-ethanol mixtures, one focusing on the x- range 0.050 - 0.212 at 303 to 333 K and 72 to 308 bar [J. Chem. Eng. Data, 201 1 , 56: 3363-3366], the other has studied the entire x-range but at the constant P and T conditions of 100 bar and 313 K [Ber. Bunsenges. Phys. Chem., 1996, 100: 1368-1371] As neither of these studies are done over the same conditions as this Example 2, a direct comparison of the data is not possible. However, by (6) and (7), the /(/ _/ parameter is independent of the molar volume and the polarisation of the pure components, which is affected by temperature. Therefore, kij should agree well between studies. Estimated from the literature values of e _G (c) at 100 bar and 313 K, kij is -0.60. Thus, the value of kij determined in this Example 2 - 0.63 ± 0.02, falls close to what can be seen in literature data. The operation of the feedback control system, as demonstrated in Fig. 23, allowed for control of the polarity of the fluid, and together with known P and T parameters to set the density, offered a way of precisely controlling the solvent power of the CXL. By utilizing the fitting model together with the determined kij, the e _r set points of 10 and 15, corresponds to a tuning of the CXL molar fractions to either 0.528 or 0.714. Thus, with this sensor in place, a new level of control is made possible for microflow systems using CXLs. Depending on the intended application, either e _r or x can be precisely tuned. The more noise response of e _r Fig. 23, clearly exposes the challenges of controlling microflows by relying on external measurement techniques, e.g., pumps, exposing the need for small integrable sensors. As demonstrated in Fig. 23, detecting phase transformations, with their associated change in density, is possible.

The relative permittivity sensor had a highly linear response between capacitance and relative permittivity over the explored e _r range of 1 to 36 and had a precision within 1 %. With a controlled composition of the flow, C02-expanded ethanol with molar fractions of ethanol between 0.06 and 0.90 was generated at 21 °C and 82 bar, producing fluids with tunable e _G between 1.72 and 21.40. The measured relationship between composition and e _r was agreed well with a dielectric mixing model, having an r ² of 0.995. From the model, the interaction parameter kij, was determined to be -0.63 ± 0.02. The system was shown to work in a closed control system and constant C02-expanded ethanol flows could be made, even if the backpressure varied. Thus, we demonstrated both how precise tuning of CXLs and binary fluids can be achieved in microflows.

A relative permittivity sensor for microflows of high-pressure fluids is presented. The sensor allowed for high composition control of high fluidity fluids, such as C02-expanded liquids, in microfluidics and analytical flow systems. C02-expanded ethanol with a variable composition ranging from 6 to 90 mol. % ethanol was generated in a microfluidic system, producing fluids with tunable e _G between 1.72 and 21.40. Using the sensor, a closed control system was realised to control the relative permittivity and composition, giving tunable and stable C02-expanded ethanol flows.

Description of supporting equipment

For fluid setup A in Fig. 7A, two high-pressure piston pumps (DM100 ISCO, Teledyne) containing internal pressure sensors was used to deliver the flow of both CO2 and methanol. The CO2 piston pump was chilled to keep the CO2 dense. Cooling was provided from a water bath that contained two recirculating heaters (E100, Lauda) and was connected to a compressor chiller (RK20, Lauda). The tubing leading to the FRB had check valves (41AF1 , High Pressure Equipment Company) and filters with a pore size of 10 pm (A-106, IDEX) mounted on them. To regulate the backpressure, a pressure sensor (PA-1 1 , Keller) and a backpressure regulator (26-1700 Tescom) were installed after the FRB. For fluid setup B in Fig. 7B, only the chilled CO2 high-pressure piston pump was used to deliver the flow of both fluids. For the flow of methanol, a cylinder (TOC1 -6, High Pressure Equipment Company) containing a movable piston was used. By use of the piston, the cylinder had two chambers of variable volume. One chamber was connected to the CO2 pump and the other chamber was filled with methanol connected to the FRB. When CO2 is allowed to pass into the cylinder, pressure is exerted on the piston and a flow of methanol to the FRB occurs. The piston had a PTFE seal. To fill and empty the cylinder, valves were used (1 1AF1 , High Pressure Equipment Company). For fluid setup B in Fig. 7B and fluid setup C in Fig. 7C, backpressure regulation and the total flow rate measurement, Qtot, was achieved by using another high-pressure piston pumps together with a pressure sensor (PA-1 1 , Keller). Fluid setup C in Fig. 7C used the same equipment as fluid setup B in Fig. 7B, but the pumping of the CO2 pump was turned off. The temperature sensors were measured using a 4-terminal connection and the signal was logged to a data acquisition unit (34901 , Agilent). The backpressure sensor was logged using a multimeter (2000, Keithley).

Fabrication of the non-planar electrodes in the permittivity sensor

The main fabrication steps of the mixing and sensor chip are described elsewhere [J. Micromech. and Microeng., 2016, 26: 095009; J. Micromech. and Microeng., 2017, 27: 015018]. The metal thin films of the permittivity sensor were made after all channel structures had been etched on the wafers. The purpose of this was to achieve the 3D-pattern where the electrodes followed the pattern on the wafer, down into the previously etched channels. The metal thin films were formed by first sputtering (CS730S, Von Ardenne) the wafer with a 300 nm masking layer of Mo, then applying an adhesion promoting primer (FIDMS) using a priming oven (2000, Star) followed by coating the wafers with 12 m of resist (AZ9260, Microchemicals) using a spray coater (101 , EVG). After exposure and development of the resist, the Mo was patterned using an etching solution consisting of 51 , 3 and 3 vol% of concentrated H3PO4, CH3COOH, and HNO3 in water, respectively. This was followed by etching the glass down 130 nm using a buffered oxide etch (BOE 1 :7, J. T Baker). Following this, 30 nm of Ta followed by 100 nm of Pt was sputtered (K675XD, Emitech). After deposition, the Pt-Ta coated resist was lifted with acetone in an ultrasonic bath and the underlying Mo etch mask was then removed by etching, exposing the electrode pattern embedded into the glass.

Experimental setup

Two high-pressure piston pumps (DM100 ISCO, Teledyne), having internal pressure sensors to regulate the pressures ¾P and Pi _p , supplied the microfluidic system with CO2 and ethanol, Fig. 16a. The piston pump for CO2 was cooled to 6 °C, and all tubing and valves leading to the restrictors of the mixing chip was submerged in water, having a temperature of 5 °C. Check valves were installed on both fluid lines. A pressure sensor (PA-1 1 , Keller) and a backpressure regulator (26-1700 Tescom) were mounted after the microfluidic system. For imaging of the chips, a stereoscope (SMZ800, Nikon) was used with a high- speed camera (Miro M310, Vision Research). The temperature of the fixture holding chips was measured to be 21 ± 1 °C. The temperatures were measured using either 4-wire Pt100 sensing elements or K-type thermocouples, connected to a data acquisition unit (34901 , Agilent). The backpressure, Pf _b , was logged using a multimeter (2000, Keithley). The fluid interfaces consisted of silica capillaries and acted not only as fluid interfaces but also as restrictors and, depending on the dimensions, were used to configure the pressure difference between ? _2p and Pi _p . and Pf _b - For this microfluidic system, the ethanol and CO2 inlet capillaries are 32 and 100 mm long with an inner diameter of 40 and 20 pm, respectively. The outer diameter is 1 10 pm. A 20 mm long capillary with an inner diameter of 40 m was used between the sensor and the mixing chip. After the sensor, a 43 mm long capillary of the same inner diameter was used. To hold the chips and the polyether ether ketone (PEEK) tubing, they were mounted on a fixture made from a printed circuit board (PCB), having milled openings under the chip to allow for light transmission. The PCB had electrical paths and pads, connecting the sensor to a coaxial cable with an SMA connector. Conductive glue (CW2400, Circuit works) and a milled copper coated polyimide foil was used to connect the connection pads of the chip to the electrical connections of the fixture. Fluid interfaces, described elsewhere [J. Micromech. and Microeng., 2017, 27: 015018], where made using silica capillaries and epoxy to connect to either 1/16” PEEK tubing or between the two chips. Sensors for monitoring the backpressure and various temperatures were used and by a customized program (Matlab R2017, Mathworks), the response of all measuring devices was logged and the pumps controlled.

The embodiments described above are to be understood as a few illustrative examples of the present invention. It will be understood by those skilled in the art that various modifications, combinations and changes may be made to the embodiments without departing from the scope of the present invention. In particular, different part solutions in the different embodiments can be combined in other configurations, where technically possible. The scope of the present invention is, however, defined by the appended claims.