A microfluidic control board for high-pressure flow, composition, and

Sep 30, 2018 - Flow control is central to microfluidics and chromatography. With decreasing dimensions and high pressures, precise fluid flows are oft...
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A microfluidic control board for high-pressure flow, composition, and relative permittivity Martin Andersson, Karolina Svensson, Lena Klintberg, and Klas Hjort Anal. Chem., Just Accepted Manuscript • DOI: 10.1021/acs.analchem.8b02758 • Publication Date (Web): 30 Sep 2018 Downloaded from http://pubs.acs.org on October 8, 2018

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is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

A microfluidic control board for high-pressure flow, composition, and relative permittivity Martin Anderssona, Karolina Svensson, Lena Klintberg and Klas Hjort Uppsala University, Centre of Natural Hazards and Disaster Science, CNDS, and Department of Engineering Sciences, Division of Microsystem Technology, Box 534, SE-75121 Uppsala, Sweden a

Corresponding author: [email protected]

Abstract Flow control is central to microfluidics and chromatography. With decreasing dimensions and high pressures, precise fluid flows are often needed. In this paper, a high-pressure flow control system is presented, allowing for the miniaturization of chromatographic systems and the increased performance of microfluidic setups by controlling flow, composition and relative permittivity of two-component flows with CO2. The system consists of four chips: two flow actuator chips, one mixing chip and one relative permittivity sensor. The actuator chips, throttling the flow, required no moving parts as they instead relied on internal heaters to change the fluid resistance. This allows for flow control using miniaturized fluid delivery systems containing only a single pump or pressure source. Mobile phase gradients between 49% to 74% methanol in CO2 were demonstrated. Depending on how the actuator chips were dimensioned, the position of this range could be set for different method-specific needs. With the microfluidic control board, both flow and composition could be controlled from constant pressure sources, drift could be removed, and variations in composition could be lowered by 84%, resulting in microflows of CO2 and methanol with a variation in the composition of ±0.30%. Keywords flow control, high-pressure microfluidics, control systems, CO2-expanded liquids, relative permittivity

Introduction Microscale fluid flows are encountered in a multitude of analytical and diagnostic applications and for many of them, their performance is highly linked to the ability to achieve well-defined and stable flows. Chromatography, where a flow through a column is used to separate chemical compounds, is a prime example as the quality of separation is depending on the stability of both flow rate and fluid composition 1. By having systems that can tune flow rate and composition, analytical systems become versatile as they can be optimized for different analytical questions. In microfluidics, high numbers of flow paths and intricate working mechanisms are common 23, imposing an even greater need of fluid control. In analytical chromatography, flow must be delivered through narrow channels or pores at high flow rate and the instruments must handle fluid at high pressures. In microchip-based chromatography, where columns are integrated on microfluidic chips 4,5, the requirements of

pressure tolerance and miniaturization meet. The reduced dimensions allow for dedicated instruments, especially for proteomics, where low sample volumes are encountered and efficient coupling to mass-spectrometry is needed 6. High-pressure microfluidics is also utilized for other applications: devices that investigate multicomponent systems 7, extract lignin oxidation products 8, study cavitation 9 and investigate the deposition of asphaltenes 10. The high-pressure regime enables low viscosity fluids with high density, like supercritical CO2 11 or CO2-expanded liquids 12. Microfluidic studies of CO2-ethanol and CO2-methanol flows have been presented13. The combination of high pressure and need for control puts extensive requirements on the equipment 14, which increase the cost. With compressible fluids, volumetric flow metering can lead to errors due to fluid compression. To evade this, post-compression metering pistons, thermal mass flow meters, or thermodynamically models are often used 15. Separations, extractions, and synthesis are often performed with multicomponent fluids and the composition of the mixture is critical and must be tuned or ran in gradients, resulting in the need of having extra pumps. This leads to systems with both large footprints and high technical complexity; excluding applications where size, cost or the number of fluid streams are important factors. However, this also offers a challenge: How can the control of highpressure microflows be miniaturized? For low-pressure applications, there are several miniaturized components, other than pumps, that provide flow rate control. Most often valves are used, actuated by pneumatics 16, direct force 17 or phase changes 18. At high pressure, soft elastic materials fail to provide enough structural support and high-pressure tolerant microfluidic chips are typically made from glass or glass-silicon, sustaining pressures up to 690 and 500 bar, respectively 9,19. Silicon and stainless steel allow for miniaturized high-pressure tolerant membrane valves (~ 200 bar) 20,21. For flow rate control, throttling valves are needed, giving a predictable change of flow by an incremental change of actuation—preferably over a large range and with a high degree of proportionality. While membrane valves are worth more investigation, their designs make throttling challenging. Furthermore, membrane valves have problems such as sticking, clogging and membrane deformation. Rather than changing the physical restriction that the fluid passes through (i.e. valves), these limitations can be worked around by an alternative approach—changing the fluid’s ability to pass the restriction. This concept is explored in this paper. By use of heating elements, actuation on flow rates is achieved without any mechanical components. The demonstrated miniaturized system achieves control over flow rate, relative permittivity, and composition of CO2-methanol, a mobile phase of high interest in chromatography. Background Fluid delivery setups and chromatography High-pressure flow is typically generated using displacement pumps with integrated systems for control of flow rate or pressure. This is exemplified in fluid setup A, figure 1, where two fluids meet at the mixing point (blue box, figure 1) and create a single mixed fluid, i.e. a mobile phase. This requires one flow controlled pump for each component. By using separating containers (e.g. piston separated chambers or loops) to hold extra fluid components and a common source of pressure, flow can be driven by from only one pump (fluid setup B) 13 or a pressurized container (fluid setup C). To enable the composition to be tuned in this simplified system, an extra control element is required: a flow regulating board (FRB).

The FRB is demonstrated by creating controlled mobile phases relevant for both supercritical fluid chromatography (SFC) and enhanced fluidity liquid chromatography (EFLC). In SFC, low viscosity CO2 constitutes the main solvent. CO2 is mainly a non-polar solvent and in order to separate more polar analytes, polar cosolvents are often added. Additions of up to 50% methanol in CO2 are practiced 22. Likewise, in EFLC, water-methanol based mobile phases containing up to 50% CO2 have also been investigated with the intention of creating mobile phases with lower viscosity 23. While fluid delivery systems ideally cover the entire compositional range, systems dedicated for a specific analytical method can operate under a more narrow compositional range, e.g. hydrophilic interaction EFLC often uses a CO2 content of 0-30% 24. Within this region, it is vital to be able to control the composition in detail— providing crucial versatility and means of method optimization.

Figure 1. Schematic of three fluid setups, A, B and C. The two fluids, CO2 (1.) and a cosolvent (2.), are driven to a mixing point (blue box) and subsequently to an application (red box). After the application, regulation of the back-pressure (BPR) may be required. (a) In fluid setup A, two piston pumps deliver the two fluids separately. (b) In fluid setup B, the two fluids are delivered by a single CO2 pump and a piston separated chamber with preloaded cosolvent. (c) In fluid setup C, a compressed CO2 container is used. Rr is a defined restriction.

Compositional measurements from the relative permittivity For a fluid, the relative permittivity,  , is dependent on the polarization per unit volume 25, , 

    



 

 

 



!,

(1)

where "# is Avogadro’s constant, $% is the molar volume,  is the molecular polarizability, &' is the dipole moment, ( is a correction factor, and )* is Boltzmann’s constant. From (1), it follows that the temperature and pressure dependence of  is determined by changes to $% and the temperature dependent term &' (⁄3)* , . For fluids with a significant dipole moment,  decreases with increasing temperature. For example, methanol has a dipole moment, &' , of 1.69 and at 11 °C  is 36.7, and at 24 °C,  is less, 32.7 26. The polarization of CO2 is instead altered by pressure and temperature through the molar volume, $% , as it has zero dipole moment and shows larger compressibility. For fluid mixtures, the relative permittivity is dependent on the pure components and interactions between the components in the mixture 25 . For mixtures of methanol and CO2, two studies 27, 28 have investigated the relative permittivity over a variety of temperatures, pressures, and compositions and identified a sigmoid dependence on composition. Hence, in this paper, a sigmoid function with four coefficients is used to describe the relationship between relative permittivity and composition,

expressed as the molar fraction of methanol in CO2. By the inverse, a measurement of relative permittivity can be expressed in terms of molar fraction methanol in CO2 as, /0  1 

23 24

 24

3 7

− 1! .

(2)

By (2), measurements of the composition can be done by measuring the relative permittivity of methanol-CO2 mixtures. Variations of the temperature and pressure alter the polarization, and must be kept constant. Flow actuation A valve manipulates flow by changing flow restrictor dimensions. However, flow can also be manipulated by changing the properties of the fluid, passing a flow restriction. In this paper, this feature is exploited. By heating fluids passing a flow restriction, two properties affecting the flow will change: the viscosity and the molar volume. Described as a combined product and indexed as 1 for CO2 and 2 for methanol, the viscosity and molar volume products 8 $ and 8 $ affects flow. In this paper, a fluid model is developed (see supporting information, SI) which describes the relevant flow restrictions and their connection between flow rates, composition, pressures, 8 $ , and 8 $ . With the presented FRB, the viscosity and molar volume product can easily be manipulated using the heat actuated flow restrictors—making it possible to change the flow rates and composition of a mobile phase.

Experimental Section Experimental setup Three types of fluid setups were used, figure 1. The FRB was placed at the mixing point (i.e. the blue box in figure 1). For a full description of the different supporting equipment, details regarding the mounting of the FRB, and the control system, see SI. The FRB, figure 2a, had chips for actuation, mixing and sensing, working together in a closed-loop control system. Fluids entered two actuator chips (hCS and hCO2), where internal heaters changed the fluid resistance and outlet temperature sensors measured the fluid temperature. The fluids were then combined in a mixing chip (MIX) and the relative permittivity was measured in a sensor chip (SEN). Without activation, the composition and the total flow rate stabilized to a static baseline, determined by the dimensions of the restrictions, the current fluid properties, and pressure differences. When activated, a specific composition and total flow rate could be set dynamically by finding the heater duty cycle ratios, yCS and yCO2, of hCS and hCO2, needed to make measured values correspond to setpoint values. Two different closed-loop control systems, described in SI, were used: system I controlled both the relative permittivity and the total flow rate; system J controlled only the relative permittivity. The four components of the FRB, figure 3, were mounted on a cooled printed circuit board, which acted as a support for the chips and allowed for fluid and electrical interfaces. The actuator chips, figure 2b, were surface mounted with their top open pads, figure 2c, facing the pads of the printed circuit board. The actuator chips, kept at 5.7 ± 0.5 °C, were in thermal

contact with a cooling fixture. The mixing chip and the relative permittivity sensor, mounted on top of the board, had a temperature of 10.7 ± 0.5 °C. The actuator chips, figure 2b-2e, were made in two different versions: One with a 16.7 µm deep restrictor and the other with an 8.7 µm deep restrictor. The heaters consisted of 11 resistor elements, powered in parallel, and distributed to 6 pads on each side of the chips. The resistance in the thin film varied with different chips but was in the range of 30-35 Ω for the temperature sensors and 400-550 Ω for each resistor element. The mixing chip, the relative permittivity sensor and fabrication are described elsewhere 29,30.

Figure 2. (a) The flow regulating board (FRB): two actuator chips (hCS, hCO2), connected to fluid sources with the pressures P2 and P1; one mixing chip (MIX) and; one relative permittivity sensor (SEN). The actuator chips (b), made from two borosilicate glass wafers (blue and grey-blue), had 15 nm Ta and 100 nm Pt thin film conductors (dark grey) leading to 20 connection pads at the sides of the chip (c). The fluid path (teal) consists of a fluid restrictor, which is a 77.6 mm long meander. (d) Cross section of the fluid restrictor. The heater (top) had direct contact with the fluid and cooling was applied from the opposite side (bottom). (e) Close-up of the restrictor channel outlet showing the end of a heating resistor (H) as well as the outlet temperature sensor, giving the outlet temperatures T1 or T2 for either hCO2 or hCS, respectively. The direction of flow is indicated by an arrow.

Measurements The relative permittivity, using (2), measures the mobile phase composition, /0 , which enables compositional measurements for fluid setup B and C. Input flow rates from the pumps (fluid setup A) give a reference composition, / , which allows for investigations of the functionality of the FRB. This reference composition can then be compared to an estimated composition, /: , derived from a fluid model (see SI) of the flow restrictions in the system. An FRB where both actuator chips had 16.7 µm deep restrictors were used to investigate the functionality. Powered separately, the following parameters were recorded: the relative permittivity,  ; the output temperatures, , and , ; and volumetric flows, < and < corresponding to both CO2 and methanol. The pressures of CO2 and methanol before the restrictions, = and = , as well as the backpressure, =2 , were held constant by the pumps to 78.5, 92.8, and 70.5 bar, respectively. Power was applied by either a square-wave or step function of increasing magnitude. The square-wave (having periods of 400 s) alternated the power between zero and a maximum power output, chosen so that the output temperatures never exceeded 85 °C. By this, the dynamic response of the FRB was characterized by two parameters: time constants, >, and dead times, ?. By the time constants, a measurement of the time required to reach 63.2% of the full response is given and by the dead times, a measurement is given of when a response is initially seen. The step function had a step length of 200 s and a step height of 2.8 % of the full duty cycle. For each step, a measurement point was taken using 142 s of data (centered over the step), giving 35 and 27 measurement points

of hCS and hCO2, respectively. 8 $ and 8 $ were estimated with the outlet temperatures measurements and the average pressure over the FRB. The sensor was calibrated using measurements of two pure components, i.e. CO2 and methanol. The performance of the FRB was demonstrated in three modes using fluid setup B. For the first mode, constant pressure where delivered to the FRB and control system I was used. Here, hCO2 and hCS had 16.7 µm deep restrictors. For the second mode, fluid setup B delivered a constant total flow rate. Here, the FRB used control system J with 8.7 µm and 16.7 µm deep restrictors for hCO2 and hCS, respectively. A slope function applied gradient setpoints to the relative permittivity. For the third mode, the input pressure and the pump flow rate was unregulated, mimicking the pumpless operation of fluid setup C. Here, control system J and a capillary restriction Rr (figure 1) were used together with two 16.7 µm deep restrictors. Results Functionality of FRB

Figure 3. The flow regulating board (FRB) mounted on a cooling fixture. On it, the 4 chips hCS, hCO2, MIX and SEN were mounted, as seen in figure 2.

The FRB response, figure 4a-b, with temperature and relative permittivity when powered, corresponds to increases of methanol in the mixed flow. The time constants and dead times for the responses are shown in table 1. The relative permittivity dead times, ? , were longer than those for the output temperature, ?, , illustrating the fact that the relative permittivity sensor is located downstream. The sample loop time of the experimental setup (the time between two measurement points) was 1.4 ± 0.2 s—comparable to the output temperature dead times. Therefore, the data acquisition and control implementation limit the performance. By the step function measurement, the relative permittivity as a function of composition, figure 4c, determined b1, b2, b3 and b4 of (2) to 1.66, 2.58, 0.81 and 45.05 (r2 = 0.9998). Table 1. Time constants (>) and dead times (?) for the response in relative permittivity and output temperature.

(s) hCS hCO2

> 

6.6 5.9

>

8.1 4.2

?

2.9 2.9

? 1.4 1.4

Figure 4. Operation of either hCS (a) or hCO2 (b) using power applied in a square wave (grey line). As power was applied, both the outlet temperature (T1 or T2, blue), and the relative permittivity ( , red) increased to stable conditions. When power is off, the relative permittivity assumes a value of 11 ± 2 while the total flow rate is 95 µL/min. (c) The relative permittivity as a function of reference composition (x2). Data points (blue dots) over the region 0.344 to 0.773 are shown together with the sigmoid fitting curve (black line) and measurements of the pure components (black diamonds).

Figure 5a-b shows the composition and the relative permittivity as a function of outlet temperature for hCS and hCO2. The molar fraction and relative permittivity correlated over the explored range. hCS responded linearly, 0.44 % / °C. hCO2 differed, having two regimes: in the first, from 8.0 to 26.6 °C, hCO2 responded negatively with increasing temperature; in the second, above 26.6 °C, positively, roughly 0.40 % / °C. The composition estimate, /: , from the fluid model (see SI) correlated with the reference composition, / , for hCS and the first regime of hCO2, but not with the second hCO2 regime. Figure 5c-d shows the corresponding flow rates from each pump and the total flow rate. For hCS, heating did not change the total flow. As the methanol flow rate increased, the CO2 flow rate decreased. When heating hCO2, the CO2 flow rate decreased but the methanol flow rate was unaffected, resulting in a decreased total flow rate. The different behaviors influenced the functionality. hCS tuned composition without affecting the total flow rate, but hCO2 did. Together, they allowed for control of both parameters.

Figure 5. Operation of either hCS (a, c) or hCO2 (b, d). During operation, only one actuator is powered, having the other actuator turned off. (a) Relative permittivity ( , red dots); reference composition (x2, blue triangles); and the fluid model estimate of the composition (/: , blue dashed lines) as a function of outlet temperature (T1 or T2) for each powered actuator chip. The outlet temperature of the unpowered actuator chip was 4.7−7.4 °C (a) and 4.8−6.1 °C (b), respectively. (c, d) Relative permittivity as a function of input flow rates for either CO2 (< , blue squares) or methanol (< , red triangles) together with the total flow rate (Qtot, orange diamonds). During the operation of hCS, Qtot varied around an average flow rate of 69 µL/min. For hCO2, Qtot decreased with 3.4 µL/min per unit of  . The baseline relative permittivity was 10.5 ± 2.

Figure 6. The products of viscosity and molar volume of either methanol ( 8 $ , red circles) or CO2 (8 $ , blue squares) as a function of outlet temperature. Values are calculated from the measured outlet temperatures and the average pressures over the FRB using references 31–34. A local minimum of 8 $ is seen at 30.9 °C.

The product of viscosity and molar volume of the fluids in the actuators chips were estimated, figure 6. For the hCS actuator, the product 8 $ decreases due to a large drop in the viscosity—from 699 to 279 µPa·s. This gives less restriction through the actuator, which results in a higher flow rate. For hCO2, as the outlet temperature of CO2 increases, density and viscosity can be expected to drop from 911 to 155 kg/m3 and 94.5 to 19.4 µPa·s, respectively. Over this range, 8 $ forms a local minimum with two regimes. Relative permittivity, composition and flow rate control at constant pressure In figure 7, control system I was demonstrated, showing how both the relative permittivity, and the total flow rate was controlled—independently and simultaneously—under a constant pressure driven flow by a single pump (fluid setup B). With the control system, the relative permittivity was set to 6 and the total flow rate was set to 50 µL/min. Before the system was

turned on, the relative permittivity was 2.90 ± 0.30 and the total flow rate was 79 ± 13 µL/min, forming a static baseline. By activating the system, the setpoints were reached, giving a relative permittivity of 5.99 ± 0.05 and a total flow rate of 49 ± 6 µL/min. This corresponds to offsets from the setpoints of 0.15% and 1.6%, respectively. Variations in the relative permittivity reduced by 84%. Before the FRB was turned on, the composition, /0 , was 12.8% ± 2.8%. When the system is activated to the setpoint, the composition was 23.7% ± 0.3%.

Figure 7. Total flow rate, Qtot, (top) and relative permittivity,  , (bottom) as a function of time. Flow is delivered at constant pressure using a single pump (fluid setup B). The baseline (blue) of Qtot and  was 79 ± 13 µL/min and 2.90 ± 0.30, respectively. When control is activated (red) to a total flow rate setpoint of 50 µL/min and relative permittivity setpoint of 6, Qtot and  reaches 49 ± 6 µL/min and 5.99 ± 0.05, respectively. Two replicate experiments, for both activated and deactivated mode, are shown. The backpressure was 64.5 ± 0.05 bar.

Composition control at constant total flow To create composition gradients, a single pump (fluid setup B) delivered fluid at a constant flow rate. This represents conditions typical for chromatography, where the pressure can vary and the pump keeps the total flow rate fixed. Relative permittivities of up to 26 were possible to control, giving gradients from 49 % to 74 %, figure 8. The steepest gradient was 6.4% /min. With the maximum heating power used, compositional spans above 32% resulted in a slow response.

Figure 8. Molar fraction, /0 , as a function of time while running gradients of the relative permittivity. Fluid setup B was used at a constant flow rate of 25 µL/min. After 2 min, 4 different gradients were initiated by increasing the relative permittivity setpoint from 16 to 26, corresponding to /0 of 0.49 to 0.74, over 4, 8.5, 14, and 19.5 min. During the gradient, the inlet pressure varies between 72 and 75 bar. The backpressure was 64.5 ± 0.05 bar. The baseline relative permittivity was 14.3 ± 0.6.

Composition control at variable pressure

Figure 9. (Top) Relative permittivity ( ) as a function of time with varying inlet pressure (P1). From 0−220 s, flow is delivered from a single pump at a constant P1. At 220 s, (dotted line) pressure regulation is turned off, replicating conditions of fluid setup C. Control system J was set to give a relative permittivity of 20 (dashed line). (Bottom) The duty cycle ratio for hCS (yCS, red) and hCO2 (yCO2, blue) as a function of time during the same experiment. The backpressure was 64.5 ± 0.05 bar. The baseline relative permittivity was 16.4 ± 0.7.

In figure 9, the inlet pressure varied, demonstrating a pumpless situation (fluid setup C) where increased actuation power compensates for changes in composition imposed by pressure loss. Beyond 220 s, compressed CO2 drives the flow while the FRB keeps composition constant. The total flow rate drops from 26 µL/min at 74 bar to 15 µL/min at 69 bar. Discussion By both the fluid model (see SI) and a description for errors due to compressibility 35, approximatively laminar and incompressible flow occurs in hCS, figure 5a, and in the first regime of hCO2, figure 5b. For CO2, Reynolds numbers are about 200 when no heat is applied, but increase to 760 close to the critical temperature (31 °C). In the second regime, the compressibility is expected to be 1.8 ·10-7 Pa-1 at 72°C and even higher around the critical temperature, requiring a more advanced fluid model. In figure 6, 8 $ decreases with temperature in the first regime, causing the flow restriction in hCO2, R , to decrease with temperature and increase the CO2 proportion in the mobile phase. In the second regime, the opposite is true. At the local minimum, thermal properties change 31 as CO2 transform from a liquid to a gas, or, at supercritical conditions, to a liquid-like to a gas-like supercritical fluid. In figure 5b, the local minimum of the reference composition, / , occured at 26 °C, i.e. 5 °C lower than for the fluid model estimate, /: . This difference highlights the complexity of the fluids thermal profile in the restrictor. With the fluid model, the behavior in figure 5c-d can be understood. At the T-junction of the mixing chip, the outlet pressures from the actuator chips and the inlet pressure of the relative permittivity sensor is the same. As hCS is heated, the methanol proportion and viscosity of the mixture increases, which subsequently increases the restriction over the relative

permittivity sensor (denoted BC ). Meanwhile, both the backpressure and the total flow rate are constant. Consequently, the pressure at the T-junction must rise. Simultaneously, hCO2 is unheated and therefore, its fluid resistance (denoted B ) is constant. Since also the CO2 inlet pressure is kept constant, the pressure difference over hCO2 decreases, lowering CO2 flow. By heating hCS, the flow of methanol increases and the flow of CO2 decreases, resulting in a constant total flow rate. In comparison, when instead hCO2 is heated, BC increases in a similar manner. Yet here, the total flow rate decreases, suggesting that the pressure at the Tjunction does not change. This agrees with the constant flow of methanol, seen in figure 5d. For the response of relative permittivity and outlet temperature, the time constants were larger than the dead times (i.e. > > ? and > > ? ) and the processes were therefore lagdominant—a feature beneficial for control 36. The flow residence time between the T-junction and the relative permittivity sensor was a major parameter that affected the dead time. Hence, with a volume of 1.8 µL, dead-time dominance should occur at 17 µL/min. By further miniaturization, especially of the mixing chip that comprises 82% of the volume, lagdominance could be kept at lower flow rates. For example, if only the sensor volume is considered, dead-time dominance will occur at a flow rate of 2.8 µL/min. In addition, the sample loop time needs be reduced, so that it does not control the dead time. Use of dedicated electronics and robust transient control models37 could be explored. The FRB allows for mapping parameters. If the composition of flowing CO2-alcohol mixtures is both changed and determined by alternating pump pressures and volumetric piston changes, variations of the CO2 properties are introduced into the fluid occupied in the pump and tubing. This gives flow deviations 29. Notably, the FRB can vary composition while keeping the majority of CO2 at a fixed inlet pressure—hindering density variations in the pump. With our power limitation, a 32% span of the whole compositional range could be set. For larger span, higher temperatures are needed in the actuator chip. The pressure tolerance in glass chips is affected by stress corrosion, a temperature dependent effect that can cause 45% lower long-term pressure tolerance at 80 °C compared to ambient temperature 38. Furthermore, embedded electrodes can also affect the strength 30. Yet, the pressure tolerance also depends on channel dimensions19 and as the heating was localized to the narrow restrictor channels, this effect might be mitigated. The FRB can be optimized for specific analytical methods. For the FRB used in figure 8, the restrictor channel depths are lower for hCO2 than for hCS, which favor methanol rich flows. With compositions between 49% to 74%, the range targets EFLC. For EFLC methods which require higher proportions of methanol, the channel depth ratio must be changed. Similarly, for the FRB used in figure 7, the equally deep channel restrictors give a static composition of 12%, a range applicable for SFC. By using actuator chips in parallel, the total flow rate regime can be changed. In conclusion, the FRB can be designed and optimized for a specific chromatographic method in mind. Conclusions An integrated microfluidic control system for flow, composition and relative permittivity of high-pressure microflows has been demonstrated. Temperature controlled actuation of flow is possible by changing both viscosity and molar volume. 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. 32% of the compositional span could be covered and by changes to the static design of the system, its position could be set. The control system removed drift and reduced variation by 84%. Compositions with a variation of ± 0.30% were generated.

Acknowledgements We acknowledge that the project has funding from the Kamprad Family Foundation and funding for laboratory facilities by the Knut and Alice Wallenberg Foundation. Conflicts of interest The authors have no conflicts of interest. References

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