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# Thermally-actuated microfluidic membrane valve for point-of-care applications

## System overview

The three-layer PDMS structure is shown in Fig. 1a. In the top layer (dark grey), the microfluidic channels are patterned. The middle layer (green) is a PDMS membrane that is ~200 μm thick, the bottom layer (light grey) is a thick PDMS block which houses support ports for inserting capillary tubes. The capillary tube is filled with oil and a resistance wire is inserted for heating. The other end of the capillary is sealed with epoxy glue. Two types of imaging have been used, ‘top imaging’ and ‘side imaging’; camera positions are shown in Fig. 1a, b. When the valve is in OFF-state—no heating (Fig. 1c)—the microfluidic channels operate as normal. When DC power is applied to the resistance wire, the oil heats up, expands and restricts flow in the microfluidic channel (Fig. 1d).

For proof-of-concept demonstration of the valve, top imaging (Fig. 1a) was used with a Y-junction microfluidic chip shown in Fig. 2 (entire microfluidic chip design shown in Fig. S1). The Y-junction microfluidic chip was supplied with water from one inlet while food dye was used in the other inlet where the valve is located. After the two flows meet, a pixel intensity recording line (see ‘Materials and methods’) is used to log data for analysis (Fig. 2). Peripheral configuration 1 has been used for this experiment, see ‘Materials and methods’ for details.

To demonstrate how the valve works, time-lapse images during valve operation are shown in Fig. 3. The heating is turned on at t = 0 s when the two interfaces meet stably in the middle of the bigger channel (Fig. 3a). As the oil heats up, it expands and applies pressure on the membrane to restrict flow coming from the dye inlet. Over time, the interface recedes to a bare minimum (Fig. 3b–d) as expected from a sieve valve41. Supplementary Video 1 shows the valve operation in real time.

## Results and discussion

### Theoretical power requirement

To characterise the microvalve presented in this paper, firstly, we focus on determining power requirements for turning on (heating) one valve. This is an important parameter for portable applications, especially those which employ a large number of valves. The power requirement is initially calculated theoretically and later compared with experimental results.

To theoretically calculate the power requirements for turning on one valve, we will start with the assumption that pressure in the heated oil section will be sufficient to overcome the pressure in the microfluidic channel. According to a mathematical model developed to estimate pressure increase due to thermal expansion of a trapped liquid42,43; the expected pressure rise is 10.88 bar per K (see Supplementary Information for details). This is an overestimate because the model assumes homogeneous material properties surrounding the blocked-in liquid, however, in this paper, one end of the capillary tube is sealed with epoxy glue and the other with PDMS membrane. Notwithstanding, 10.88 bar per K is more than enough to overcome a pressure of several hundred millibars, which is commonly used to drive microfluidic flows.

An estimate on the volume expansion required to block the flow in the microfluidic channel could be calculated as ΔV = 50 nL using the volume of a rectangular prism where the width and length are that of the microfluidic channel and the diameter of the valve (500 μm × 2000 μm) (shown as a dashed rectangle in Fig. 2) while the height is the height of the microfluidic channel (50 μm). The temperature change, ΔT, in the oil required to generate volume expansion equal to 50 nL can be calculated using the volume expansion formula44:

$${{\Delta }}T=\frac{{{\Delta }}V}{{V}_{0}\beta }$$
(1)

where V0 is the initial volume and β is the volume expansion coefficient of the oil. Next, we will use specific heat formula to find the required energy, Q, to change the temperature by ΔT:

$${{\Delta }}T=\frac{Q}{m{c}_{p}}$$
(2)

where m and cp are the mass and the specific heat of the oil. To find power requirement, W, we use Q = WΔt where Δt is the time it takes to actuate the valve. We will also substitute the density formula into Eq. (2) given by m = ρV0 where ρ is the density of the oil. Substituting the above and equating Eqs. (1) and (2), we get:

$$W({{\Delta }}V,{{\Delta }}t)=\frac{\rho {c}_{p}}{\beta }\frac{{{\Delta }}V}{{{\Delta }}t}$$
(3)

It is interesting to note, assuming ΔT stays within an acceptable range (e.g. no boiling; this is revisited later in this section), the power requirement during heating is expressed as a function of fluid properties, the required volume change and the time it takes to turn on the valve (Eq. (3)). Relevant properties of the fluids used in this study are given in Table 1.

Using the required volume expansion and the properties of the oil used in this study as well as water for comparison, Fig. 4a shows the power requirement as a function of actuation time, Δt. As can be seen, there is a significant trade-off between the required power and the actuation time. Also, were water to be used as the expansion liquid, it would have required much more energy due to the high specific heat of water.

### Experimental power requirement

To measure how long it takes to actuate the valve, a side imaging (Fig. 1b) experiment was carried out where the expansion and contraction of the valve along with the microchannel could be observed via a camera. Peripheral configuration 2 has been used for this experiment, see ‘Materials and methods’ for details. In this experiment, an equilibrium was sought where zero net heating energy into the expansion medium was targeted. Arduino microcontroller was programmed so that the heating was on for 1.2 s and off for 5.5 s. In these time-frames, it was observed that net energy into the expansion medium was close to zero. When the net energy was positive, the valve was observed to expand and the valve would stay closed during the cooling period. When the net energy was negative, the valve would cool down over time and would not block the microchannel any more. More importantly, during 1.2 s of heating and 5.5 s of cooling, it was observed that the expansion of the valve was enough to close the microchannel (see Supplementary Video 2).

To verify this, a constant-pressure, top imaging experiment has been carried out with peripheral configuration 3, see ‘Materials and methods’ for details. In this experiment, it was found that 1.2 s was not enough to fully close the valve, instead, 2 s of heating and 9 s of cooling was used to turn the valve on and off (see Supplementary Video 3). This difference is attributed to the additional thermal mass and pressure in the system due to the emulsion flowing inside the microchannel which was not the case for the side imaging experiment where the microchannel was open to air (Fig. 1b). Based on the top imaging experiment, the fastest time it takes to close or open the valve has been established as 2 s and 9 s, respectively.

A vertical dashed line has been shown on Fig. 4a corresponding to the closing time of 2 s. This line intersects the olive oil and water curves at 0.064 W and 0.487 W, respectively. From this, we infer that, theoretically, 0.064 W is required to fully close the valve. Power consumption during heating up was experimentally calculated by measuring the voltage across the heater, Vh and using previously measured resistance (room temperature) of the heated wire, R, according to ‘Joule heating’ formula given as $$W={V}_{h}^{2}/R$$. Experimental results show that 0.73 W is provided to the resistance wires when the heating is turned on with peripheral configuration 2 (see ‘Materials and methods’) at maximum power (100% duty cycle).

There is a significant discrepancy between the theoretical (0.064 W) and the experimental results (0.73 W). We believe this is explained by the losses in the system which are not accounted for in the theoretical calculations. The major losses in this study have been determined as heating of the wires and other components in the electrical circuit (see Fig. S2) along with heat lost to the environment. Finally, ΔV is expected to be larger than the calculated value of 50 nL (Eq. (3)) due to the elasticity of the PDMS. While the elasticity of the channels could be minimized by using another material such as glass, the heat lost to the environment is beneficial when it comes to re-opening of the demonstrated thermal valve.

To investigate Eq. (3) further, a side imaging (Fig. 1b) experiment was designed. Peripheral configuration 2 has been used for this experiment, see ‘Materials and methods’ for details. In this experiment, power was changed from 100% duty cycle to 35% duty cycle in increments of 5%. Below 35% duty cycle, the valve operation was simply too slow or the power was insufficient to overcome ambient cooling. At every power level, after 5-min cool-down, the time elapsed to reach a predetermined valve expansion was measured. This ensured that ΔV was kept constant across experiments. The expected power requirement and time elapsed according to Eq. (3) was plotted as a solid line (denoted ‘Theoretical’, Fig. 4b). The experimental data points are shown as blue circles denoted ‘Experimental’. At each power level, the measurement was repeated at least two times. It can be seen that the experimental results follow a similar trend to the expected curve. A regression analysis shows that the R2 value is 0.806 (Fig. 4b). Furthermore, the form of Eq. (3) with an adjustable constant of proportionality, A, (Wt) = At) was used for fitting a curve to the experimental data points; this is shown as a dashed line denoted ‘Curve Fit’. Regression analysis shows that the R2 value is improved and is 0.848 for the fitted curve (Fig. 4b).

### Chemical concentration

To showcase the tuning of a water/dye dilution mixture, a series of top imaging (Fig. 1a) experiments have been performed by measuring the interface settling location. Peripheral configuration 1 has been used for this experiment, see ‘Materials and methods’ for details. The Y-junction microfluidic chip (see Fig. 2 and Fig. S1) has been used. In this set of experiments, referring to Fig. S1, port 1 was supplied with water, port 2 was supplied with dye, port 5 was the outlet and ports 3–4 were closed. The flow rates on both inlets have been kept constant and the valve has been actuated at different power levels to allow the dye-water interface to settle in a final location. This way, the chemical concentration of the output is modified in a continuous flow microfluidic chip. Alternatively, peripheral configuration 2 (see ‘Materials and methods’) could be used to control the interface location real time using a feedback control loop. As an example, this could be used to generate droplets of varying chemical concentrations using a chip similar to the one described by Park et al. 46.

At each power level reported in this Fig. 5, steady-state interface location is reported. For some of the data points, the interface settling location is shown visually. Initially, there is no actuation and the system is at rest. At this state, the interface slightly fluctuates due to the stepper motor in the syringe pump. Therefore, the zeroth data point is shown as a box plot captured over 60 s at 12 fps in Fig. 5 (see ‘Experimentation and data analysis’ for further details). It can be seen that the interface settles slightly below 600 μm. The location of the interface along the intensity line is measured from bottom to top and the length of the intensity line is 1 mm; the initial settling is slightly biased for the dye channel (40–60% water–dye mixture). At 0.33 W input power (Fig. 5), the interface settles at around 250 μm rendering the outlet a 75%–25% water–dye mixture. At higher power levels (>0.5 W), the dye flow is reduced to a bare minimum (<10%, Fig. 5 inset 0.66 W and 1 W); not fully closed as the channels are rectangular making this a sieve (leaky) valve 41.

To further investigate the leaky nature of the valve, a top imaging experiment has been carried out with peripheral configuration 3 where an emulsion flow—to visualize the flow—is driven by constant pressure (see ‘Materials and methods’). With a mid-level power applied to close the valve, it can be seen in Supplementary Video 4 that the flow is leaky around the edges of the microchannels until the valve fully blocks and stops flow successfully (t = 1:13 s, Supplementary Video 4). It’s been observed that flow remained leaky during the experiments with syringe pumps (Fig. 3(D), therefore, the successful closure is attributed to the constant-pressure driven flow. The leakiness is caused by the mismatch between the rectangular microchannel cross-section and hemispherical membrane (Fig. 1d). In the literature, it’s been shown that rounded channel structures could be used for fabricating fully closing valves47; rounded microchannels could be obtained via wet etching glass microfluidic chips or reflowing photoresist48. Lee et al.47 have used sieve (leaky) valves and fully closing valves together in a microfluidic device where the sieve valves have been used to trap bigger particles, anion exchange beads, while still allowing flow to filter through thus creating an anion exchange column.

### Multiple valves

Supplementary Video 5 shows two valves operating in succession. Side imaging (Fig. 1b) and peripheral configuration 2 (see ‘Materials and methods’) was used to carry out these experiments with the exception that the fluidic layer was not installed. There were three valves during this experiment, however, only two of them could be visualised at the same time. The power was supplied was from the 12 V output of a computer power supply (GPT500S, Channel Well Technology Co., Ltd.). Metal Oxide Semiconductor Field-Effect Transistors (MOSFETs) were used as switches to turn the valves on or off. MOSFETs are controlled by a voltage signal applied at the gate terminal; this was provided by digital pins with pulse-width modulation (PWM) capability on an Arduino Uno microcontroller board. Arduino Uno offers 6 PWM pins, however, Arduino Mega offers 15. The power supply is capable of providing 456 W on the 12 V rail which can operate more than 100 valves. This shows that the scaling out with the proposed valves is feasible on a technical and cost point-of-view.

### Durability

Supplementary Video 6 shows a side imaging (Fig. 1b) experiment carried out for testing the durability of a valve. Peripheral configuration 2 (see ‘Materials and methods’) was used for this experiment. The valve was heated for 200 s and cooled for 200 s. An image was captured every 200 s so that consecutive images of the valve being on and off could be seen. Supplementary Video 6 is constructed as a time-lapse video (30 fps) from the 1295 images captured, the experiment approximately ran for 3 days. The valve failed at image 1170; after 585 actuations in 65 h of operation (see Supplementary Videos for further details). For a disposable chip aimed at point-of-care assays, it is believed that this durability will be sufficient. The main mode of failure has been observed as leaking due to local heat damage to the epoxy glue (Fig. 1a). This could potentially be alleviated by using a high-temperature resistant epoxy to improve the durability further, however, it should be noted that epoxy glue represents 40% of the total cost of one valve, therefore, this might have an impact on the overall cost of the proposed valve.

### Temperature change

Next, we will investigate the temperature change required by the presented system. Recalling how the required temperature change, ΔT, was cancelled out to obtain Eq. (3), it is necessary to ensure that ΔT is an acceptable value (e.g. no boiling). To verify this, we use Eq. (1) to plot temperature change as a function of the initial volume, V0 (Fig. 6). Here, we assume 25 °C room temperature and limit ΔT at a maximum of 75 °C as this corresponds to the boiling point of water. It is expected that boiling in the expansion medium will be catastrophic for thermally actuated valves. Herein, we only consider the following media: olive oil, FC-40, water and paraffin wax. Fig. 6 shows ΔT up to 75 °C for these substances. The inset shows a table for all the substances noting the V0 value when ΔT = 75 °C as well as the ΔT value for V0 = 15.4 μL and 38.5 μL. These are the expansion media volumes with which the experiments have been carried out (Table 2). The expected temperature change for the 15.4 μL and 38.5 μL valves are 4.64 °C and 1.86 °C, respectively. In this work, minimal temperature increase is targeted for the valve to safely work with sensitive biological samples. Using the mathematical framework provided in this paper, thermally actuated valves with different characteristics could be designed. For example, if the valve will be deployed in the field in a hot environment, it could be designed so that the required temperature change (ΔT) is high to ensure it will not spontaneously close. Conversely, low temperature change (ΔT) could be preferred for operating in cold environments.

Measuring these values experimentally for comparison proved to be challenging with the current setup, however, an experiment was carried out to measure the maximum temperatures that could be reached with the current setup. For this experiment, a thermocouple was placed right above the valve, where the microfluidic channel would be. Side imaging (Fig. 1b) and peripheral configuration 2 (see ‘Materials and methods’) was used for this experiment. With a duty cycle of 100%, the valve was kept on for 40 s and the maximum temperature increase was measured as 11 °C by the thermocouple connected to a multimeter (1 °C precision, RS PRO RS14, RS Components Ltd., UK).

While paraffin wax, amongst the other media considered in this paper, has worse performance at higher initial volumes as shown by the higher temperature changes required in the inset table in Fig. 6, it outperforms the other expansion media when operated near its melting point. This should be considered when designing thermally actuated valves using paraffin as the expansion medium. The melting point of paraffin could be modified by changing the hydrocarbon composition35; it is around 40 °C (ΔT = 15 °C) for the composition reported by Ogden et al.49. Paraffin is, therefore, better suited to applications with low initial volume requirement.

For example, the thermally actuated valve using paraffin as the expansion medium reported by Carlen et al.29,34 features a volume (V0) of 1.26 nL. When heated up to ~90 °C, it is shown to deflect 3 μm. In the work reported by Pitchaimani et al.37, the expansion medium is fluorocarbon oil (FC-40) with a volume of 0.79 μL; the required ΔV is reported as 8.2 nL while the minimum temperature change was 27 °C. Actuation times ranged from 7 to 80 s when applied power was between 50 and 80 mW. For comparison, with olive oil as the expanding medium, this work features a ΔV of 50 nL, expected temperature change of 5 °C and a measured maximum temperature increase of 11 °C whilst the fastest actuation time was measured to be 2 s.

## Data availability

All connected data to this manuscript is available from the authors upon reasonable request.

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## Acknowledgements

The authors would like to thank Mr. Allan Lee for his help in building the valves and the Arduino-MOSFET control circuitry. C.J.R. and M.S. acknowledge salary and research support from the Wellcome Trust 212490/Z/18/Z. C.J.R. additionally is grateful for support from EPSRC EP/S016538/1, BBSRC BB/T011947/1 and the Imperial College Excellence Fund for Frontier Research.

## Author information

Authors

### Contributions

C.J.R. conceived the project and acquired funding. M.S. conducted the experiments and analysed the results. M.S. wrote the original draft, both authors reviewed and edited the manuscript.

### Corresponding author

Correspondence to Christopher J. Rowlands.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

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Sesen, M., Rowlands, C.J. Thermally-actuated microfluidic membrane valve for point-of-care applications. Microsyst Nanoeng 7, 48 (2021). https://doi.org/10.1038/s41378-021-00260-3