Capillaric field effect transistors

Abstract

Controlling fluid flow in capillaric circuits is a key requirement to increase their uptake for assay applications. Capillary action off-valves provide such functionality by pushing an occluding bubble into the channel using a difference in capillary pressure. Previously, we utilized the binary switching mode of this structure to develop a powerful set of fundamental fluidic valving operations. In this work, we study the transistor-like qualities of the off-valve and provide evidence that these structures are in fact functionally complementary to electronic junction field effect transistors. In view of this, we propose the new term capillaric field effect transistor to describe these types of valves. To support this conclusion, we present a theoretical description, experimental characterization, and practical application of analog flow resistance control. In addition, we demonstrate that the valves can also be reopened. We show modulation of the flow resistance from fully open to pinch-off, determine the flow rate-trigger channel volume relationship and demonstrate that the latter can be modeled using Shockley's equation for electronic transistors. Finally, we provide a first example of how the valves can be opened and closed repeatedly.

Keywords: Microfluidics; Nanofabrication and nanopatterning.

Fig. 1. Construction and operational principle of the off-valve as a capillaric field effect transistor (cFET).

a Circuit symbol, structure and operational principle of the cFET. An air bubble is expanded into the main channel via a trigger channel to control flow resistance in the former. b Symbol and basic operation of an electronic JFET. In this structure, the depletion region reduces the cross-section of the conducting channel, restricting electrical current flow. Despite different physical mediums, the similar geometries of these structures allow for significant theoretical and operational overlap

Fig. 2. Electrical analogy model, and fluidic and gas resistances of the cFET.

a Dynamic electrical analogy model for the closing behavior of a cFET. The model is overlaid on a representation of the physical structure to show the physical quantities they represent. Two capillary pressures, P_tr and P_m, and four resistances, R_f,tr, R_g,tr, R_g,m, and R_f,m, are used to model the cFET behavior. b The fluid and gas resistances, and the main channel capillary pressure change as a function of the displaced trigger channel volume. Note: These graphs show the expected form of these properties only

Fig. 3. CAD rendering of the analog resistance mode test chip.

The device was fabricated using micromilling in Polymethylmethacrylate, as reported previously, and consisted of 36 cFET structures arranged in parallel between two large distribution channels with inlets A to D. The trigger channel volume of each cFET incrementally increases from right to left to create a full range of occluding bubble states. Inset shows a close-up illustrating how the trigger channel volume was incrementally increased by lengthening the trigger channels

Fig. 4. The radius of the occluding bubble, as determined by the test device.

a Optical micrographs showing the shape of the occluding bubble for 36 cFETs with trigger channel volumes varying from 5.7 to 40.7 nL (top to bottom, right to left). Occluding bubbles contact the main channel wall, and thus pinch-off fluid flow, at a volume of approximately 26 nL. The shape of these bubbles was used to calculate main channel capillary pressure as function of displaced volume. b Plot of the occluding bubble radius as a function of displaced volume. A circular arc was fitted to each meniscus/bubble shown in a using a gradient descent fitting algorithm. Each point represents the radius of an arc that was fitted to the meniscus shape. Outliers are indicated as red triangles. Inset shows an example of the circular arc fitting (line) against the extracted meniscus shape (X), overlaid onto an image of the meniscus

Fig. 5. The closing time of the cFET as a function of trigger channel depth and water contact angle.

a Contour plot of the closing time. The trigger channel depth was evaluated from 20 to 150 μm and the contact angle from 0° and 60°. For the main channel geometry in this example (200 μm deep) the minimum closing time is approximately 11 milliseconds. b Results of the modeled closing time, compared to the previously reported experimental results

Fig. 6. Photograph showing the total liquid flow through the parallel resistor branches in proportion to the fluid resistance of the cFET devices.

Labels indicate the testing (A, B) and filling (C, D) inlets. In this example the device was filled with blue dye-colored water from inlet C and tested by adding yellow colored water to inlet B (FCTB). The image demonstrates the controllability in the resistance of the cFET devices

Fig. 7. Flow rate–volume (Q–V) relationship for the cFET device.

a Plot of the Q–V relationship for the cFET device, as measured from the test chip. The chip was tested with a hydrostatic pressure applied between diagonally opposite pairs of inlets. This was done to visualize any potential influence of the distribution channels. The results are shown normalized to the mean response to illustrate the effect of the trigger channel volume more clearly. Devices were filled from inlet C and tested via inlet B (FCTB), or filled from D and tested via A (FDTA). b A Shockley equation form fitted to the Q–V response shown in a

Fig. 8. Nonlinear flow mechanics of a cFET under substantial applied pressure.

a Laplace pressure, as derived from the bubble shape, of the source and the drain menisci as a function of applied pressure. Bubble movement modifies the restricted flow path, and therefore creates an overall nonlinear flow response. Inset: Representative image of the cFET when a strong pressure is applied. b Experimentally measured flow resistance of the cFET device under increasing pressure. The curve indicates nonlinear liquid conduction in the cFET due to the movement of the occluding bubble

Fig. 9. Demonstration of the closing and reopening of a cFET device by venting of the void volume.

a Photograph of the capillary logic chip design used for the reopening demonstration. A capillary pump actuates fluid flow through two off-valves/cFETs of which only the second valve is used for the demonstration. This second cFET has four trigger channels with externally accessible inlets. Three of these inlets are closed off with semiconductor dicing tape, providing an airtight seal. b Example of the switching between closed and reopened cFET states. Filled trigger channels 1 and 2 expand a bubble into the main channel (left). After the dicing tape covering channel 3 is punctured the bubble recovers, reopening the cFET (right). c Image sequence showing the bubble expansion and retraction over three transitions. At $t_1$ the cFET is shown in the closed state with only one trigger channel providing the volume. When trigger channel 2 is vented at $t_2>t_1$ the cFET reopens. At $t_3$ the cFET is closed again with the help of trigger channel 2, and reopened at $t_4$by piercing the tape membrane over trigger channel 3. This transition is repeated a third time at $t_5$, closing the cFET again with the help of trigger channel 3, and reopened it at $t_6$ via trigger channel 4. While the main purpose of this experiment was to show that the occluding bubble has a restoring force, and is able to reopen if required, it also illustrates that the volume of the actuating bubble is an adjustable function of the number of trigger channels