Non-linear microfluidic devices

Construction of fluidic set-ups analogous to electronic circuits was quite an active area in 60th and early 70th. Rather advanced devices, such as fluidic diodes, oscillators, flip-flops, amplifiers and logic gates were build and integrated to even more sophisticated systems. All those devices relied on non-linear phenomena in flows at high Reynolds numbers, Re, and in particular on highly inertial fluidic jets, which could be deflected or made turbulent. This inherent dependence on inertial effects at high Re puts a basic limitation on size of those fluidic circuits. When the size is reduced, achieving sufficiently high Reynolds numbers requires increasingly high driving pressures and becomes impractical at some sub-millimeter scale. Thus, unlike semiconductor electronics, the fluidic diodes, flip-flops and logic gates could not be miniaturized, that restricted their applications.
We have managed to build a set of micro-scale non-linear fluidic devices: a non-linear resistor, a rectifier and a flip-flop memory, which can operate at arbitrarily low Reynolds number. These devices do not have any moving mechanical parts, and their operation becomes possible due to non-linear mechanical properties of the viscoelastic working fluid, which is a dilute aqueous solution of a high molecular weight polymer. Strength of the elastic effects depends on the Weissenberg number, Wi, which is a product of a characteristic rate of deformation in the flow and the polymer relaxation time. Since, the non-linear elastic effects are essentially independent on Re, they are not reduced, when the set-up is miniaturized.
One of the most profound non-linear elastic effects in flows of polymers solutions is dramatic growth of flow resistance in extensional flows. Extensional flow occurs, when there is a contraction in a channel. The fluid elements get extended along the flow direction, when they are entering the contraction. When the rate of extension becomes comparable with the inverse polymer relaxation time, at Wi of about unity, the polymer molecules get unraveled in the flow and the resistance can sharply increase. That is exactly the case for the non-linear resistor, that we have built, which is a curvilinear channel with regularly spaced contractions. Building microfluidic devices with soft lithography and rapid prototyping gave us a unique opportunity to try about 50 different versions of the non-linear resistor and to optimize its performance. The non-linear growth of the resistance above Wi = 1 in our device is unprecedented in either macroscopic, high Re, fluidics or high Wi polymer fluid dynamics. When the driving pressure is doubled, the flux through the channel increases by only 7%. So, the non-linear resistor can also be considered as the first microfluidic control device stabilizing the flux.
A fluidic rectifier is an analogue of a diode. It is a channel with different resistances for flows in opposite directions (see Images). A macroscopic fluidic rectifier was patented in 1920 by Nikola Tesla. The microscopic rectifier that we have constructed is a chain of triangular segments building a straight channel with variable width. The rectifying effect of the channel with a polymer solution is quite strong. In a broad range of fluxes the difference of required driving pressures for opposite directions can be a factor of more that two.
The fluidic flip-flop is a switchable bistable system with memory. The memory is due to the elastic longitudinal stresses, which develop in a flow of the polymer solution through the contraction. It resembles the phenomenon the "open siphon" well known in polymer fluid dynamics, when a stream of a stretched elastic liquid proves to be very stable to perturbations, and keeps flowing along the same stream lines. Switching between two states of a flip-flop can be done quite reliably at a time scale of 30 ms, which can be reduced using a polymer with a shorter relaxation time. The two metastable states can differ either by flux (current), by up to a factor of 2.5, or local pressure (voltage), by up to 0.3 psi. Such a significant pressure difference can allow actuation of some other functional element, cascading the devices and building complex integrated microfluidic circuits.
The polymer solutions we used were water based and had low viscosities (about 2-3 cPs) and relaxation times (about 10 ms). It is only due to the microfluidic flow environment, that the elastic properties of the polymer solutions are revealed. So, the same microfluidic devices can be used to measure short relaxation times of the aqueous polymer solutions. We are also trying to investigate polymer solution flows at mesa-scales, when the width of the channel is comparable with the size of the polymer molecules and the distances between them.

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