Profiling a soft solid layer to passively control the conduit shape in a compliant microchannel during flow

TL;DR

This paper introduces a passive method to control microchannel shapes during flow by tuning a soft solid layer's properties, enabling pre-determined geometries without fabrication or active actuation, validated through theoretical modeling and patterning techniques.

Contribution

It develops a nonlinear differential equation model for soft coating deformation to passively achieve desired microchannel shapes during flow, expanding microfluidic control strategies.

Findings

Successfully tuned four microchannel geometries using the model.

Passive shape control is feasible without active actuation.

Slip length patterning has limited effect on shape control.

Abstract

The shape of a microchannel during flow through it is instrumental to understanding the physics that govern various phenomena ranging from rheological measurements of fluids to separation of particles and cells. Two commonly used approaches for obtaining a desired channel shape (for a given application) are (i) fabricating the microchannel in the requisite shape and (ii) actuating the microchannel walls during flow to obtain the requisite shape. However, these approaches are not always viable. We propose an alternative, passive approach to {\it a priori} tune the elastohydrodynamics in a microsystem, towards achieving a pre-determined (but not pre-fabricated) flow geometry when the microchannel is subjected to flow. That is to say, we use the interaction between a soft solid layer, the viscous flow beneath it and the shaped rigid wall above it, to tune the fluid domain's shape. Specifically, we study a parallel-wall microchannel whose top wall is a slender soft coating of arbitrary thickness attached to a rigid platform. We derive a nonlinear differential equation for the soft coating's fluid--solid interface, which we use to infer how to achieve specific conduit shapes during flow. Using this theory, we demonstrate the tuning of four categories of microchannel geometries, which establishes, via a proof-of-concept, the viability of our modeling framework. We also explore slip length patterning on the rigid bottom wall of the microchannel, a common technique in microfluidics, as an addition `handle' for microchannel shape control. However, we show that this effect is much weaker in practice.