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

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