Flow and deformation characteristics of a flexible microfluidic channel with axial gradients in wall elasticity

Axial gradients in wall elasticity may have significant implications in the deformation and flow characteristics of a narrow fluidic conduit, bearing far-reaching consequences in physiology and bio-engineering. Here, we present a theoretical and experimental framework for fluid-structure interactions in microfluidic channels with axial gradients in wall elasticity, in an effort to arrive at a potential conceptual foundation for in vitro study of mirovascular physiology. Towards this, we bring out the static deformation and steady flow characteristics of a circular microchannel made of polydimethylsiloxane (PDMS) bulk, considering imposed gradients in the substrate elasticity. In particular, we study two kinds of elasticity variations - a uniformly soft (or hard) channel with a central strip that is hard (or soft), and, increasing elasticity along the length of the channel. The former kind yields a centrally constricted (or expanded) deformed profile in response to the flow. The latter kind leads to increasingly bulged channel radius from inlet to outlet in response to flow. We also formulate an analytical model capturing the essential physics of the underlying elastohydrodynamic interactions. The theoretical predictions match favourably with the experimental observations and are also in line with reported results on stenosis in mice. The present framework, thus, holds the potential for acting as a fundamental design basis towards developing in vitro models for micro-circulation, capable of capturing exclusive artefacts of healthy and diseased conditions.