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research-article

Deformation of Microchannels Embedded in an Elastic Medium

[+] Author and Article Information
VIvek Ramachandran

Integrated Soft Materials Lab, Carnegie Mellon University, Pittsburgh,Pennsylvania 15213
vivek.ramachandran@epfl.ch

Carmel Majidi

Integrated Soft Materials Lab, Carnegie Mellon University, Pittsburgh,Pennsylvania 15213
cmajidi@andrew.cmu.edu

1Corresponding author.

ASME doi:10.1115/1.4040477 History: Received April 29, 2018; Revised May 30, 2018

Abstract

The deformation of microfluidic channels in a soft elastic medium has a central role in the operation of lab-on-a-chip devices, fluidic soft robots, liquid metal electronics, and other emerging soft-matter technologies. Understanding the influence of mechanical load on changes in channel cross-section is essential for designing systems that either avoid channel collapse or exploit such collapse to control fluid flow and connectivity. In this manuscript, we examine the deformation of microchannel cross sections under far-field compressive stress and derive a ``gauge factor'' that relates externally applied pressure with change in cross-sectional area. We treat the surrounding elastomer as a Hookean solid and use 2D plane strain elasticity, which has previously been shown to predict microchannel deformations that are in good agreement with experimental measurements. Numerical solutions to the governing Lam\'e (Navier) equations are found to match both the analytic solutions obtained from a complex stress function and closed-form algebraic approximations based on linear superposition. The application of this theory to soft microfluidics is demonstrated for several representative channel geometries.

Copyright (c) 2018 by ASME
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