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Viscous-elastic dynamics of power-law fluids within an elastic cylinder

Evgeniy Boyko, Moran Bercovici*, and Amir D. Gat†

  • Faculty of Mechanical Engineering, Technion–Israel Institute of Technology, Haifa, Israel

  • *mberco@technion.ac.il
  • †amirgat@technion.ac.il
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Phys. Rev. Fluids 2, 073301 – Published 12 July, 2017

DOI: https://doi.org/10.1103/PhysRevFluids.2.073301

Abstract

In a wide range of applications, microfluidic channels are implemented in soft substrates. In such configurations, where fluidic inertia and compressibility are negligible, the propagation of fluids in channels is governed by a balance between fluid viscosity and elasticity of the surrounding solid. The viscous-elastic interactions between elastic substrates and non-Newtonian fluids are particularly of interest due to the dependence of viscosity on the state of the system. In this work, we study the fluid-structure interaction dynamics between an incompressible non-Newtonian fluid and a slender linearly elastic cylinder under the creeping flow regime. Considering power-law fluids and applying the thin shell approximation for the elastic cylinder, we obtain a nonhomogeneous p-Laplacian equation governing the viscous-elastic dynamics. We present exact solutions for the pressure and deformation fields for various initial and boundary conditions for both shear-thinning and shear-thickening fluids. We show that in contrast to Stokes' problem where a compactly supported front is obtained for shear-thickening fluids, here the role of viscosity is inversed and such fronts are obtained for shear-thinning fluids. Furthermore, we demonstrate that for the case of a step in inlet pressure, the propagation rate of the front has a tnn+1 dependence on time (t), suggesting the ability to indirectly measure the power-law index (n) of shear-thinning liquids through measurements of elastic deformation.

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Phys. Rev. Fluids 2, 073301– Published 12 July, 2017
  • Received 23 March 2017

©2017 American Physical Society

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