Slightly deformable Darcy drop in linear flows

Y. N. Young, Yoichiro Mori, Michael J. Miksis

Research output: Contribution to journalArticle

Abstract

A two-phase flow model is developed to study the small deformation of a poroelastic drop under linear flows. Inside the drop a deformable porous network characterized by an elastic modulus is fully immersed in a viscous fluid. When the viscous dissipation of the interior fluid phase is negligible (compared to the friction between the fluid and the skeleton), the two-phase flow is reduced to a poroelastic Darcy flow with a deformable porous network. At the interface between the poroelastic drop and the exterior viscous Stokes flow, a set of boundary conditions are derived by the free-energy-dissipation principle. Both interfacial slip and permeability are taken into account and the permeating flow induces dissipation that depends on the elastic stress of the interior solid. Assuming that the porous network has a large elastic modulus, a small-deformation analysis is conducted. A steady equilibrium is computed for two linear applied flows: a uniaxial extensional flow and a planar shear flow. By exploring the interfacial slip, permeability, and network elasticity, various flow patterns about these slightly deformed poroelastic drops are found at equilibrium. The linear dynamics of the small-amplitude deviation of the poroelastic drop from the spherical shape is governed by a nonlinear eigenvalue problem, and the eigenvalues are determined.

Original languageEnglish (US)
Article number063601
JournalPhysical Review Fluids
Volume4
Issue number6
DOIs
StatePublished - Jun 5 2019

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