Numerical simulations of two-phase electroosmotic shearing with viscoelastic fluids

Abstract

This work investigates the numerical modeling and two-dimensional simulation of electroosmotic two-phase flows involving complex fluids in rectangular channels with no pressure difference. We apply mainly the non-linear Poisson-Boltzmann (PB) model for charge distribution coupled to the Navier-Stokes equations, constitutive equations for viscoelastic fluids, and the interface transport by Volume-of-Fluid with Piecewise-Linear Interface Construction. The numerical framework is implemented in the HiG-Flow system, which simulates incompressible flows in hierarchical cartesian meshes of arbitrary refinement represented by generalized trees with interpolations by a robust meshless moving least squares method. In two-phase systems, we analyze droplet deformation under both neutral and electroosmotic shear, exploring the impact of permittivity variations between matrix and droplet fluids. Our results suggest that the Korteweg-Helmholtz force may play a crucial role in interface deformation patterns, while viscoelasticity demonstrates itself capable of moderating surface tension effects and stabilizing deformations in uniform and non-uniform permittivity cases.