Numerical simulations of emulsions in shear flows

TL;DR

This paper develops a modified volume of fluid method for simulating emulsions in shear flows, analyzing their rheology and effective viscosity behavior in a plane Couette flow with detailed stress contributions.

Contribution

It introduces a new computational approach combining volume of fluid with fractional step and Poisson solvers, applied to emulsion rheology in shear flows.

Findings

Effective viscosity decreases with deformation and shear, showing shear-thinning.

Viscosity exhibits a non-monotonic relation with volume fraction, with a maximum observed.

Flow behavior shifts from shear to rotational dominance as volume fraction increases.

Abstract

We present a modification of a recently developed volume of fluid method for multiphase problems, so that it can be used in conjunction with a fractional step-method and fast Poisson solver, and validate it with standard benchmark problems. We then consider emulsions of two-fluid systems and study their rheology in a plane Couette flow in the limit of vanishing inertia. We examine the dependency of the effective viscosity on the volume-fraction (from 10% to 30%) and the Capillary number (from 0.1 to 0.4) for the case of density and viscosity ratio 1. We show that the effective viscosity decreases with the deformation and the applied shear (shear-thinning) while exhibits a non-monotonic behavior with respect to the volume fraction. We report the appearance of a maximum in the effective viscosity curve and compare the results with those of suspensions of rigid and deformable particles and capsules. We show that the flow in the solvent is mostly a shear flow, while it is mostly rotational in the suspended phase; moreover this behavior tends to reverse as the volume fraction increases. Finally, we evaluate the contributions to the total shear stress of the viscous stresses in the two fluids and of the interfacial force between them.