Hydrodynamics of Immiscible Binary Fluids with Viscosity Contrast: A multiparticle collision dynamics approach

TL;DR

This paper develops a multiparticle collision dynamics (MPC) simulation method for layered immiscible fluids with different viscosities, accurately capturing flow profiles, shear stresses, and colloidal mobilities near interfaces, with computational efficiency.

Contribution

The paper introduces a novel MPC-based model for simulating immiscible binary fluids with viscosity contrast, validated against continuum hydrodynamics and force multipole calculations.

Findings

Flow profiles match continuum results

Shear stress functions agree with theory

Colloidal mobilities near interfaces are accurately predicted

Abstract

We present a multiparticle collision dynamics (MPC) implementation of layered immiscible fluids $A$ and $B$ of different shear viscosities separated by planar interfaces. The simulated flow profile for imposed steady shear motion and the time-dependent shear stress functions are in excellent agreement with our continuum hydrodynamics results for the composite fluid. The wave-vector dependent transverse velocity auto-correlation functions (TVAF) in the bulk-fluid regions of the layers decay exponentially, and agree with those of single-phase isotropic MPC fluids. In addition, we determine the hydrodynamic mobilities of an embedded colloidal sphere moving steadily parallel or transverse to a fluid-fluid interface, as functions of the distance from the interface. The obtained mobilities are in good agreement with hydrodynamic force multipoles calculations, for a no-slip sphere moving under creeping flow conditions near a clean, ideally flat interface. The proposed MPC fluid-layer model can be straightforwardly implemented, and it is computationally very efficient. Yet, owing to the spatial discretization inherent to the MPC method, the model can not reproduce all hydrodynamic features of an ideally flat interface between immiscible fluids.