Modeling Droplets with Slippery Interfaces

TL;DR

This paper introduces a numerical model for simulating multiphase fluids with interfacial slip, capturing complex behaviors in systems like polymer mixtures and droplet flows, validated against experiments and used to explore slip effects.

Contribution

A novel hybrid Navier-Stokes projection method with Immersed Interface handling for simulating multiphase flows with slip at interfaces in 2D and 3D.

Findings

Model shows excellent agreement with experimental data.

Interfacial slip significantly affects droplet and filament dynamics.

The method enables detailed exploration of slip effects in various flow scenarios.

Abstract

Many multiphase fluid systems, such as those involving immiscible polymers or liquid-liquid systems with surfactants, have shown a breakdown of the no-slip condition at the material interface. This results in systems where the tangential velocity of the inner and outer fluid can differ, with the jump in velocity dependent not only the material properties of the interface but also the stresses applied by the surrounding fluid. In this work a numerical model is presented which is capable of investigating general multiphase fluid systems involving interfacial slip in both two- and three-dimensions. To make the system computationally feasible, a hybrid Navier-Stokes projection method is used, whereby the viscosity, density, and pressure are assumed to be continuous across the interface while the velocity field can experience a jump, which is handled via the Immersed Interface Method. The numerical model is compared to experimental results involving polymer-polymer mixtures and computational results for droplets in extensional flows, showing excellent agreement with both. It is then used to explore the influence of interfacial slip in a number of common multiphase fluid systems, including the shearing of a planar interface, droplet and filament relaxation, and droplets in shear flow, both unbounded and wall-bound.