The effective shear and dilatational viscosity of a particle-laden interface in the dilute limit

TL;DR

This paper theoretically computes the effective shear and dilatational viscosities of dilute particle-laden interfaces, revealing their dependence on contact angle and implications for interface stability and simulations.

Contribution

It introduces a perturbation-based theoretical framework for calculating viscosities considering contact angle deviations from 90°, a novel approach in dilute particle-laden interface analysis.

Findings

Dilational viscosity depends strongly on contact angle.

Dilatational viscosity exceeds shear viscosity for all contact angles.

Theory's applicability to stability analysis and numerical simulations.

Abstract

The effective dilatational and shear viscosities of a particle-laden fluid interface are computed in the dilute limit under the assumption of an asymptotically vanishing viscosity ratio between both fluids. Spherical particles with a given contact angle of the fluid interface at the particle surface are considered. A planar fluid interface and a small Reynolds number are assumed. The theoretical analysis is based on a domain perturbation expansion in the deviation of the contact angle from $90^\circ$ up to the second order. The resulting effective dilatational viscosity shows a stronger dependence on the contact angle than the effective shear viscosity, and its magnitude is larger for all contact angles. As an application of the theory, the stability of a liquid cylinder decorated with particles is considered. The limits of validity of the theory and possible applications in terms of numerical simulations of particle-laden interfaces are discussed.