Effective surface dilatational viscosity of highly concentrated particle-laden interfaces

TL;DR

This paper derives the effective surface dilatational viscosity of a particle-laden interface at high concentration, focusing on hexagonal particle arrangements and viscous dissipation in narrow gaps.

Contribution

It introduces a new analytical approach to calculate surface viscosity considering high particle concentration and specific geometric arrangements.

Findings

Effective viscosity increases with particle concentration.

Viscous dissipation is dominated by narrow gaps between particles.

Hexagonal packing assumption simplifies the viscosity calculation.

Abstract

The effective surface dilatational viscosity is calculated of a flat interface separating two immiscible fluids laden with half-immersed monodisperse rigid spherical non-Brownian particles in the limit of high particle concentration. The derivation is based upon the facts that (i) highly-concentrated particle arrays in a plane form hexagonal structure, and (ii) the dominant contribution to the viscous dissipation rate arises in the thin gaps between neighboring particles.