Analytical prediction for the steady-state behavior of a confined drop with interface viscosity under shear flow

TL;DR

This paper develops a comprehensive analytical model to predict the steady-state deformation and inclination of a drop under shear flow, accounting for confinement and interface viscosity effects, applicable across diverse physical conditions.

Contribution

It merges existing models for confined and unconfined drops with and without interface viscosity to create a unified analytical prediction framework.

Findings

Predicts steady-state deformation and inclination angle across various conditions.

Robust against changes in viscosity ratio.

Applicable to both confined and unconfined drops with interface viscosity.

Abstract

The steady-state behavior of a single drop under shear flow has been extensively investigated in the limit of small deformation and negligible inertia effects. In this work, we combine the calculations proposed by Flumerfelt [R. W. Flumerfelt, J. Colloid Interface Sci. 76, 330 (1980)] for unconfined drops with interface viscosity, with those by Shapira & Haber [M. Shapira and S. Haber, Int. J. Multiph. Flow. 16, 305 (1990)] for confined drops without interface viscosity. By merging these two approaches, we provide comprehensive analytical predictions for steady-state drop deformation and inclination angle across a wide range of physical conditions, from confined to unconfined droplets, including or excluding the effect of interface viscosity. The proposed analytical predictions are also robust concerning variations in the viscosity ratio, making our model general enough to include any of the above conditions.