Shape Fluctuations in Randomly Stirred Dilute Emulsions

TL;DR

This study analyzes how droplets in dilute emulsions fluctuate in shape when subjected to random stirring, accounting for interactions between droplets and deriving their shape correlation functions.

Contribution

It extends the analysis of shape fluctuations in emulsions beyond the dilute limit by including interactions and shape deviations in a systematic way.

Findings

Derived autocorrelation functions for droplet shape fluctuations.

Explicitly formulated interactions between deformable objects.

Analyzed shape fluctuations governed by surface tension.

Abstract

In this paper we consider the effects of the interaction between droplets or other deformable objects in an emulsion under random stirring of the host fluid. Our main interest is to obtain autocorrelation functions of the shape fluctuations in such randomly stirred host fluids, beyond the dilute limit regime. Thus, a system of deformable objects immersed in a host liquid that is randomly stirred is considered, where the objects interact with each other via the host liquid. Keeping expressions in the first order in the density of objects and in deviation of objects shapes from spherical, the shape of each object is expanded in spherical harmonic modes and the correlations of these modes are derived. The special case of objects that are governed by surface tension is investigated. The interaction between objects is explicitly formulated and the deformation correlations are obtained.