Dynamic interactions between deformable drops in the Hele-Shaw geometry

TL;DR

This paper presents a model for the collision and coalescence of deformable drops in a Hele-Shaw cell, highlighting the role of hydrodynamics and interfacial deformation through a film capillary number, with implications for measuring interaction forces.

Contribution

The study introduces an analytic and numerical model linking hydrodynamic effects and interfacial deformations in deformable drop interactions within Hele-Shaw geometry.

Findings

The model emphasizes the importance of dynamic interaction history for stability and coalescence.

The film capillary number characterizes the interplay between viscous and interfacial forces.

The geometry allows inference of time-dependent forces from drop separation measurements.

Abstract

A model has been developed to describe the collision and possible coalescence of two driven deformable drops in the Hele-Shaw cell. The interdependence between hydrodynamic effects and interfacial deformations is characterised by a film capillary number: Ca_f = (\mu v/\sigma)(R_o/h_o)^(3/2) as revealed by an analytic perturbation solution of the governing equations for a system with continuous phase viscosity \mu, interfacial tension \sigma, drop radius R_o, characteristic relative velocity v and separation h_o between the drops. Numerical solutions of the model demonstrate the importance of the full dynamic history of the interacting drops in determining stability or coalescence. The geometry of the Hele-Shaw cell allows for the possibility of using the model to infer the time dependent force between colliding drops by measuring their separation.