Dynamic interactions between deformable drops in the Hele–Shaw geometry

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: Caf = (μv/σ)(Ro/ho)3/2 as revealed by an analytic perturbation solution of the governing equations for a system with continuous phase viscosity μ, interfacial tension σ, drop radius Ro, characteristic relative velocity v and separation ho 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.