Droplet shape fluctuations in agitated emulsions—Beyond the dilute limit

•Formalism for dealing with droplet shapes in random velocity fields is developed.•The interaction with the other droplets of the emulsion is taken into account.•The formalism is used to investigate shape of droplets governed by surface tension.•It is shown that the interaction between droplets suppresses deformation mode.•The suppression occurs at low frequencies relative to the deformation–decay rate.

The paper investigates the interaction between dispersed droplets in an emulsion under random stirring of the host fluid. The main interest is to examine the autocorrelation of the shape fluctuations in such randomly stirred host fluids, beyond the dilute limit regime. Keeping expressions to leading order in the density of droplets and in deviation of droplets shapes from spherical, the shape is expanded in spherical harmonic modes and the correlations of these modes are derived. The special case of droplets that are governed by surface tension is investigated in detail. The correlations of the deformations that are obtained for this special case are damped relative to the deformation correlations in the dilute regime. The dependence of the damping on frequency is also discussed.