Hydrodynamic instability of a thin viscous film between two drops

Abstract

Linear stability analysis is employed to derive analytical expressions for the growth rate of disturbances applied to a thin plane-parallel film trapped between two drops. From these expressions, the band of unstable wavenumbers and the “most dangerous” wavenumber are identified for systems in the absence and presence of insoluble surfactant. Marangoni effects are shown to exert a stabilizing influence and reasonably good agreement with experimental observations is found. Subsequent nonlinear analysis indicated amplification of the disturbance growth rate beyond that suggested by linear theory as the film proceeded toward rupture.