Planar liquid sheets surrounded by another immiscible liquid at low capillary Reynolds numbers

Abstract

This paper investigates the stability of planar liquid sheets surrounded by another immiscible liquid. A relation between the temporal growth rate and the wavenumber is derived using the classical stability theory. In the limit of dominant viscous stresses, the dispersion relation yields negative values for the growth rate of instability across the entire range of wavenumbers. The low capillary Reynolds number regime, or equivalently the large Ohnesorge-number limit, shows that such planar liquids in liquid systems are stable regardless of the viscosity mismatch between the two liquids for both sinuous and varicose perturbations.