Effect of stretching on interfacial stability

The effect of stretching on the stability of a horizontal interface between two fluids with different viscosities and densities is discussed. A local elongational flow acts to reduce the amplitude of perturbations and increase the wavelength of periodic waves, and thereby alter the instantaneous growth rate of disturbances. Linear stability analysis for Stokes flow reveals that, in the case of a horizontal interface between two semi-infinite fluids subjected to orthogonal stagnation-point flow, interfacial stretching is not able to suppress the Rayleigh-Taylor instability of unstably stratified fluids. In contrast, stretching is able to suppress the growth of periodic waves on the surface of a flat film resting on a horizontal surface. Numerical simulations based on the boundary-integral method for Stokes flow confirm that localized perturbations on the film surface are suppressed when the elongational flow is sufficiently strong.