Instability of interfaces in phase-separating binary fluids at a finite Reynolds number

Abstract

We investigate a stability of a lamellar domain in phase-separating binary fluids under an external flow. Using the Navier–Stokes and the Cahn–Hilliard equations, we take into account effects of diffusion and surface tension at an interface. Stability eigenvalues are evaluated for various values of the Péclet number, the spacing between the interfaces, and the Reynolds number. It is found that the lamellar domain becomes unstable at a finite wavenumber before the flow when the Reynolds number increases. The instability of the interface occurs on conditions that the interface is situated near a wall or the Péclet number is large. The instability stems from the interaction between disturbances of the flow and the diffusive interface.