Effect of surface viscosity on the capillary instability of an annular layer or viscous thread

Abstract

The capillary instability of two annular layers confined between two concentric cylinders is considered under conditions of Stokes flow. The inner cylinder, the outer cylinder or both cylinders may be absent, yielding an interior or exterior annular layer or a thread suspended in an infinite medium. The interface exhibits constant surface tension and develops viscous interfacial tensions due to the interfacial flow driven by the instability. A linear stability analysis for axisymmetric perturbations is carried out confirming the stabilizing effect of the surface viscosity over a broad range of conditions. In the case of a thread suspended in vacuum, the surface viscosity is not able to emulate an external medium viscosity. Numerical solutions of a simplified system of evolution equations for long waves using a particle method suggest that surface viscosity prevents thread break-up after a finite evolution time.