Stability of an elastico-viscous liquid film flowing down an inclined plane

Abstract

AbstractAn analysis is made of the stability of a layer of an elastico-viscous liquid flowing down an inclined plane in the presence of two-dimensional disturbances. The modified Orr-Sommerfeld equation is solved by a regular perturbation technique for disturbances of large wavelengths. It is shown that in the absence of surface tension, the layer is more unstable as compared with that for an ordinary viscous liquid if Q1 > Q2, Q1 and Q2 being stress relaxation and strain retardation parameters respectively.