Surface Tension Driven Instability in a Horizontal Liquid Layer with a Deformable Free Surface. II. Overstability

Abstract

The theory described in the first paper of this series [M. Takashima: J. Phys. Soc. Jpn. 50 (1981) 2745] is extended to include the possibility that surface tension driven instability in a horizontal thin liquid layer confined between a solid wall and a deformable free surface can set in as purely oscillatory motions. Linear stability theory is applied to derive a time-dependent eigenvalue relationship. Numerical computations are carried, and it is found that whichever side of the liquid layer is a free surface oscillatory modes of instability can occur when and only when the temperature of the solid wall is lower than that of the air phase.