The neutral stability of surface-tension driven cavity flows subject to buoyant forces—II. Oblique disturbances

Abstract

A horizontal free-surface cavity contains a fluid which maintains a steady Couette—Poiseuille return flow circulation in the central region of the zone. This circulation is maintained by a surface-tension gradient along the free surface, set by fixing the endwalls at different temperatures. The zone is subject to various buoyant forces by altering either the gravitational field or the zone depth. The hydrodynamic stability of the zone is considered by superimposing a small perturbation upon the two-dimensional steady basic flow. The three-dimensional oblique-wave instabilities are considered for a variety of fluids. For example, cavities of low Pr (Sn, Si) and high Pr (NaNO3, H2O) materials are studied. For a given material (Pr), the physical properties and gravitational environment dictate the critical temperature gradients, zone depth, and type of the most dangerous disturbance for the steady return flow. Minimum nondamping container geometries may be determined from the oblique-wave critical parameter sets. If the choice of experimental container does not allow for the expression of the most dangerous disturbance, then the critical curves for the longitudinal and transverse wave types (Part I) need to be explored with respect to their critical wavelength, direction, and energy.