Exact solution to stationary onset of convection due to surface tension variationin a multicomponent fluid layer with interfacial deformation

Abstract

Stationary onset of convection due to surface tension variation in an unboundedmulticomponent fluid layer is considered. Surface deformation is included and general fluxboundary conditions are imposed on the stratifying agencies (temperature/composition) disturbance equations. Exact solutions are obtained to the general N-componentproblem for both finite and infinitesimal wavenumbers. Long wavelength instability may coexistwith a finite wavelength instability for certain sets of parameter values, often referred to asfrontier points. For an impermeable/insulted upper boundary and a permeable/conductive lowerboundary, frontier boundaries are computed in the space of Bond number, Bo, vsCrispation number, Cr, over the range 5×10 −7 ⩽ Bo ⩽ 1. Theloci of frontier points in ( Bo, Cr) space for different values of N,diffusivity ratios, and Marangoni numbers collapsed to a single curve in ( Bo, D̃ Cr) space, where D̃ is aMarangoni number weighted diffusivity ratio.