Hydrodynamic stability of marangoni films:II. A Preliminary analysis of the effect of interphase mass transfer

Abstract

The stability of vertical laminar falling films sobjected to interphase mass transfer ond surface-tension gradients in the direction of flow is investigated by linear perturbation analysis. The perturbations considered are vertical waves or rivulets as described by Ludviksson and Lightfoot for nonisothermal films. Perturbations of this type are thought to lead to the maldistribution of flow observed in distillation and gas absorption by Zuiderweg and Harmens and by Francis and Berg.Three unstable regions are predicted, one corresponding closely to that found by Ludviksson and Lightfoot, and two new ones, previously unreported, resulting from interphase mass transfer across the free surface.These predictions confirm the conclusions of Zuiderweg ond Harmens for situations in which surface tension increases upward, and they provide a means of estimating the range of unstable gradients. Experimental evidence for instability predicted when the surface tension increases downward is inconclusive, Further investigation of this region, which is of considerable importance, is recommended.

Interfacial Hydrodynamics: An Over View

“…Earlier in 1971, Wang et ai. [74] where f3 is the thermal expansivity and v is the kinematic viscosity. The Rayleigh number is a ratio of buoyancy forces (due to temperature-induced density variation) to viscous forces and arose first in Rayleigh's original stability analysis [71 J of the buoyancy-only problem of a horizontal fluid layer heated from below.…”