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



The stability of vertical laminar falling films subjected to interphase mass transfer and 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 and 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.