Effect of the Surface Deformation on Marangoni Instability in Chemical Reaction

Abstract

The problem of the onset of instability driven by surface tension gradients (the Marangoni effect) in an isothermal gas-liquid reaction process is investigated by using a linear theory. Including a deformation of free surface, effects of capillary and gravity waves are considered. These effects are important for the disturbance of small wave-numbers. It is shown that there exist two distinct mechanisms of instability, either with the essential effects of surface deformation or without them. For the former, the critical Marangoni number linearly depends on the ratio of the Weber number to the Crispation number and on the reaction parameter, on the other hand, for the latter, it depends on the reaction parameter and the diffusivity ratio. By considering different conditions at lower surface, two cases are treated in a similar manner and it is examined how these affect on instability.