Marangoni flow driven instabilities and marginal regeneration

Fingering instabilities in films moving along wetted surfaces, dimpling in horizontal liquid films, and the drainage of vertical soap films by margina l regeneration are caused by surface tension gradients along the perimeter of the thin film. These gradients lead to a mechanical instability which in volves Marangoni type liquid flow. It is possible to describe the condition s for the onset of marginal regeneration with a critical number of the rati o between the driving force for the Marangoni flow and the friction of film elements that move relative to their surroundings. This ratio is called th e Mysels number. A linear stability analysis leads to a scaling relation la mbda approximate to h (Ca)(-1/3) between the wavelength h of the instabilit y and the capillary number Ca (Ca = etaV(s)/gamma). In experiments with sev eral Marangoni-driven instabilities this scaling relation has been found; i t illustrates the general applicability in the understanding of flow phenom ena of this type. (C) 2001 Academic Press.