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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 marginal regeneration are caused by surface tension gradients along the perimeter of the thin film. These gradients lead to a mechanical instability which involves Marangoni type liquid flow. It is possible to describe the conditions for the onset of marginal regeneration with a critical number of the ratio between the driving force for the Marangoni flow and the friction of film elements that move relative to their surroundings. This ratio is called the Mysels number. A linear stability analysis leads to a scaling relation lambda approximately h(Ca)(-1/3) between the wavelength lambda of the instability and the capillary number Ca (Ca=/etaV(s)/gamma. In experiments with several Marangoni-driven instabilities this scaling relation has been found; it illustrates the general applicability in the understanding of flow phenomena of this type. Copyright 2001 Academic Press.