Growth criterion for small dry spots in the falling liquid films

Abstract

In thin films of liquid falling over an inclined surface random (or non-random) small dry spots shut and disappear or expand into the large-scale dry spots depending on the initial spot sizes and parameters of the liquid film. On consideration of the gravity forces, inertial forces of the film and surface tension, affecting the elements of a roller surrounding the dry spot, we have formulated a criterion, which helped us to answer the following question: if this spot shuts or not? This criterion includes the numbers of Bond and Reynolds and the contact wetting angle as the determining parameters. It is generalization of the known Hartley — Murgatroid criterion, which allows determination of the zone of falling film metastability, i. e., determination of the critical film thickness, below whose value the formation of stable dry spots is possible. It is shown that the critical values of parameters of the initial dry spot depend on the shape and sizes of a roller surrounding this spot.