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Marangoni-buoyant boundary layers. (English) Zbl 0589.76118
Summary: In the framework of the research activities of the dissipative regions that can be originated in boundary driven flows such as thermal Marangoni flows, here we study the boundary layers that may generate when beside the Marangoni effects there is also a buoyant effect due to gravity. In particular we neglect the normal component of the gravity vector, so we do not consider the interface curvature. Looking toward similar solutions, we find the condition for the existence of such solutions, then we integrate the nonlinear system of ODE, transformed in an initial value problem with a shooting technique based upon a quasi-linearization algorithm. Results are given for both cases when gravity is favorable or contrary to the main Marangoni effect.

76R99 Diffusion and convection
76M99 Basic methods in fluid mechanics