Question

Fluid motion induced by surface tension variation is called the Marangoni effect.

Fluid motion induced by surface tension variation is called the Marangoni effect Consider a liquid layer of thickness h on a solid flat plate. The liquid is exposed to ambient air but the surface tension σ is not constant. It varies longitudinally (in the x direction) due to a temperature gradient, which induces the liquid to move along the interface I. Write the governing equations for the liquid layer with u-uly) 2. Derive the boundary condition at the liquid surface. Consider an element dx on the interface, and indicate the three forces acting on this surface. (Hint: shear stress exerted by the liquid, shear stress exerted by the ambient air, and the surface tension on each side of the element). Ignore the minor effect of the shear stress exerted by the air, and write the force balance equation for the surface element to obtain the boundary condition at dy dx 3. Obtain the solution for u(y) 4. The dependence of the surface tension on the temperature T is given by the equation where T(x) is a linear temperature distribution, σ is the surface tension at temperature To and γ is a constant. Find the temperature distribution if T=To at x=0, and T. at x=L. 5. Rewrite the velocity profile in terms of the temperature gradient and determine the induced flowrate

Answer 1

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