We develop a general methodology for the inclusion of variable surfacetension into a Volume-of-Fluid based Navier-Stokes solver. This new numericalmodel provides a robust and accurate method for computing the surface gradientsdirectly by finding the tangent directions on the interface using heightfunctions. The implementation is applicable to both temperature andconcentration dependent surface tension, along with the setups involving alarge jump in the temperature between the fluid and its surrounding, as well asthe situations where the concentration should be strictly confined to the fluiddomain, such as the mixing of fluids with different surface tensioncoefficients. We demonstrate the applicability of our method to thermocapillarymigration of bubbles and coalescence of drops characterized by differentsurface tension.
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