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Quasistatic evolution of sessile drops and contact angle hysteresis. (English) Zbl 1276.76016
Authors’ abstract: “We consider the classical model of capillarity coupled with a rate-independent dissipation mechanism due to frictional forces acting on the contact line, and prove the existence of solutions with prescribed initial configurations for the corresponding quasistatic evolution. We also discuss in detail some explicit solutions to show that the model does account for contact angle hysteresis, and to compare its predictions with experimental observations.”
The model is based on a Young formula, see formula (2.5) and on related formulas, see formulas (2.19). Concerning these formulas the following papers are of interest [R. Finn, Phys. Fluids 22, No. 1, Paper No. 017103, 10 p. (2010; Zbl 1183.76202); R. Finn, J. McCuan and H. C. Wente, J. Math. Fluid Mech. 14, No. 3, 445–453 (2012; Zbl 1306.76011)].

MSC:
76B45 Capillarity (surface tension) for incompressible inviscid fluids
76T99 Multiphase and multicomponent flows
49K20 Optimality conditions for problems involving partial differential equations
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