We present a multiscale method to simulate the flow of two immiscible incompressible fluids in contact with solids. The macro model in our method is based on a level set method with sharp interface treatment. The contact line is tracked explicitly and moves according to a slip velocity that depends on the apparent contact angle of the interface with the solid. The relation between apparent contact angle and slip velocity is determined in a micro model based on the phase field method. The phase field method seeks for an equilibrium slip velocity in a box around the contact point, given a static contact angle at the solid and the apparent contact angle in the far field. The dimensions of the box are chosen in the range of physical diffusion length scales at the contact point. We present numerical results of the multiscale method for capillary-driven flows which demonstrate the convergence of results in the macro model and compare the behavior with other approaches in contact line dynamics.
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