Energy decaying phase-field model for fluid-particle interaction in two-phase flow

In this paper, we study a phase-field model for the dynamics of a solid particle in two-phase ow. The governing system in our model is a coupled system of Navier{Stokes equations, Cahn{Hillard equations for the multiphase ow, and Newton's law for the motion of the particle. The effect of the wettability of the particle and the motion of the contact line are modeled by the generalized Navier boundary condition. To show that our model is physically consistent, we show that the model can be derived from the principle of minimum energy dissipation (entropy production) and has the energy decaying property. Using the method of matched asymptotic expansions, we also derive the sharp interface limit for our model.