Abstract: A semi-implicit phase field method for droplet evolution is proposed. Using the phase field Cahn-Hilliard equation, we are able to track the interface in multiphase flow. The idea of a semi-implicit finite difference scheme is reviewed and employed to solve two nonlinear equations, including the Navier-Stokes and the Cahn-Hilliard equations. The use of a semi-implicit method allows us to have larger time steps compared to explicit schemes. The governing equations are coupled and then solved by a GMRES solver (generalized minimal residual method) using modified Gram-Schmidt orthogonalization. To show the validity of the method, we apply the method to the simulation of a rising droplet, a leaky dielectric drop and the coalescence of drops. The numerical solutions to the phase field model match well with existing solutions over a defined range of variables.
Abstract: The frequency dependence of the phase field
model(PFM) is studied. A simple PFM is proposed, and is tested in a
laminar boundary layer. The Blasius-s laminar boundary layer
solution on a flat plate is used for the flow pattern, and several
frequencies are imposed on the PFM, and the decay times of the
interfaces are obtained. The computations were conducted for three
cases: 1) no-flow, and 2) a half ball on the laminar boundary layer, 3) a
line of mass sources in the laminar boundary layer. The computations
show the decay time becomes shorter as the frequency goes larger, and
also show that it is sensitive to both background disturbances and
surface tension parameters. It is concluded that the proposed simple
PFM can describe the properties of decay process, and could give the
fundamentals for the decay of the interface in turbulent flows.