Abstract
The lattice Boltzmann method based on the Diffuse-Interface Model for the simulation of the flow of multiphase fluids is extended to allow the fluid components to have different viscosities. A convective Cahn-Hilliard equation for capturing interface is resolved by an additional lattice Boltzmann equation. To allow the different phases to have different viscosities, the relaxation time depends only on the sign of the order parameter. Numerical surface tension obtained from the Laplace's law agrees very well with the respective analytical solution for any viscosity ratio. The velocity profiles of the LBM show good agreement with those of the analytical solutions for the Poiseuille flow and Couette flow in channels filled with different phase viscosities without pseudo velocity on the interface. In the simulation of evolution of a single finger in a Hele-Shaw cell, the finger widths and terminal velocities show good agreements with the results of the previous studies.
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