Investigation of Multiphase Flows near Micro-textured Walls using Lattice Boltzmann Method

摘要

During the last decade, interest in multiphase flows near textured surface has revived due to its importance in microfluidics and the study of the self-cleaning property of some biological surfaces (often called “Lotus Effect”). Here we investigate the three dimensional multiphase flows near solid walls with textures, e.g., array of small pillars, using the free energy based lattice Boltzmann method (LBM). The model uses two sets of distribution functions along some fixed directions which evolve every discrete time step. It incorporates the physics of surface tension and wetting on a solid wall using a prescribed free energy functional which effects are reflected through the equilibrium distribution functions and the collision step of LBM. Through the Chapman-Enskog multiscale expansion, the Navier-Stokes equations including the surface tension effect and the Cahn-Hilliard equation for the order parameter can be obtained at the long wavelength and long time limits. In dealing with the wetting boundary conditions, the method proposed in [2] is adopted. Drop behaviors near a single pillar and multiple pillars as shown in Fig. 1 have been studied. It is found that the model can simulate the static equilibrium and dynamic evolution of drops to a reasonably satisfactory level. It is noted that similar work has been performed [1] using the single component model for which only one set of distribution function is used. However it is limited to very small density ratio. In the present simulations, with the newly improved model [3], the density ratio can be much larger and represents practical fluids.