Numerical simulation of dynamic wetting in ternary fluids flows on curved substrates

Abstract

To simulate dynamic wetting in ternary fluids flows on curved substrates. We improve the diffuse interface immersed boundary (DIIB) method in Liu and Ding (2015) by proposing a four-component diffuse interface model and a ternary fluids moving contact line (MCL) model. Firstly, the improved DIIB method can simulate the ternary fluids flows on curved substrates and maintain the mass conservation of each phase. Then, the ternary fluids MCL model can allow the motion of MCLs and ensure the wetting conditions at the same time, although multiple MCLs among the substrates and fluid phases exist. We validate the accuracy of our method by comparing the theoretical and numerical shapes of two separate droplets and a compound drop on cylinders at equilibrium. Good agreements are achieved and the numerical results converge with mesh refinement. To show the flexibility and robustness of this method, we also perform two interesting applications: the impact of a compound droplet onto a sphere and oil recovery in porous media.