Color-gradient lattice Boltzmann model for simulating droplet motion with contact-angle hysteresis

摘要

Lattice Boltzmann method (LBM) is an effective tool for simulating the contact-line motion due to the naturenof its microscopic dynamics. In contact-line motion, contact-angle hysteresis is an inherent phenomenon, but itnis neglected in most existing color-gradient based LBMs. In this paper, a color-gradient based multiphase LBMnis developed to simulate the contact-line motion, particularly with the hysteresis of contact angle involved. Innthis model, the perturbation operator based on the continuum surface force concept is introduced to model theninterfacial tension, and the recoloring operator proposed by Latva-Kokko and Rothman is used to produce phasensegregation and resolve the lattice pinning problem. At the solid surface, the color-conserving wetting boundaryncondition [Hollis et al., IMA J. Appl. Math. 76, 726 (2011)] is applied to improve the accuracy of simulationsnand suppress spurious currents at the contact line. In particular, we present a numerical algorithm to allow for theneffect of the contact-angle hysteresis, in which an iterative procedure is used to determine the dynamic contactnangle. Numerical simulations are conducted to verify the developed model, including the droplet partial wettingnprocess and droplet dynamical behavior in a simple shear flow. The obtained results are compared with theoreticalnsolutions and experimental data, indicating that the model is able to predict the equilibrium droplet shape as wellnas the dynamic process of partial wetting and thus permits accurate prediction of contact-line motion with thenconsideration of contact-angle hysteresis.