An Extended Phase-Field Lattice-Boltzmann Model for Multiphase Flows with Contact Angle Hysteresis on a Curved Boundary

The interpolation algorithms on curved solid boundaries easily result in numerical instability under some extreme contact angle conditions due to root operation. In this article, we developed an extended phase-field lattice-Boltzmann (LB) model specifically for solving the contact angle hysteresis problems on curved solid boundaries. Based on the phase-field LB model, a new improved unidirectional interpolation algorithm for wetting conditions is proposed. The new improved unidirectional interpolation does not need to distinguish whether the interpolation is performed in the <i>x</i> or <i>y</i> direction by the magnitude of the slope of the normal vector. An alternative solution is provided as a candidate that enhances the numerical stability of the interpolation algorithm. Furthermore, its corresponding contact angle hysteresis scheme is extended and incorporated into the phase-field LB model, so an extended phase-field LB model is built. We test the extended phase-field LB model by three benchmark cases, and the extended phase-field LB model may accurately capture the two-phase interface and three-phase contact angle regardless of whether or not there is hysteresis. The extended phase-field LB model is applied to investigate the droplet slipping process on the cylindrical surface with hysteresis. Four slip modes of droplet contact points under different hysteresis windows are identified. We explore the droplet slipping characteristics with hysteresis under the conditions with different surface tension, shear rate, capillary number, and viscosity ratio.