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In this work, the motion of a 2-D drop on a surface with given wettabilitygradient is studied numerically by a hybrid lattice-Boltzmann finite-differencemethod using the multiple-relaxation-time collision model. We incorporate thegeometric wetting boundary condition that allows accurate implementation of acontact angle hysteresis model. The method is first validated through threebenchmark tests, including the layered Poiseuille flow with a viscositycontrast, the motion of a liquid column in a channel with specified wettabilitygradient and the force balance for a static drop attached to a surface withhysteresis subject to a body force. Then, simulations of a drop on a wall withgiven wettability gradient are performed under different conditions. Theeffects of the Reynolds number, the viscosity ratio, the wettability gradient,as well as the contact angle hysteresis on the drop motion are investigated indetail. It is found that the capillary number of the drop in steady state issignificantly affected by the viscosity ratio, the magnitudes of thewettability gradient and the contact angle hysteresis, whereas it only showsvery weak dependence on the Reynolds number.

Numerical Study of Drop Motion on a Surface with Wettability Gradient and Contact Angle Hysteresis