Understanding the spreading and retraction dynamics of droplet impact on a moving hydrophobic surface

In this work, the impact of droplets on a moving hydrophobic surface is numerically investigated at moderate Reynolds and Weber numbers. Compared with impact on a stationary substrate, the surface velocity U_w is expected to significantly influence droplet spreading and retraction. To quantitatively assess the effect of U_w, the volume-of-fluid (VOF) method is employed, following validation against experimental data. Through numerical simulations, we identify several regimes governing spreading and retraction within present parameter space, analyze the results using scaling laws, and quantitatively evaluate the influence of the dimensionless wall velocity U_w^∗ on impact dynamics. The results show that the maximum wetted area on a moving surface during spreading follows two simple scaling laws, separated by an effective impact number P_w=P1+Uw∗2^3/5. During the initial stage of retraction, a nearly constant retraction rate is observed. Two simplified theoretical models are proposed, which show good agreement with numerical results, with the regimes distinguished by an effective Ohnesorge number Oh_w=Oh1+U_w^∗.