Simulation of droplet dynamics in an inclined channel considering contact angle hysteresis using the cascade lattice Boltzmann method

Modeling droplet dynamics on solid surfaces with rough or chemically heterogeneous walls is crucial in various industrial applications. In such cases, the downstream and upstream contact lines of the droplet usually move incongruously, leading to droplet deformation known as the contact angle hysteresis (CAH) phenomenon. In this work, we developed a cascaded multicomponent Shan-Chen lattice Boltzmann method to simulate droplet dynamics considering the CAH. Specifically, the Peng-Robinson equation of state is added to one component to improve the density ratio of the model. By modifying the fluid-fluid interaction force scheme, we achieve thermodynamic consistency and independent adjustment of the surface tension. We also implement the modeling of CAH by applying geometric wetting boundaries with a hysteresis window. Based on this model, we first simulated pinned droplets in inclined channels with different hysteresis windows. We obtain the critical tilt angle of the droplet at the onset of sliding, which agrees with the theoretical result. For sliding droplets in the inclined channel, our results reveal that a slight tilt angle is unfavorable for the upstream portion of the droplet sliding, while a large tilt angle is favorable for the entire droplet sliding. A small receding angle results in a large droplet deformation at the quasi-steady state. Finally, by periodically transitioning between different hysteresis windows, enabling exclusive sliding of the upstream contact line during the first half period and subsequent sliding of the downstream contact line during the second half period, we successfully observed the stick-slip phenomenon of the droplet.