Spontaneous droplet movement has gained increased interest in many applications, including microfluidics and microfabrication. This study focuses on the numerical investigation of driving mechanisms of spontaneous droplet motion. The numerical model using the phase-field method was validated by available experimental data. In this study, a heterogeneous wettability condition is implemented to reproduce contact angle hysteresis for the accurate prediction of spontaneous droplet dynamics. Through analysing the capillary pressure within the droplet, the driving mechanism is identified as being governed by the pressure difference between the two interfaces which depends on channel configuration, wettability, and contact angle hysteresis. The impact of channel deformability was further studied, revealing that channel deformability leads to significant changes in velocity or even reversed droplet movement direction. This study provides a novel numerical framework for controllable spontaneous droplet movement in flexible channels.

Understanding multiphase flow in porous media is essential for diverse engineering applications, from large-scale carbon geosequestration to small-scale fuel cells. Pore-doublet models, despite their geometrical simplicity, offer a powerful framework to study the complex interplay between capillary and viscous forces during multiphase flow. This work revisits some recent advances in the understanding of immiscible fluid displacement processes provided by pore-doublet studies, and highlights their ability to capture key interfacial phenomena such as Haines jumps and to map displacement regimes through phase diagrams. While these models do not capture the full heterogeneity of real porous systems, they often exhibit strong agreement with larger-scale observations. Recent advances in microfluidics fabrication techniques further enhance the capability and efficiency of using pore-doublet models to investigate immiscible displacement processes. Several promising research directions for extending pore-doublet approaches are identified.