A Dynamic Model for Thermocapillary Migration of Liquid Bridges in Confined Gaps

Abstract

Thermocapillary migration of confined liquid bridges is important for passive liquid transport in microfluidic, lubrication, and energy systems. Here, we develop a two-dimensional reduced-order dynamic model for liquid-bridge migration in narrow gaps with geometric confinement. The model couples thermocapillary driving force, geometry-induced capillary driving force, contact-angle hysteresis, and viscous dissipation and is assessed against published silicone-oil experiments involving thermocapillary migration between parallel plates and geometry-driven migration in nonparallel channels. The comparisons show that the model captures the main migration trends under both thermal and geometric driving. The analysis clarifies how thermocapillary driving, viscous resistance, contact-line hysteresis, and channel tapering jointly regulate the transient and quasi-steady migration dynamics. We further propose phase diagrams and derive an analytical depinning criterion to identify the conditions for pinning, forward migration, and reverse migration, revealing how thermal gradients and geometric confinement compete or cooperate to determine the migration mode. These results provide a theoretical basis for passive control of confined liquid transport under spatially nonuniform thermal and geometric conditions.