Coupled thermophoretic and thermocapillary effects on the motion of a particle near an immiscible fluid interface

Thermophoretic transport near fluid interfaces governs a wide array of natural and technological processes, yet a unified theoretical framework that simultaneously captures particle-surface slip phenomena and interfacial thermocapillarity has remained absent from the literature. This study bridges that critical gap by developing a semi-analytical framework, solved via the boundary collocation method, to investigate the motion of a spherical particle in a viscous fluid near an immiscible fluid–fluid interface. The model’s novelty lies in its comprehensive integration of thermal creep, mechanical slip, and thermal stress slip at the particle surface with the transformative influence of thermocapillary (Marangoni) flow. Following rigorous validation against established rigid-wall limits, our analysis reveals physical phenomena that fundamentally diverge from classical predictions for solid boundaries. Most notably, strong interfacial thermocapillary flow is shown to counteract the expected hydrodynamic retardation of an insulating particle, even inverting its motion into a regime of net acceleration. Furthermore, our results challenge the traditional view of mechanical slip as a simple drag-reducer, uncovering a non-monotonic dual role where slip initially weakens the thermophoretic drive before its drag-reducing effect becomes dominant. We also demonstrate for the first time that the impact of thermal stress slip can reverse from enhancing to hindering at higher Knudsen numbers, a complex behavior contingent upon the thermal properties of the secondary fluid. These findings establish a more complete physical picture of thermophoresis in multiphase systems, providing a powerful predictive toolset with direct implications for designing advanced thermal precipitators, engineering “smart fluids” with tunable transport properties, and fabricating novel composite materials through the controlled deposition of particles at interfaces.