Coupled thermal and interfacial effects on the motion of a compound droplet near a planar surface

Abstract

In this study, we present a semi-analytical investigation of the thermocapillary motion of a concentric compound droplet suspended in an unbounded immiscible fluid near a hydrophobic planar wall. The droplet consists of an inner core encapsulated by an outer liquid shell, with both interfaces assumed spherical under low capillary number conditions. The compound droplet and its core translate along the axis normal to the wall with distinct migration velocities. The analysis is performed in the creeping-flow regime and accounts for coupled thermal and hydrodynamic interactions among the inner and outer interfaces and the nearby wall. Imposed temperature gradients generate Marangoni stresses at both interfaces, driving thermocapillary motion. This motion is strongly influenced by wall-induced distortion of the temperature and velocity fields. Semi-analytical solutions of the Stokes and energy equations are obtained using a collocation technique. These solutions yield accurate and well-converged migration velocities over a wide range of droplet–wall separations. The results demonstrate that the wall significantly modifies the magnitude of thermocapillary migration. This modification occurs through enhanced viscous dissipation and asymmetric interfacial stresses. The coupled effects of thermal conductivity ratios, viscosity contrasts, interfacial tension gradients, and geometric confinement are systematically elucidated. This work extends existing theories by incorporating multi-interface coupling and wall effects within a unified semi-analytical framework. It is directly relevant to the controlled manipulation of encapsulated droplets in microfluidics, targeted drug delivery, microscale thermal management, and cell-mimicking transport near solid boundaries.