Transient behavior of the thermocapillary migration of drops under the influence of deformation

TL;DR

This study investigates the transient thermocapillary migration of deformable drops using numerical methods, revealing how deformation influences drop velocity under temperature variations.

Contribution

It introduces a local capillary number to quantify temperature effects on interfacial tension and analyzes deformation impacts on drop velocity during migration.

Findings

Drop deformation increases as interfacial tension decreases.

Drop velocity decreases when density is lower than the surrounding fluid.

Drop velocity increases when density is higher than the surrounding fluid.

Abstract

The transient thermocapillary migration of drops with nontrivial deformation is studied. The finite difference method is employed to solve the incompressible Navier-Stokes equations coupled with the energy equation; the front-tracking method is adopted to track the moving deformable drop interface. In the hot region, deformations of drops increase with the decrease of interfacial tensions. In order to indicate the temperature impact on the interfacial tension, a local capillary number ($Ca_l$) is introduced. It is found that, when the drop density is smaller/larger than that of the bulk fluid, the drop velocity decreases/increases with the increase of the drop deformation.