Thermocapillary Droplet Flow in Small-scale Containers: the Effect of Gravity

Abstract

We numerically investigate the motion of a Fluorinert FC-75 droplet suspended in silicone oil in a cylindrical container under a vertical temperature difference. The top and bottom walls are maintained at 343 and 283 K, the sidewall is adiabatic, and the droplet is initially placed at mid-height. Ansys Fluent with the Volume of Fluid method is used to solve the coupled momentum and energy equations. Container heights from 2.5 to 60 mm are examined, with droplet diameter scaled with container size, under zero gravity, normal gravity, and combined thermocapillary-buoyancy forcing. In zero gravity, the droplet migrates toward the hot upper wall, but its mean migration speed decreases as container height increases because the axial temperature gradient weakens and confinement distorts the isotherms. Under normal gravity, the denser FC-75 droplet settles toward the cold wall. Under combined forcing, containers with heights of 3 mm or less exhibit near cancellation between buoyancy and thermocapillary, whereas for heights of 15 mm or more the motion approaches the gravity dominated limit. At a fixed height of 2.75 mm, varying droplet diameter reverses the net drift. This transition is captured by a Marangoni-buoyancy balance criterion, which predicts a critical diameter of about 0.203 mm for quasi-equilibrium. Three-dimensional simulations show deformation only in the buoyancy dominated regime. These results identify confined configurations that approximate microgravity behavior and provide a practical criterion for droplet positioning and transport.