Numerical Investigation of the Effects of High Reynolds and Marangoni Numbers on Thermocapillary Droplet Migration

Abstract

This paper presents the results of the thermocapillary motion of a spherical droplet under Marangoni flow conditions, which takes place in a zero-gravity environment where buoyancy effects become insignificant. In such an environment the droplet moves from the cold region to the warm region due to the variation of surface tension induced by the temperature gradient. This two-phase flow problem is formulated using a 3D CFD model linked with four user-defined functions (UDFs) where the liquid–liquid interface is tracked using the “volume of fluid (VOF)” method and the “geometric reconstruction” scheme. The droplet interface was captured using the “Piece-wise Linear Interface Calculation (PLIC)” approach as a part of the VOF method. A constant temperature gradient was assumed in the stagnant liquid bounded medium. The results obtained cover low, intermediate, and high thermal Marangoni numbers (MaT ≤ 105), which were not covered before in numerical or space onboard experimental results. It was found that the droplet deforms as it elongates in the direction of the temperature gradient. The scaled droplet velocity decreases as the thermal Marangoni number increases for the full range of MaT. In addition, the scaled droplet velocity has been correlated with the thermal Marangoni number of a single droplet migrating in the zero-gravity condition, based on the results of the present work.