Fluid transfer within a stagnant liquid presents a significant challenge in zero-gravity conditions due to the lack of buoyancy effects. This challenge can be overcome by the utilisation of the Marangoni effect, or more specifically thermocapillary migration. The thermocapillary migration of droplets is driven by temperature gradients within the multiphase system which bring about a surface tension gradient driving the flow from the cold to the hot region. The migration speed of the droplet is significantly impacted by the heat transfer both inside the droplet and in its surroundings. This paper presents the analysis of drop movement in a stagnant liquid using computational fluid dynamics (CFD). The commercial software package Ansys-Fluent v.13  is used to solve the governing continuum conservation equations for two-phase flow using the Volume of Fluid (VOF) method to track the liquid/liquid interface in 2D domain. This approach has been shown to be a valuable tool for studying the phenomena of liquid-liquid interaction. A strong agreement has been found with experimental observations conducted in microgravity. The inherent velocity of drops has been found to decrease with increasing Marangoni number. This finding is in line with the previous space experiments of Xie et al. (2005)  and in contrast to the numerical results of Ma (1999)  using the same liquid for the droplet and the host liquid. Data obtained in the present numerical study has been used to derive an expression predicting the scaled droplet velocity as a function of Marangoni number. A numerical study of the interaction of two spherical droplets undergoing thermocapillary migration in microgravity is also presented. The temperature thrust from the leading droplet towards the trailing droplet was found to disturb its migration velocity, but the trailing droplet was found to have no influence on the migration of the leading droplet.