Direct numerical simulation of thermocapillary flow based on the Volume of Fluid method

Abstract

A numerical method for direct simulation of thermal Marangoni effects at dynamically deformable interface of two-phase incompressible fluids is developed. The approach is based on the Volume of Fluid (VOF) method with special focus on the numerical treatment of the temperature surface gradient because of its decisive role as the driving force of the flow. The surface gradient calculation is split into computing its length and direction in order to satisfy the correct thermal boundary condition at the interface without losing mobility of the interface. The method is applied to three different types of thermocapillary flow, namely thermocapillary migration of a droplet in an ambient fluid with linear temperature gradient, thermocapillary convection in a liquid layer under linear temperature gradient along the interface, and Marangoni convection due to Bénard–Marangoni instability. In the first case, different aspects of the dynamics of the migration are considered for validation such as the terminal migration velocity, the initial acceleration and quantification of the wall effects. The simulation also considers high convective heat transfer and covers a wide range of Marangoni numbers up to 5000, where good agreement with both theoretical and experimental results is achieved. In the second case, the convection velocity in the liquid layer is compared with an analytical result. In the final application, pattern formation due to the Bénard–Marangoni instability in a liquid layer in square geometry of small aspect ratio is investigated for realistic Biot number and dynamically deformable fluid interface. The results show good agreement with experiments from literature, where our numerical simulation also predicts cell pattern for a particular aspect ratio which is outside the limitation of the above cited experimental work.