Numerical investigation of surface-tension-driven convection in a liquid droplet (on the effects of Marangoni number and Prandtl number)

摘要

A method is developed to analyze the three-dimensional transient Marangoni convection in a liquid droplet that is heated from a concentric warm rigid sphere set in the center and cooled uniformly from its surroundings. As the field is unstable and is very sensitive to the temperature gradients along the surface, it is required for the numerical scheme to be highly accurate and be free from the effects of the polar singularties. For the purpose, a spherical harmonic spectral method was developed to analyze the flow and temperature fields in the droplet on the spherical coordinates. In this study, effects of Ma and Pr on the convection are investigated. It is found that the convection develops faster as Ma or Pr is larger.