Similarity simulation for Marangoni convection around a vapor bubble during nucleation and growth

Marangoni convection occurs around vapor bubbles during nucleation and growth due to the temperature variation along the surface. The surface tension variation resulting from the temperature gradient along the surface causes Marangoni convection. Marangoni convection is of importance in crystal growth melts and may influence other processes with liquid–vapor interfaces, in addition to boiling. The influence of Marangoni induced convection is more obvious under microgravity but also occurs in earth gravity. This paper presents a similarity solution for Marangoni induced flow both for the velocity profile and the temperature profile, assuming developing boundary-layer flow along a surface with various imposed temperature profiles. The surface velocity, the total flow rate and the heat transfer characteristics are given for various temperature profiles and various Prandtl numbers. Since the predicted boundary layer thickness would be much less than the diameter of vapor bubbles during nucleate boiling, the bubble surface curvature effects can be neglected and this analysis can be used as a first estimate of the effect of Marangoni flow around a vapor bubble.