Numerical investigation of bubble-induced Marangoni convection

The liquid motion induced by surface tension variation, termed the thermocapillary or Marangoni effect, and its contribution to boiling heat transfer has long been a very controversial issue. In the past this convection was not the subject of much attention because, under terrestrial conditions, it is superimposed by the strong buoyancy convection, which makes it difficult to obtain quantitative experimental results. The scenario under consideration in this paper may be applicable to the analysis of boiling heat transfer, specifically the bubble waiting period and, possibly, the bubble growth period. To elucidate the influence of Marangoni convection on local heat transfer, this work numerically investigates the presence of a hemispherical bubble of constant radius, R(b)= 1.0 mm, situated on a heated wall immersed in a liquid silicone oil (Pr= 82.5) layer of constant depth H= 5.0 mm. A comprehensive description of the flow driven by surface tension gradients along the liquid-vapor interface required the solution of the nonlinear equations of free-surface hydrodynamics. For this problem, the procedure involved solution of the coupled equations of fluid mechanics and heat transfer using the finite-difference numerical technique. Simulations were carried out under zero-gravity conditions for temperatures of 50, 40, 30, 20, 10, and 1 K, corresponding to Marangoni numbers of 915, 732, 550, 366, 183, and 18.3, respectively. The predicted thermal and flow fields have been used to describe the enhancement of the heat transfer as a result of thermocapillary convection around a stationary bubble maintained on a heated surface. It was found that the heat transfer enhancement, as quantified by both the radius of enhancement and the ratio of Marangoni heat transfer to that of pure molecular diffusion, increases asymptotically with increasing Marangoni number. For the range of Marangoni numbers tested, a 1.18-fold improvement in the heat transfer was predicted within the region of R(b)< or = r< or = 7R(b).