Numerical investigation of thermocapillary flow around a bubble

The thermocapillary how induced by agas bubble in a Newtonian liquid layer subjected to a stable temperature stratification is investigated. This how is analyzed for a special configuration when the surface tension and buoyan t forces oppose one another. The driving mechanism is the surface tension g radient related to the Marangoni number whereas the stabilizing effects are the viscous and buoyant forces related to the Prandtl and the Rayleigh num bers. In a previous work, this flow has been investigated experimentally fo r a few combinations of these three parameters. In order to make a mon syst ematic study of the influence of these parameters, numerical simulations ar e used as a decisive tool. Indeed, it allows the contribution of the differ ent mechanisms to be evaluated. To validate the finite element model, devel oped for this purpose, the numerical results are first compared to experime ntal ones. Then, the influence of these three dimensionless parameters on t he how pattern and the magnitude of the flow is analyzed. This sensitivity study is supplemented by a convergence study. It appears that the Rayleigh number modifies the how pattern but has little influence on the strength of the primary vortex induced by the bubble. On the other hand, the Marangoni and Prandtl numbers induce Little change in the flow pattern but they resp ectively enhance and reduce the strength of the primary vortex. This system atic analysis leads us to propose an empirical relationship for the strengt h of the flow. (C) 1999 American Institute of Physics. [S1070-6631(99)00901 -0].