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].