The onset of convection occurs when the Rayleigh number reaches some critical value. The velocity with which a bubble will rise as a result of convection is given by the Stokes velocity
convection will be important when the transport time across the bubble is smaller than or equal to the diffusion time to the surface
Define the Rayleigh number as
where is the thermal expansion coefficient, is the kinematic viscosity, and is the thermal diffusivity. It is also equivalent to
where is the Grashof number and is the Prandtl number. The critical Rayleigh
number actually turns out to be much larger than indicated in this simple calculation. In the Bénard
configuration (fixed top surface), for example, convection occurs when
