Approximate Solution for a Nonisothermal Gas Bubble Growth over a Spherical Heating Element

Recent experimental evidence has shown that single bubble generation on miniature heating elements is a competitive alternative to massive bulk bubble generation for the study of gas/vapor bubble growth dynamics. The inherent two-dimensionality of the problem leads to significant deviations of the bubble growth with respect to the bulk bubble growth which can be approximated by the classical one-dimensional (spherically symmetric) theory. In the present work, an approximate theory is developed, valid for a certain region of the problem parameters, which permits computation of the bubble radius evolution curves. On the basis of these results, the effect of the two-dimensionality (axial symmetry) of the problem on the bubble growth characteristics is assessed. The approximate solution developed here is of particular interest, since the complete solution using computational fluid dynamics (CFD) techniques is not practically feasible at this moment because of the large number of size and time scales involved in the problem.