Deformed Gas Bubble

Let us consider diffusion to a bubble rising in a fluid at high Reynolds numbers. The shape of the bubble substantially depends on the Weber number 

At small We, the shape of the bubble is nearly spherical at large We, the bubble becomes a spherical segment this is partly due to flow separation in the rear area. 

The Weber numbers We of the order of 1 constitute a practically important intermediate region in which the bubble is strongly deformed but still preserves its symmetry with respect to the midsection. For such We, the shape of the bubble is well approximated by an oblate ellipsoid of rotation with semiaxes a and b = xa, where the semiaxis b is perpendicular to the flow and x - 1  

Since the boundary condition for the normal stresses must be satisfied at the front and rear stagnation points as well as along the boundary of the midsection of the bubble, we have the following relationship between the Weber number We and the ratio x of the major to the minor semiaxis of the ellipsoid [291]  

Numerical estimates [291] show that the maximum difference between the actual curvature and the corresponding value for the approximating ellipsoid does not exceed 5% for We 1 (x 1.5) and 10% for We 1.4 (x 2). 

---