The shape of an axisymmetric bubble in uniform motion

We consider in a frame fixed to a bubble translating with steady speedU, the inviscid, axisymmetric, irrotational motion of the liquid past it. If all speeds are normalized byU and lengths by {ie437-1}, whereT is the surface tension of the liquid-bubble interface, it can be shown that the unknown bubble shape and field depend on a single parameter {ie437-2} alone, where the pressures are the ones in the bubble and far away respectively. WhenΓ is very large the bubble is almost spherical in shape while for Γ<- Γ^* ≈ -0.315, bubbles whose exteriors are simply connected do not exist. We solve the non-linear, free boundary problem for the whole range Γ^* < Γ < ∞ by the use of an analytical representation for the bubble shape, a surface singularity method to compute potential flows and a generalized Newton’s method to continue inΓ. Apart from providing explicit representations for bubble shapes and detailed numerical values for the bubble parameters, we show that the classical linearized solution for largeΓ is a very good approximation, surprisingly, to as low values of Γ as 2. We also show that Miksiset al [1] is inaccurate over the whole range and in serious error for large and smallΓ. These have been corrected.