SMALL-AMPLITUDE PERTURBATIONS OF SHAPE FOR A NEARLY SPHERICAL BUBBLE IN AN INVISCID STRAINING FLOW (STEADY SHAPES AND OSCILLATORY MOTION).

The method of domain perturbations is used to study the problem of a nearly spherical bubble in an inviscid, axisymmetric straining flow. Steady-state shapes and axisymmetric oscillatory motions are considered. The steady-state solutions suggest the existence of a limit point at a critical Weber number, beyond which no solution exists on the steady-state solution branch which includes the spherical equilibrium state in the absence of flow (e. g. the critical value of 1. 73 is estimated from the third-order solution). In addition, the first-order steady-state shape exhibits a maximum radius at theta equals 1/6 pi which clearly indicates the barrel-like shape that was found earlier via numerical finite-deformation theories for higher Weber numbers. The oscillatory motion of a nearly spherical bubble is considered in two different ways, which are described in the paper, along with study results.