G Bubble Dynamics in a Quiescent Fluid

We conclude this chapter with an important one dimensional flow problem, namely the motion induced by changes in the volume of a single bubble that is suspended in an incompressible fluid that is at rest at infinity. If the bubble is spherical, as is usually assumed, the motion of the fluid is strictly radial, that is, ur / 0. ih, = u,p = 0 hence the flow is ID but not unidirectional. 

In this section, we consider these problems in some detail, although with the major simplifications of assuming that the processes are isothermal and that the liquid is incompressible. As we shall see, the governing equations for even this simplified ID problem are nonlinear, and thus most features can be exposed only by either numerical or asymptotic techniques. In fact, the problem of single-bubble motion in a time-dependent pressure field turns out to be not only practically important, but also an ideal vehicle for illustrating a number of different asymptotic techniques, as well as introducing some concepts of stability theory. It is for this reason that the problem appears in this chapter. 

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