Collapse of Spherical Cavities in Viscoelastic Fluids

An analysis is given of the collapse of a spherical cavity in a large body of an incompressible viscoelastic liquid. Proceeding from a linear rheological model for the liquid, one obtains a nonlinear integro-differential equation for the motion of the cavity. Analytical solutions are derived for certain limiting values of the parameters governing collapse, and some numerical solutions are presented for various other values. As one of the more interesting results of this work, it is found that elasticity in the liquid can significantly retard the collapse of a void and produce prolonged, oscillatory motion whenever the relaxation time of the fluid is moderately large in comparison to the Rayleigh collapse time. This is in sharp contrast to the catastrophic collapse which will aways occur for voids in purely viscous liquids. Both numerical and approximate analytical solutions are presented to demonstrate the damping effect of liquid viscosity on the cavity motion.