Viscous and Nonlinear Effects in the Oscillations of Drops and Bubbles

Citation

Prosperetti, Andrea (1974) Viscous and Nonlinear Effects in the Oscillations of Drops and Bubbles. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/FRDP-DV27. https://resolver.caltech.edu/CaltechETD:etd-11072006-111631

Abstract

NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. The thesis is divided into three parts. In Part I the nonlinear oscillations of a spherical gas bubble in an incompressible, viscous liquid are investigated analytically by means of an asymptotic method. The effect of surface tension is included, and it is shown that thermal and acoustic damping can be accounted for by the suitable redefinition of one parameter. Approximate analytical solutions for the steady state oscillations are presented for the fundamental mode as well as for the first and second subharmonic and for the first and second harmonic. The transient behaviour is also briefly considered. The first subharmonic is studied in particular detail, and a new explanation of its connection with acoustic cavitation is proposed. The approximate analytical results are compared with some numerical ones and a good agreement is found. In Part II the characteristics of subharmonic and ultraharmonic modes appearing in the forced, steady state oscillations of weakly nonlinear systems are considered from the physical, rather than mathematical, viewpoint. A simple explanation of the differences between the two modes, and in particular of the threshold effect usually exhibited by subharmonic oscillations, is presented. The principal resonance in the case of weak excitation is also briefly considered. Finally, in Part III the problem of two viscous, incompressible fluids separated by a nearly spherical free surface is considered in general terms as an initial value problem to first order in the perturbation of the spherical symmetry. As an example of the applications of the theory, the free oscillations of a viscous drop are studied in some detail. In particular, it is shown that the normal mode analysis of this problem available in the literature does not furnish a solution correct for all times, but only an asymptotic one valid as [...].

Thesis Files