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- W1566324008 abstract "In order to provide some theoretical background and to motivate the more refined theory introduced herein, some encouraging known theoretical results on bubble-ring cavitation inception are reviewed. This review is followed by the development of the theory of bubble-ring cavitation cutoff. Its outcome, when compared with experiment, shows the need for a more refined inception theory. The above comparison and the basic ideas behind the cutoff theory's formulation suggest a possible approach for a refinement based on a multiple scales expansion. This seems reasonable because the forcing function pulse in laboratory time f, varies slowly compared with the characteristic bubble time,, which characterizes the response time of a typical microscopic cavitation nucleus. The ratio of these two times gives a small parameter, , appearing in the forcing function, with the result that this problem involves only a soft excitation. Expanding the forced Rayleigh-Plesset equation and its initial conditions to the second order in c, the zeroth-order problem is found to be the well-known autonomous nonlinear equation with nonhomogeneous initial conditions, giving free oscillations of a typical nucleus. The first-order system is a nonautonomous linear system with homogeneous initial conditions which governs the forced bubble growth. The second-order system consists of a linear autonomous differential equation and homogeneous initial conditions. It is needed to establish integrability conditions for the first-order solution. The first-order solution is left for future research and the zeroth-order problem is analyzed in the phase plane. Then a novel approximate integration, = t(u), is given in terms of elliptic integrals and functions. It was not possible to invert this solution and so the inverse u = u() is found numerically. These data are then used to find an analytical approximation for use in future first-order calculations." @default.
- W1566324008 created "2016-06-24" @default.
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- W1566324008 date "1988-09-01" @default.
- W1566324008 modified "2023-09-28" @default.
- W1566324008 title "Bubble Dynamics and Cavitation Inception Theory" @default.
- W1566324008 doi "https://doi.org/10.5957/jsr.1988.32.3.155" @default.
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