Application of dynamical system scaling to bubble dynamics

Abstract

Dynamical System Scaling (DSS) provides a useful method for analyzing, categorizing and scaling time-dependent processes. A key feature of DSS is the temporal displacement rate, D, which relates the natural process time to the reference clock time. Because of its property of being invariant under a two-parameter affine transformation, it provides an underlying basis for process scaling. Application of DSS to bubble dynamics serves to elucidate the physical significance of the temporal displacement rate and its role in scaling a variety of bubble dynamics processes. In particular, prior studies in bubble dynamics did not recognize the role that bubble interfacial acceleration has on scaling. It is a central feature in the definition of the temporal displacement rate. This paper shows that the temporal displacement rate consists of the sum of the internal dimensionless groups that govern the bubble dynamics. Preserving the temporal displacement rate and boundary conditions for a prototype and a scaled model results in similitude of the time-dependent normalized bubble size, growth rates and interfacial accelerations for different fluid conditions. For vapor bubble growth in a superheated liquid, it is shown that inertial controlled bubble growth occurs when D = 0 and thermally controlled bubble growth occurs when D = 1.