A micro mechanics model for cavitation

Our objective in this paper is to model the evolution, convection, growth, collapse and nucleation, of a dilute suspension of a large number of spherical small bubbles dispersed in an incompressible Newtonian liquid continuum. We introduce the time-dependent local number density of bubbles in order to describe the time evolution of the micro bubble suspension. The micro mechanics evolution law-expresses a relationship between an objective time rate of the number density function and the time rate of nucleation of bubbles. The mathematical model is numerically solved using a Bubnov-Galerkin spectral method that seeks the approximation to the solution function using a Chebyshev expansion in the bubble volume growth variable. The proposed model is tested with an application to a uniformly dispersed population of expanding spherical bubbles as a consequence of an imposed reduction of pressure. The corresponding population evolutions have been graphically displayed showing a behaviour that agrees with the expected.