On a differential equation for a gas bubbles collapse mathematical model
Abstract
In this paper we present a mathematical model for estimate the collapse time of a gas bubble in a vane of a oil gerotor pump. This amount of time cannot be greater of the total time spent by the pump for filling and then emptying out a vane in a single revolution, otherwise there is a loss of lubrication between internal and external gears. We assume that oil is incompressible and viscous, the bubble has a spherical shape and it is not translating into the external fluid. The analytical treatment of the model shows that the Navier-Stokes equations for the velocity field of the oil can be reduced to a single non linear ordinary differential equation for the variation in time of the bubble radius. The collapse time estimated by a numerical resolution of this equation and the collapse time calculated from an analytical resolution of the linearized equation are substantially equal.
Cite
@article{arxiv.math/0606445,
title = {On a differential equation for a gas bubbles collapse mathematical model},
author = {Gianluca Argentini},
journal= {arXiv preprint arXiv:math/0606445},
year = {2007}
}
Comments
From a paper accepted for talk at AITC-AIT 2006, 5th International Congress on Tribology, Sept. 20-22, 2006, Parma University, Italy