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 NavierStokes 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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 June 2006
 arXiv:
 arXiv:math/0606445
 Bibcode:
 2006math......6445A
 Keywords:

 Mathematics  Classical Analysis and ODEs;
 Mathematics  Mathematical Physics;
 Mathematics  Numerical Analysis;
 Mathematical Physics;
 Physics  Fluid Dynamics;
 34A05;
 34A34;
 35Q30
 EPrint:
 From a paper accepted for talk at AITCAIT 2006, 5th International Congress on Tribology, Sept. 2022, 2006, Parma University, Italy