A Model of Lubrication Filtration

Despite its obvious economic importance, the filtration process has seldom, if ever, been scientifically studied from the perspective of tribology. It is not well known among tribologists that a theory of filtration has been developed over some 50 years and is currently used with success in environmental engineering for the filtration of water and aerosols. This approach forms the basis for the present work. The filter porous medium is modeled as an array of spherical “collectors.” Forces and moments are balanced on a contaminant particle suspended in the fluid flowing through the array. Solution of the resulting equations yields the particle trajectories. Filtration capture efficiency is then the fraction of particles entering the filter which ultimately collide with a collector. For tribology applications, forces and moments on a particle are due to viscous fluid friction and van-der-Waals effects, the latter providing the final adhesive capture forces. Efficiency is predicted as a function of filter depth, porosity, and grain size; fluid viscosity; and particle size. Results agree qualitatively with the known behavior of filters. As opposed to existing empirical models, the effect of variable changes can be predicted, and the proposed model does not depend on a particular particle size distribution.