Derivation of Modified Reynolds Equation: A Porous Media Model With Effects of Electrokinetics

Abstract

A lubrication theory that includes the effects of electrokinetics and surface microstructure is developed. A porous layer attached to the impermeable substrate is used to model the microstructure on a bearing surface. The Brinkman-extended Darcy equations and Stokes equations are modified by considering the electrical body force and utilized to model the flow in porous media and fluid film, respectively. The stress jump boundary conditions on the porous media/fluid film interface and the effects of viscous shear and electric double layer (EDL) are also considered when deriving the modified Reynolds equation. Under the usual assumptions of lubrication and Debye–Hückel approximation for low surface potential, the velocity distributions, the apparent viscosity, and the modified Reynolds equation are then derived. The apparent viscosity is expressed explicitly as functions of the Debye length, the electroviscosity, the charge density, the stress jump parameter, and the porous parameters (permeability, porosity, and porous film thickness). The considerations of EDL near the interface and the charge density of the flow in the porous media increase the apparent viscosity. The existence of porous film also increases the apparent viscosity as well. Both effects are important for flow within microspacing and lubrication problems. The apparent viscosity and the performance of 1D slider bearings are analyzed and discussed. The results show that the apparent viscosity and the load capacity increase as the permeability decreases, the stress jump parameter decreases, the charge density increases, the inverse Debye length decreases, or the porosity decreases.