Mathematical Model of Surface Roughness and Solute Dispersion in Squeeze Film Lubrication

ABSTRACT

A mathematical model of surface roughness and solute dispersion (hyaluronan) in squeeze film lubrication is presented in this paper to replicate the synovial joint lubrication. Surface roughness is represented by a stochastic process defined by non‐zero mean, variance, and skewness. Newtonian viscous fluid is considered as a lubricant. The distribution of solute particles is modelled using a convection–diffusion equation, which takes care of consolidation, trapping, and biochemical reactions of solute particles. The solution for dispersion of solute particles is obtained with the help of the Crank–Nicolson finite difference scheme. Results for load‐carrying capacity and solute concentration are presented graphically, and it is observed that negatively skewed roughness has a significant effect on the solute dispersion and load‐carrying capacity.