Effect of non-Newtonian lubrication on the separation of a sphere from a flat

A numerical analysis is presented to study the effect of lubrication with non-Newtonian fluid on the separation flow of a fully flooded sphere from a flat under the condition of constant applied load. Different non-Newtonian fluid models were utilized to account for the microstructure and rheology of additives suspended in the film lubricant, namely those models for couple stress, micropolar, and power-law fluids. The equation of motion of the sphere was used to examine the effect of the sphere inertia on accelerating the separation process as the film viscous force decreases. This required solving the film pressure field, which is derived from a modified Reynolds equation and later computed numerically by a forth-order Runge–Kutta integration scheme. Several parameters were examined such as the time to complete separation, the length scale of the additives, the variation in lubricant's viscosity due to the presence of the additives, the sphere mass and radius, and the applied force on the sphere. Compared to the Newtonian fluid case, the results of the numerical solution indicated that there is a delay on the separation time for large non-Newtonian parameters, i.e., parameters representing additives characteristic length, additives concentration, and power-law indices.