Simulation of Lubricated Squeezing Flow of a Herschel-Bulkley Fluid Under Constant Force

Abstract

Lubricated squeezing flow (LSF) of a Herschel-Bulkley fluid between parallel disks under constant force was theoretically analyzed. An analytical expression for the fluid thickness as a function of time was obtained in terms of a hypergeometric function. The fluid thickness profiles in LSF were simulated for a range of each of the model parameters (n, K, T0). The solution obtained in this study reduces to the corresponding analytical equations previously derived for LSF of Newtonian and power-law fluids. The simulations for Herschel-Bulkley fluid were compared with the response of Newtonian and power-law fluids. The dependence of the limiting fluid thickness (i.e. H(t)/H0 at 180 s) on model parameters is presented.