The viscous squeeze-film behaviour of shear-thinning fluids (Q1101274)

A finite element technique is proposed to predict the purely viscous squeeze-film behaviour of an arbitrary shear-thinning fluid confined between parallel discs and subjected to a constant load. The technique requires establishment of the distribution of viscosity in the gap. The variable viscosity is modelled by a discrete number of Newtonian fluids, with each fluid lying in a region bounded by lines of constant shear rate. Each of these Newtonian regions is further divided into regions which appear as ``finite element'' rectangles in the r-z plane. The equations governing squeeze-film flow are applied to this finite element network and an ordinary differential equation is ultimately derived which governs the gap decrease with time. Solving this equation is not simple because the coefficients of two terms change as the gap decreases. When the number of Newtonian fluids is sufficient, the technique predicts the squeeze-film time of a power-law fluid to within a fraction of a percent. Application of the technique to synovial fluid in the human ankle joint reveals that under a normal standing load, fluid viscosity prevents the cartilage surfaces from touching for only a fraction of a second.