Persistence of Non-Newtonian Squeeze Films in Joints

Abstract

The fluid found between cartilage surfaces in joints is a dilute solution of an unbranched long chain polymer, which causes the synovial fluid to follow the power law model of a shear thinning fluid over a range of 5 orders of magnitude of the shear rate. An analysis was performed to determine the pressure distribution and load-velocity relationships for a squeeze bearing containing a shear thinning fluid, bounded by paraboloid surfaces, and sub­jected to a constant squeeze load.

In the simple case of parallel flat plates the pres­sure distribution was found to be independent of the film thickness, and varied slightly with the flow index; con­striction of the edges of the fluid film caused the pres­sure distribution to flatten out. The squeeze time, de­fined as the time required for a pair of surfaces to be squeezed together at constant load from some initial film thickness to some final film thickness h₂, was found to vary as h ^−(1/n+1)₂ Clearly, the squeeze times increase dramatically for shear-thinning fluids over isoviscous fluids, in thin films. For films with constricted edges, the increase in squeeze time due to the shear thinning behavior is even more pronounced.

These results suggest that the presence of hyaluronic acid in synovial fluid can explain the long times required for the extrusion of the fluid film from between cartilage surfaces. The formation of an edge constriction, which readily occurs with soft bearing surfaces, increases the squeeze times tremendously, indicating that the shear-thinning lubricant and the compliant surface, acting as a non-Newtonian elastohydrodynamic bearing, can explain the persistence of fluid films in synovial joints during high-load portions of the loading history.