The Role of Synovial Fluid Filtration by Cartilage in Lubrication of Synovial Joints--IV. Squeeze-film Lubrication: the Central Film Thickness for Normal and Inflammatory Synovial Fluids for Axial Symmetry Under High Loading Conditions

The axially symmetric problem of synovial film filtration and synovial gel formation at normal approach of cartilage surfaces in the human hip joint loaded by a compressive force has been solved numerically in Part III of this paper [Hlavácek and Novák, J. Biomechanics 28, 1193-1198 (1995)] for the Newtonian viscous phase of the biphasic synovial fluid and for low loads only. Because of a high non-linearity of the problem the method used there breaks down for higher loads. On anticipating that for a high step loading the fluid pressure in the central part of the squeezed synovial film is close to the pressure in a dry frictionless contact, the synovial film filtration at the film centre is governed by two ordinary differential equations that are easy to solve. The central gel film thickness thus obtained, i.e. the film thickness at the moment, when the filtered fluid turns into a stable gel is about 1 micron for the normal synovial fluid (with a non-Newtonian viscous phase of the synovial fluid) and changes very little if the geometric, material and loading parameters of the problem vary within the physiological range. The inflammatory case (with a more or less Newtonian viscous phase) yields values by one order lower at least. The results of stress analysis in the cartilage for this mixture model suggest the reason for vertical cracking at the free cartilage surface and horizontal splitting at the tide mark observed in osteoarthritic joints.