The role of synovial fluid filtration by cartilage in lubrication of synovial joints--III. Squeeze-film lubrication: axial symmetry under low loading conditions.

A mixture model of synovial fluid filtration and synovial gel formation at normal approach of cartilage surfaces in the human synovial joints loaded by a compressive force has been recently presented in Parts I and II of this paper (Hlavácek, 1993, J. Biomechanics 26, 1145-1150; 1151-1160). In the model synovial fluid is taken as a mixture of two incompressible fluids (ideal and Newtonian viscous), while the biphasic model of Mow et al. (1980, J. Biomech. Engng 102, 73-84) is used for cartilage. A system of partial differential equations for the normal approach of axially symmetric cartilage surfaces in the human hip joint obtained in Part II is solved numerically for low loads. A shallow pocket-type configuration of the synovial film is formed shortly after the load application at time t = 0. For constant loads the fluid film pressure profile follows very closely that in a dry frictionless contact. To this approximation and with the exception of a close vicinity of the squeeze-film edge the flux of the ideal fluid across the synovial fluid-cartilage interface varies quadratically with the radial distance r and decreases as t-1/2 with time. The ideal fluid is forced into cartilage at the central region and out of cartilage at the low-pressure periphery of the squeezed synovial film. The maximum gel-forming concentration (the 20-fold of the original value) of the hyaluronic acid-protein macromolecular complex of the synovial fluid is reached at the film centre first, then the gel film starts spreading quickly sideways. Later, the process slows down approaching the value r/2 1/2 where r is the radius of a dry frictionless contact. The final gel-film thickness decreases very slowly with the increasing r for 0 < or = r < r/2 1/2.