THE ROLE OF SYNOVIAL-FLUID FILTRATION BY CARTILAGE IN LUBRICATION OF SYNOVIAL JOINTS .3. SQUEEZE-FILM LUBRICATION - AXIAL SYMMETRY UNDER LOW LOADING CONDITIONS

A mixture model of synovial fluid filtration and synovial gel formatio n at normal approach of cartilage surfaces in the human synovial joint s loaded by a compressive force has been recently presented in Parts I and II of this paper (Hlavacek, 1993, J. Biomechanics 25, 1145-1150; 1151-1160). In the model synovial fluid is taken as a mixture of two i ncompressible 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 a pproach of axially symmetric cartilage surfaces in the human hip joint obtained in Part II is solved numerically for low loads. A shallow po cket-type configuration of the synovial film is formed shortly after t he load application at time t = 0. For constant loads the fluid film p ressure profile follows very closely that in a dry frictionless contac t. 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 distan ce r and decreases as t(-1/2) with time. The ideal fluid is forced int o cartilage at the central region and out of cartilage at the low-pres sure periphery of the squeezed synovial film. The maximum gel-forming concentration (the 20-fold of the original value) of the hyaluronic ac id-protein macromolecular complex of the synovial fluid is reached at the film centre first, then the gel film starts spreading quickly side ways. Later, the process slows down approaching the value (r) over til de 2(1/2) where (r) over tilde is the radius of a dry frictionless con tact. The final gel-film thickness decreases very slowly with the incr easing r For 0 less than or equal to r<(r) over tilde/2(1/2).