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 (Hlavá ek, 1993, J. Biomechanics26, 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. Engng102, 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 where is the radius of a dry frictionless contact. The final gel-film thickness decreases very slowly with the increasing r for .