An analysis of the squeeze-film lubrication mechanism for articular cartilage

An asymptotic analysis of a lubrication problem is presented for a model of articular cartilage and synovial fluid under the squeeze-film condition. This model is based upon the following constitutive assumptions: (1) articular cartilage is a linear porous-permeable biphasic material filled with a linearly viscous fluid (i.e. Newtonian fluid); (2) synovial fluid is also a linearly viscous fluid. The geometry of the problem is defined by assuming that (1) cartilage is a uniform layer of thickness H; (2) synovial fluid is a very thin layer compared to H; (3) the radius R of the load-supporting area (or the effective radius of curvature of joint surface, Ri) is large compared to H. Squeeze-film action is generated in the lubricant by a step loading function applied onto the two bearing surfaces. The model assumptions and the material properties yield two small parameters in the mathematical formulation. Based on these two small parameters, two coupled nonlinear partial differential equations were derived from an asymptotic analysis of the problem: one for the lubricant (analogous to the Reynolds equation) and one for the cartilage. For known properties of normal cartilage, our calculations show: (1) the cartilage layer deforms to enlarge the load-supporting area; (2) cartilage deformation acts to reduce the lateral fluid speed in the lubricant, thus prolonging the squeeze-film time which ranges from 1 to 10 s; (3) lubricant fluid in the gap is forced from the central high-pressure region into cartilage, and expelled from the tissue at the low-pressure periphery of the load-bearing region; and (4) tensile hoop stress exists at the cartilage surface despite the compressive squeeze-film loading condition. This hoop stress results directly from the radial flow of the interstitial fluid in the cartilage layer.