Formulation of synovial fluid-articular surface interface conditions, and asymptotic and numerical analyses of squeeze film lubrication of diarthrodial joints

he objective of this thesis is to formulate proper boundary value problems for the squeeze film mechanism of diathrodial joint lubrication and to obtain some model predictions. The linear KLM biphasic model derived from mixture theory is used for the articular cartilage layer on the surfaces on the bone ends. Boundary conditions for biphasic mixtures are studied in order to formulate a well posed mathematical problem, and are obtained for each of the phases at the interfaces between synovial fluid, cartilage layer and subchondral bone. These interfaces are considered as discontinuity surfaces across which the values of material properties of a biphasic mixture have jumps. These boundary conditions are derived on the basis that mass, momentum and energy must balance across the interface in addition to the imposed kinematic boundary conditions. One kinematic condition is proposed for biphasic mixtures at the interface, which reduces to the well known no-slip condition when the mixtures reduce to a single phase solid or single phase fluid. The Taylor boundary conditions for porous-permeable material is recovered in two cases where a viscous fluid is forced to flow over a porous-permeable biphasic material with relatively low permeability.;With these boundary conditions, boundary value problems are formulated for synovial joint fluid film lubrication using a biphasic model. A canonical squeeze film lubrication problem, where a rigid spherical surface moves vertically towards the cartilage surface, is investigated. Asymptotic and boundary layer analyses are carried out in detail to reduce the complexity of the governing equations, and a numerical algorithm is developed to solve the nonlinear boundary value problem. The deformation of the cartilage and the flows of the synovial and interstitial fluids are obtained to explain joint lubrication mechanism.;Among the important conclusions are: (1) The cartilage deformation facilitates pressure distribution and prevents quick exit of synovial fluid through the joint gap; (2) At the central region, when the joint gap becomes very thin (of the order of...