Squeeze Film Lubrication between Rough Poroelastic Rectangular Plates with Micropolar Fluid: A Special Reference to the Study of Synovial Joint Lubrication
The effects of surface roughness and poroelasticity on the micropolar squeeze film behavior between rectangular plates in general and that of synovial joints in particular are presented in this paper. The modified Reynolds equation, which incorporates the randomized surface roughness structure as well as elastic nature of articular cartilage with micropolar fluid as lubricant, is derived. The load-carrying capacity and time of approach as functions of film thickness during normal articulation of joints are obtained by using Christensen stochastic theory for rough surfaces with the assumption that the roughness asperity heights are to be small compared to the film thickness. It is observed that the effect of surface roughness has considerable effects on lubrication mechanism of synovial joints. 1. Introduction The study of mechanism of synovial joints has recently become an active area of scientific research. The human joint is a dynamically loaded bearing which employs articular cartilage as the bearing and synovial fluid as the lubricant. Once a fluid film is generated, squeeze film action is capable of providing considerable protection to the cartilage surface. The loaded bearing synovial joints of the human body are the shoulder, hip, knee, and ankle joints; such joints have a lower friction coefficient and negligible wear. Synovial fluid is a clear viscous fluid, a dialysate of plasma containing mucopolysaccharides. Synovial fluid usually exhibits a non-Newtonian shear thinning behavior. However, under high shear rates, the viscosity of synovial fluid approaches a constant value not much higher than that of water [1]. Therefore a Newtonian lubricant model has often been used for synovial fluid in lubrication modeling [2]. In this study the synovial fluid is modeled as non-Newtonian micropolar fluid. Articular cartilage is poroelastic or biphasic consisting of both fluid and solid phases. The importance of the unique biphasic load-carrying characteristics of articular cartilage and fluid flow inside has been recognized in the lubrication of synovial joints such as weeping and boosted lubrication theories. A more general biphasic lubrication theory was subsequently proposed by Mow and Lai [3]. However, it was not until in the 1990s that the relation between friction and interstitial fluid pressurization was comprehensively studied [4–7]. A number of friction studies have been carried out under a wide range of tribological conditions to investigate the biphasic lubrication of articular cartilage. Under both start-up and reciprocating motions of a
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