Abstract
The problem of the squeezing of a fluid film with a complex rheology is studied. The fluid is represented by the Phan-Tien and Tanner (PTT) constitutive equation. The goal of the paper is to develop an analytical approach which allows one to describe and quantify this process, which is often present in classical lubrication problems, but particularly in human joints. The present approach can potentially supplement time-consuming and costly purely numerical methods which are also susceptible to misleading artifacts. A parametric study reveals the effect of fluid elasticity compared to viscous effects and some explanation is suggested as to their possible links with joint diseases.
Highlights
The tribological effectiveness of a joint is a major factor in its longevity
The study of squeezing at a constant speed is used to evaluate the load capacity as a function of the Weissenberg number, reflecting the potential importance of the elasticity of a healthy synovial fluid compared to the diseased case of osteoarthritis
Using an analytical approach based on reasonable assumptions concerning the fluid flow, we have highlighted some of the complexities inherent in the nature of such viscoelastic fluids
Summary
The tribological effectiveness of a joint is a major factor in its longevity. There are a wide variety of proposed theories as to the mode of lubrication in human joints. Experimental studies have led researchers to associate the four phases of the gait cycle to regimes of lubrication of the knee joint, Dumbleton [1]. The squeezing effect is dominant in the phase of the cycle, called the “heel strike”, with significant hydrodynamic load carrying. The porosity of the cartilage can boost the squeezing effect, by leaking of the aqueous phase of synovial fluid through the matrix. The effective viscosity is thereby increased and helps maintain a film thickness in the micrometer range [2,3,4]
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