Fluid flow characteristics within an oscillating lower spherical surface and a stationary concentric upper surface for application to the artificial hip joint

The synovial fluid motion in an artificial hip joint is important in understanding the thermo-fluids effects that can affect the reliability of the joint, although it is difficult to be studied theoretically, as the modelling involves the viscous fluid interacting with a moving surface. A new analytical solution has been derived for the maximum induced fluid motion within a spherical gap with an oscillating lower surface and a stationary upper surface, assuming one-dimensional incompressible laminar Newtonian flow with constant properties, and using the Navier-Stokes equation. The resulting time-dependent motion is analysed in terms of two dimensionless parameters R and β, which are functions of geometry, fluid properties and the oscillation rate. The model is then applied to the conditions of the synovial fluid enclosed in the artificial hip joint and it is found that the motion may be described by a simpler velocity variation, whereby laying the foundation to thermal studies in the joint.