A New Progress in Random Hydrodynamic Lubrication for Movable Non-Rotational Curvilinear Biosurfaces with Phospholipid Bilayers

Abstract

This paper aims to highlight the result of a new progression of mathematical estimation methods of stochastic bio-hydrodynamic lubrication parameters for arbitrary, curvilinear, non-rotational, co-operating, living biological surfaces coated with phospholipid bi-layers. Movable, non-rotational, co-operating surfaces occur in various biological friction nods like the collar bone, the blade bone, the jump joint, and the wrist joint. Specifically, the author presents a synthetic and comprehensive estimation of stochastic bio-hydrodynamic lubrication parameters for co-operating, rotational cartilage bio-surfaces with phospholipid bi-layers occurring in human spherical hip joints and cylindrical elbow joints. The method of research discussed in this paper focuses on a review of stochastic analytical considerations performed by the author. This research is based on the measurements of the gap height between two movable, non-rotational bio-surfaces. The gap is restricted between two co-operating biological surfaces. After several experiments, it could be inferred that there are symmetric as well as asymmetric random increments and decrements in the gap height. Such changes are applicable to the hydrodynamic pressure, load-carrying capacity, friction forces, and wear of the co-operating biological surfaces in human friction nods and contacts. The prime purpose of this paper is to demonstrate the influence of variations in the expected values and standard deviation of the gap height on the hydrodynamic lubrication parameters that occur during the friction process. It can thus be concluded that the apparent dynamic viscosity of biological lubricant varies in the ultra-thin gap height direction, depending on the susceptibility of the superficial layer of the lubricated bio-surface. The results presented in this paper are obtained considering the 3D variations in the dynamic viscosity of the biological fluid, particularly the random variations crosswise the film thickness in non-Newtonian biological fluid properties.