Theory of Fluid Lubrication of Hydrogels and Articular Cartilage during Compression Under an Applied Load
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Theory of Fluid Lubrication of Hydrogels and Articular Cartilage during Compression Under an Applied Load J. B. Sokoloff Department of Physics and Center for Interdisciplinary Research on Complex Systems, Northeastern University, Boston, Massachusetts 02115, U.S.A. ABSTRACT A fluid lubrication model for articular cartilage was put forward by Mc Cutchen, in which a high percentage of the load is supported by fluid pressurization in the interface region separating the two cartilage coated surfaces as the cartilage is compressed under load. This reduces the friction by reducing the percentage of the load which is carried by solid material in the cartilage. For two bones which are in contact in a healthy joint, which are each coated by a layer of cartilage whose thickness is much smaller than its lateral dimensions, it will be argued that since the bone is impervious to fluid flow in healthy joints, almost all of the fluid that is expressed from the cartilage under load flows through the interface region, where it supports part of the load. This is in contrast to previous theoretical and in vitro experimental studies of this problem, in which most of the fluid does not flow into the interface. It is shown that for mean asperity height small compared to a length scale (which depends on the cartilage or hydrogel permeability, the fluid viscosity and the dimensions of the cartilage or hydrogel) a large percentage of the load is supported by fluid pressurization. INTRODUCTION Hydrogels are charged hydrophilic polymer gels. The osmotic pressure due to the counterions within the gels results in their being inflated with water to several times their dry state volume[1-4]. In Ref. 5 and Ref. 6, it was shown that in equilibrium, two hydrogel coated surfaces are separated by a thin fluid lubricating layer, resulting in very low friction. Articular cartilage consists of a collagen network filled with charged macromolecules[711]. Similar to hydrogels, the counterions inside cartilage result in osmotic pressure which inflates it. Two cartilage coated surfaces in contact do not exhibit exceedingly low friction when the cartilage is completely compressed, consistent with Refs. 5 and 6, although they are found to exhibit exceedingly low friction when initially compressed under an applied load, as a result of fluid inside the cartilage being expelled into the interface separating the cartilage coatings[1218]. The viscous friction between the fluid as it flows through the cartilage and the solid matrix supports part of the load. Since hydrogels are also swollen with fluid, when they are compressed under load[1], they also expel fluid into the interface region, and if they are about a millimeter thick or more[1-4], the time for the fluid to be expelled can be of the order of minutes[5]. If two gel or cartilage coated surfaces are in contact and if their lateral dimensions are much larger than their thickness, most of the fluid will be expelled into the interface between them, provided that the two solids to which they are attached are not
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