Lubricity of High Water Content Aqueous Gels

Abstract

Aqueous gels such as biopolymer gels, mucus, and high water content hydrogels are often qualitatively described as lubricious. In hydrogels, mesh size, ξ, has been found to be a controlling parameter in friction coefficient. In the tribology of aqueous gels, we suggest that the Weissenberg number (Wi) is a useful parameter to define different regimes, and following the original formulations in rheology, Wi is given by the polymer relaxation time (ηξ3/kBT) multiplied by the shear rate due to fluid shear through a single mesh (V/ξ): Wi = ηVξ2/kBT. At sliding speeds below a Weissenberg number of approximately 0.1, Wi < 0.1, the friction coefficient is velocity-independent and scales with mesh size to the − 1 power, µ ∝ ξ−1. De Gennes’ scaling concepts for elastic modulus, E, give a dependence on polymer mesh size to the − 3 power, E ∝ ξ−3, and following Hertzian contact analysis, the contact area is found to depend on the mesh size squared, A ∝ ξ2. Combining these concepts, the shear stress, τ, and therefore the lubricity of aqueous gels, is predicted to be highly dependent on the mesh size, τ ∝ ξ−3. Studies aimed at elucidating the fundamental mechanism of lubricity in biopolymer gels, mucus, and hydrogels have wrestled with comparisons across mesh size, which can be extremely difficult to accurately quantify. Using scaling concepts relating polymer mesh size to water content reveals that shear stress decreases rapidly with increasing water content, and plots of shear stress as a function of swollen water content are suggested as a useful method to compare aqueous gels of unknown mesh size. As a lower bound, these data are compared against estimates of fluid shear stress for free and bound water flowing through a mesh size estimated by the water content of the gels. The results indicate that the strong dependence on lubricity is likely due to a synergistic combination of a low viscosity solvent (water) coupled to a system that has a decreasing friction coefficient, modulus, and the resulting contact pressure with increasing water content. Although the permeability, K, of aqueous gels increases dramatically with water content (and mesh size), K ≅ ξ2/η, the stronger decrease of the elastic modulus and subsequent decrease in contact pressure due to an increase in the contact length, predicts that the draining time under contact, t, actually increases strongly with increasing water content and mesh size, t ∝ ξ2. Consistent with the finding of extremely high water content aqueous gels on the surfaces of biological tissues, these high water content gels are predicted to be optimal for lubrication as they are both highly lubricious and robust at resisting draining and sustaining hydration.