Biphasic Lubrication Theory of Hydrogels: Transient Response and Sample Size Effects

Hydrogels are soft and wet materials with remarkable properties. Among such properties, low friction has attracted much attention from scientists and engineers. While many studies investigated the correlation between material properties and frictional behavior, little attention has been paid to other effects, such as sample sizes. In this study, we developed a theoretical model based on the biphasic lubrication theory to describe the frictional behavior of hydrogels against a glass substrate in the rotational shear test. Consequently, we obtained analytical solutions for the time evolutions of friction coefficient, hydrostatic pressure, and elastic stress. To validate our model, we prepared cylindrical PVA (Polyvinyl alcohol) hydrogels with different radii and thicknesses and conducted friction experiments. We confirmed reasonable agreements with theoretical predictions for the transient responses and their size dependences. Interestingly, we found that the friction coefficient at the initial phase decreased drastically with decreasing thickness. Our results indicate the fundamental importance of bulk transport in surface friction of hydrogels, and the controllability of friction by varying the geometry of hydrogels.