Theory of lubrication due to polyelectrolyte hydrogels with arbitrary salt concentration and degree of compression

A Poisson-Boltzmann equation solution is used to determine the thickness of a thin fluid lubricating layer predicted to separate two polyelectrolyte hydrogels in contact for arbitrary salt concentration as a function of applied load and fixed charge and salt concentration. We consider loads ranging from 1 Pa, at which the thin fluid layer thickness is of the order of micron, up to loads of the order of a MPa, at which it is estimated to be of the order of an angstrom. This allows us to predict the thickness of this layer over the wide range of loads that can occur in various applications of hydrogels.