Shear induced formation of lubrication layers of negative normal stress gels

Many biopolymer gels generate negative normal stress, with which the polymer networks shrink in the normal of applied shear. Here we theoretically predict the sliding velocity of such a gel on a solid surface when a constant shear stress is applied to the gel. Our theory predicts that the negative normal stress drives the flow of the solvent in the gel and this produces a solvent layer between the gel and the surface. The sliding velocity of the gel is proportional to the thickness of the solvent layer and is a cubic function of the applied shear stress. With constant applied normal and shear stresses, the thickness of the solvent layer is a non-monotonic function of time with a maximum because the solvent flow from the gel to the solvent layer is dominant in the short time scale and the solvent flow from the solvent layer to the outside is dominant in a longer time scale. The maximum layer thickness depends on the ratio of the time scales of the solvent flow in the gel and in the solvent layer.