DRAINAGE OF COMPRESSED POLYMER LAYERS - DYNAMICS OF A SQUEEZED SPONGE

We have performed a hydrodynamic lubrication analysis to describe the drainage of solvent from semidilute polymer layers compressed between two solid surfaces. For strongly overlapped layers, the dynamical response is expected to be similar for adsorbed or grafted polymers. We assume the solvent is good and employ the conventional sphere-plane substrate geometry. Under these conditions, the dissipative lubrication force that acts normal to the surfaces is very different from the classical Reynolds force for Newtonian liquids. In particular, we find that the force between surfaces separated by h and approaching each other with a (constant) relative velocity h is proportional to eta-R2-GAMMA-3/2a5/2h-1/2h, where eta is the solvent viscosity, GAMMA is the number of monomers per area in the grafted or adsorbed layers, R is the radius of curvature of the spherical substrate, and a is a monomer size. This unusual result arises from Brinkman-like (plug) flow of the solvent through the polymer network affixed to the surfaces. Our analysis also provides expressions for the frequency-dependent elastic and dissipative components of the normal stress. For the case of impulsive squeezing of a polymer layer, the normal stress relaxation is found to have a power law decay over several decades, approximately t-13/11. These results should also have implications for the mechanical properties of swollen gels and for the rheology of concentrated colloidal suspensions.