Abstract
We develop a hydrodynamic theory of active permeating gels with viscoelasticity in which a polymer network is embedded in a background fluid. This situation is motivated by active processes in the cell cytoskeleton in which motor molecules generate elastic stresses in the network, which can drive permeation flows of the cytosol. Our approach differs from earlier ones by considering the elastic strain in the polymer network as a slowly relaxing dynamical variable. We first present the general ideas for the case of a passive, isotropic gel and then extend this description to a polar, active gel. We discuss two specific cases to illustrate the role of permeation in active gels: self-propulsion of a thin slab of gel relative to a substrate driven by filament polymerization and depolymerization; and non-equilibrium deswelling of a gel driven by molecular motors.