Hydrodynamic theory for multi-component active polar gels

We develop a generic hydrodynamic theory of active fluids with several components. We take into account polar order and consider the case when one component is viscoelastic. Our theory is motivated by the cytoskeleton which is a network of elastic filaments that are coupled to active processes such as the action of motor proteins which can generate relative forces between filaments as they hydrolyze a fuel (ATP). In addition to the filament gel, the system is embedded in a solvent component and free monomers constitute a third component. We derive constitutive material equations for the combined system which include reactive and dissipative couplings as well as the chemical driving by ATP hydrolysis and a possible chiral symmetry of the filaments. As an illustration of these equations, we discuss an active liquid in a simple shear gradient