Modeling viscoelastic networks in Stokes flow

Filamentous networks and elastic polymers immersed in a viscous fluid are central to many processes in biology. Here, we present a model of a discrete viscoelastic network coupled to a Stokesian fluid. The network is built out of a collection of cross-linked nodes where each link is modeled by one or more simple viscoelastic elements. The method of regularized Stokeslets is used to couple network dynamics with a highly viscous fluid in three dimensions. We use computational rheometry tests to characterize the viscoelastic structures, such as computing their frequency-dependent loss and storage moduli. We find that when linkages between nodes are modeled by Maxwell elements, the qualitative behavior of these moduli reflects that of many biological viscoelastic structures.