Modeling viscoelastic networks in Stokes flow

Abstract

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 frequencydependent 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. C 2014 AIP Publishing LLC.

Enhanced flagellar swimming through a compliant viscoelastic network in Stokes flow

“…In Wróbel et al (2014) we presented a model of a viscoelastic network coupled to a Stokesian fluid. These networks are constructed out of a collection of cross-linked nodes where each link is modelled by one or more simple viscoelastic elements.…”

“…These networks are constructed out of a collection of cross-linked nodes where each link is modelled by one or more simple viscoelastic elements. Computational rheometry tests were used to characterize the viscoelastic structures (Wróbel et al 2014). It was found that when the linkages between nodes were modelled by Maxwell elements, the rheological behaviour of the system captured that…”

“…In the coupled swimmer-viscoelastic network system, the external force will be concentrated at the discrete nodes of the network and the material points of the swimmer. We choose a regularized Stokeslet formulation of the external forcing, which has been widely used to study the hydrodynamics of microorganism motility Flores et al 2005;Gillies et al 2009;Lobaton & Bayen 2009;Olson, Suarez & Fauci 2011;Guo et al 2014), and recently to model viscoelastic networks in Stokes flow (Wróbel et al 2014).…”

“…The deformation of the links connecting two nodes results in forces applied to the viscous fluid at these nodes. In Wróbel et al (2014) we demonstrated through computational rheology tests that when the links are taken to be Maxwell elements, the loss and storage moduli measured for the network behave like those of viscoelastic biofluids such as mucus, actin networks and DNA solutions. This framework, where forces due to a discrete mesh of elastic elements are coupled to a surrounding fluid, was used by Dillon & Zhuo (2011) to investigate sperm motility in a two-dimensional Navier-Stokes fluid using an immersed boundary method.…”

“…The evolution of the network structure is tracked, along with the evolution of its stored elastic energy. We choose a discrete description of the network, made up of a collection of nodes and virtual links (Wróbel, Cortez & Fauci 2014). The virtual links are thought of as linear viscoelastic elements and are assigned their own constitutive properties.…”