Simple models for complex nonequilibrium fluids

This review is concerned with the nonequilibrium dynamics and structure of complex fluids based on simple micro- and mesoscopic physical models which are not rigorously solvable by analytic methods. Special emphasis is placed on the finitely extendable nonlinear elastic (FENE) chain models which account for molecular stretch, bending, and topology. More coarse-grained descriptions such as primitive path models, and elongated particle models are reviewed as well. We focus on their inherently anisotropic material-in particular rheological-properties via deterministic and stochastic approaches. A number of representative examples are given on how simple (often high-dimensional) models can, and have been implemented in order to enable the analysis of the microscopic origins of the nonlinear viscoelastic behavior of polymeric materials. These examples are shown to provide us with a number of routes for developing and establishing coarse-grained (low-dimensional) models devoted to the prediction of a reduced number of significant material properties. At this stage approximations which allow for an analytical treatment are discussed as well. Concerning the types of complex fluids, we cover the range from flexible to semiflexible polymers in melts and solutions, wormlike micelles, structural suspensions including ferrofluids in field-induced anisotropic or liquid crystalline phases.