A major theme of the research work of the T2PL is the development of reliable constitutive models for describing the dynamics and flow behavior of complex fluids. To this end, we rely on the use of non-equilibrium thermodynamics (NET), in particular the Generalized Bracket and GENERIC formalisms, for developing closed-form balance equations for the fundamental hydrodynamic fields. No matter what the system is (say biological or chemical), it must obey the laws of thermodynamics. In particular, when the system is beyond equilibrium (e.g., under the influence of a flow field), its time evolution must be dictated by the laws of non-equilibrium thermodynamics (NET). This is exactly the reason for employing NET in our work: by construction the new constitutive models obey the laws of NET. In our models, the underlying microstructure of the complex fluid is described by using structural variables, such as the conformation tensor for polymer chains (describing their average conformation), which are hydrodynamically coupled with the imposed flow field. The relation between microstructure (structural variables) and macroscopic observables (viscometric functions) takes eventually the form of a stress tensor equation. So far, we have developed generalized constitutive models for polymer melts, polymer solutions, polymer nanocomposites, drilling fluids and biological fluids (e.g. blood).
