Hamiltonian mechanics of complex fluids

Constitutive relations for complex fluids (e.g. polymeric fluids) are derived from the assumption that the equations that govern the time evolution of the complex fluids possess the generalised Hamiltonian structure. The constitutive relations consist of a configuration space kinetic equation, an extended local equilibrium relation, an expression for the extra stress tensor and an expression for the heat flux. In the particularly interesting case of complex fluids with spatially inhomogeneous internal structure, the extra stress tensor includes an extension of the Eriksen stress and the heat flux includes non-Fourier-type contributions.