UNIFIED VIEW OF TRANSPORT PHENOMENA BASED ON THE GENERALIZED BRACKET FORMULATION

The Hamiltonian formulation of equations in continuum mechanics through generalized brackets is presented here in order to demonstrate the inherent structure and similarity between a variety of transport phenomena. The bracket formulation presented in this paper is based upon the Poisson bracket description of continuous systems and the entropy dissipation postulated in irreversible thermodynamics. This general formulation is presented for both single-component and multicomponent systems, as well as for systems with internal structure, for example, viscoelastic fluids. Thus, in addition to providing an alternative formulation for transport phenomena (of value for possible new numerical schemes), this paper represents the initial stages of a generalization of nonequilibrium thermodynamics to complex media (i.e., materials with internal structure), which has never been accomplished to date in a fully satisfactory manner using traditional approaches.