Applications of Edelen's Dissipation Potentials to Transport Phenomena and Chemical Kinetics

Prof. J. D. Goddard
Department of Mechanical and Aerospace Engineering
University of California, San Diego, USA

Joint Seminar of the Faculties of Chemical and Aerospace Engineering 

This presentation is concerned with the application of generalized dissipation functions and the associated dissipation potentials of Edelen to a wide range of strictly dissipative mechanical and physicochemical processes. As generalizations of the classical Onsager-Rayleigh forms, dissipation potentials have been employed in plasticity theories for some seventy-five years or more, with arguments for the existence of such potentials based frequently on the assumption of extremal dissipation (or entropy generation) [4]. While plausible for special systems, such as Stokesian fluid-particle suspensions, this assumption is questionable for general viscoplastic materials or for other non-linear strictly dissipative systems. By contrast, in a remarkable and largely ignored body of work, Edelen [1, 2] offers a purely mathematical construct that yields a generalized force-dependent velocity (or “flux”) as gradient of a dissipation potential, modulo a non-dissipative term representing a “powerless” or “gyroscopic” flux.

Casting Edelen’s formulae in a more transparent form, a recent work by the speaker [3] provides the extension to Legendre-Fenchel dual potentials, emphasizing the special role of homogeneous potentials and laying down correct variational principles. This same work also illustrates how dissipation potentials allow for effcient formulation of constitutive equations for the visco-plasticity of fluid-particle suspension and granular media, including evolutionary microstructure and particle migration in strongly inhomogeneous systems.

After a review of the above work, the present talk will briey explore the prospective applications to other processes, such as complex networks of chemical and biochemical reactions.

[1] D.G.B. Edelen. A nonlinear Onsager theory of irreversibility. Int. J. Eng. Sci., 10(6):481-90, 1972.
[2] D.G.B. Edelen. On the existence of symmetry relations and dissipation potentials. Arch. Ration. Mech.  An., 51:218-27, 1973.
[3] J.D. Goddard. Edelen’s Dissipation potentials and the visco-plasticity of particulate media. Acta Mech., in press, 2014.
[4] H.Ziegler, C. Wehrli. On a principle of maximal rate of entropy production. J. Non-Equil. Thermo., 12(3):229-44, 1987.

The talk will be given in English

Wed, 30-04-2014, 13:45 (Gathering at 13:30)

Lecture Hall 6, Faculty of Chemical Eng.

Light refreshments will be served before the lecture

Applications of Edelen’s Dissipation Potentials to Transport Phenomena and Chemical Kinetics