(124b) Dissipation Potentials in the Mechanics of Fluid-Particle Suspensions

As a generalization of the classical Rayleigh-Onsager dissipation function, D.G.B. Edelen (1972-73) provides a purely mathematical construct that represents any strictly dissipative force-dependent velocity or “thermodynamic flux” as the gradient of a dissipation potential plus an additive non-dissipative “gyroscopic” flux. The present work casts Edelen's formulae in a transparent form and provides the extension to (Legendre-Fenchel) duality. Among other things, this allows for a compact and general representation of constitutive equations for visco-plastic materials such as fluid-particle suspensions and granular media.

A connection is made to theories such as those of Ziegler (1963-83) and others that are based on the assumption of extremal dissipation. While such models give a correct form for the dissipative components of force or flux they generally fail to describe non-dissipative but mechanically relevant components or to provide valid variational  principles. 

The current theory allows for evolutionary microstructure and for particle diffusion with size segregation in inhomogeneous systems. The resulting general models are compared to certain contemporary models for suspension mechanics.