(414f) Nonequilibrium Thermodynamics of Diffusion and Chemical Reactions in Multicomponent Systems

Starting with a pioneering new formalism to NonEquilibrium Thermodynamics [1] M. Grmela has opened a new avenue for a systematic modeling of the dynamics of complex systems that consistently incorporates both Hamiltonian and Irreversible Thermodynamics principles. This work has led to numerous publications, including two research monographs [2,3] and the ultimate formalization as “GENERIC” [4,5]. In the present work we review and extend the application of this theory to multicomponent diffusion and chemical reactions with the objectives (a) of further clarifying it, offering a simpler and more consistent to the previous nonequilibrium thermodynamics formulations expression, and (b) of correcting a previously proposed possible extension to consistently include inertial, differential-momenta-based, effects that may be important under conditions under which there is appreciable differential motion between the various populations of the chemical species present.

Among other applications, we show how the present formulation leads naturally to a flux -based description of relaxation phenomena in multicomponent diffusion that is fully consistent with the Stefan-Maxwell equations from kinetic theory. We also show how chemical reactions can be consistently incorporated within the general formalism in a way that can also accommodate flow-induced effects, especially from stresses when macromolecular components are involved. As particular application we discuss shear-banding micellar systems. In a series of recent papers [6-8] a new, non-equilibrium thermodynamics-based, theory was presented on the structure and rheology of shear banding rodlike micellar solutions. The basis of that theory was a proposed extension of classical description of the kinetics of reversible chemical reactions. As a result of the present improvements we offer a simpler and more consistent to the previous nonequilibrium thermodynamics formulations expression.

References

[1] Grmela M, “Bracket formulation of dissipative fluid mechanics equations”, Phys. Lett. A, 102 (1984) 355-358.

[2] Beris A N and Edwards B J, “Thermodynamics of Flowing Systems with Internal Microstructure”, Oxford University Press, New York, 1994.

[3] H.C. Öttinger, Beyond Equilibrium Thermodynamics, Wiley-Interscience, Hoboken New Jersey, 2005.

[4] Grmela, M., Öttinger, H. C., Dynamics and thermodynamics of complex fluids. I. Development of a GENERIC formalism, Phys. Rev. E, 56 (1997) 6620.

[5] Öttinger, H. C., Grmela, M., Dynamics and thermodynamics of complex fluids. Illustrations of the GENERIC formalism, Phys. Rev. E, 56 (1997) 6633.

[6] Germann, N., Cook, L.P., Beris, A.N., “Nonequilibrium thermodynamic modeling of the structure and rheology of concentrated wormlike micellar solutions,” Journal of Non-Newtonian Fluid Mechanics, 196: 51-57, (2013).

[7] Germann, N., Cook, L.P., Beris, A.N., “Investigation of the inhomogeneous shear flow of a wormlike micellar solution using a thermodynamically consistent model,” Journal of Non-Newtonian Fluid Mechanics, 207: 21-31 (2014).

[8] Germann, N., Cook, L.P., Beris, A.N., “A differential velocities based study of diffusion effects in shear banding micellar solutions.” J. Non-Newtonian Fluid Mech., 232: 43-54 (2016).