Equilibrium and Nonequilibrium-Stage Concepts

Nonequilibrium methods attempt to get around the difficulty of predicting efficiencies by doing away with the equilibrium-stage concept. Instead, they apply a transport phenomena approach for predicting mass transfer rates. The mass transfer rates are calculated continuously along the column length and not in discrete equilibrium stages. This process is similar to the transfer unit concept (Sec. 10.3.1). 

The plan of this chapter is the following. Section II gives a summary of the phenomenology of irreversible processes and set up the stage for the results of nonequilibrium statistical mechanics to follow. In Section III, it is explained that time asymmetry is compatible with microreversibility. In Section IV, the concept of Pollicott-Ruelle resonance is presented and shown to break the time-reversal symmetry in the statistical description of the time evolution of nonequilibrium relaxation toward the state of thermodynamic equilibrium. This concept is applied in Section V to the construction of the hydrodynamic modes of diffusion at the microscopic level of description in the phase space of Newton s equations. This framework allows us to derive ab initio entropy production as shown in Section VI. In Section VII, the concept of Pollicott-Ruelle resonance is also used to obtain the different transport coefficients, as well as the rates of various kinetic processes in the framework of the escape-rate theory. The time asymmetry in the dynamical randomness of nonequilibrium systems and the fluctuation theorem for the currents are presented in Section VIII. Conclusions and perspectives in biology are discussed in Section IX. 

The calculations, in this respect, become similar to those employed for single-stage flash vaporization and multistage distillation with reflux and reboil, or for absorption or stripping. All the latter utilize the concept of an equilibrium stage. It should be emphasized, however, that the adaptations are constituted to apply to the nonequilibrium rate phenomena associated with membrane permeation. The calculations are similar in form but not in content. For one thing, the permeate flow rate per unit of membrane area (that is, the permeate flux) becomes part of the distribution coefficients or K-values for each component. An extra element of trial and error is therefore introduced. 

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