Volume 24, Issue 1

Mass diffusion in multicomponent gas mixtures is governed by a coupled system of linear equations for the diffusive mass fluxes in terms of thermodynamic driving forces, known as the generalized Stefan–Maxwell equation. In computations of mass diffusion in multicomponent gas mixtures, this coupling between the different components results in considerable computational overhead. Consequently, simplified diffusion models for the diffusive mass fluxes as explicit functions of the driving forces are an attractive alternative. These models can be interpreted as an approximate solution to the Stefan–Maxwell equation. Simplified diffusion models require the specification of “effective” diffusion coefficients which are usually expressed as functions of the binary diffusion coefficients of each species pair in the mixture. Current models for the effective diffusion coefficients are incapable of providing a priori control over the error incurred in the approximate solution. In this paper a general form for diagonal approximations is derived, which accounts for the requirement imposed by the special structure of the Stefan–Maxwell equation that such approximations be constructed in a reduced-dimensional subspace. In addition, it is shown that current models can be expressed as particular cases of two general forms, but not all these models correspond to the general form for diagonal approximations. A new minimum error diagonal approximation (MEDA) model is proposed, based on the criterion that the diagonal approximation minimize the error in the species velocities. Analytic expressions are derived for the MEDA model's effective diffusion coefficients based on this criterion. These effective diffusion coefficients automatically give the correct solution in two important limiting cases: for that of a binary mixture, and for the case of arbitrary number of components with identical binary diffusivities. Although these minimum error effective diffusion coefficients are more expensive to compute than existing ones, the approximation will still be cheaper than computing the exact Stefan–Maxwell solution, while at the same time being more accurate than any other diagonal approximation. Furthermore, while the minimum error effective diffusion coefficients in this work are derived for bulk diffusion in homogeneous media, the minimization procedure can in principle be used to derive similar coefficients for diffusion problems in heterogeneous media which can be represented by similar forms of the Stefan–Maxwell equation. These problems include diffusion in macro- and microporous catalysts, adsorbents, and membranes.

We develop a general optimal control framework for a difficult class of problems of work maximization in endoreversible multistage processes which yield mechanical work with finite rates and are characterized by multiple (vectorial) efficiencies. Bellman's method of dynamic programming is used either to construct his recurrence equation or to arrive at a discrete maximum principle of Pontryagin's type, in which a Hamiltonian is maximized with respect to controls. Both these algorithms are powerful computational tools which serve to maximize the power output and evaluate optimal controls. Equations of dynamics which follow from energy and matter balances and transfer equations are difference constraints for optimizing work. Irreversibilities caused by the energy and mass transport are essential. Variation of efficiencies is analyzed in terms of heat and mass fluxes as natural control variables. Enhanced bounds for the work released from an engine system or added to a heat-pump system are evaluated. Lagrangians and Hamiltonians of work functionals and discrete canonical equations are effective; they reach their continuous counterparts in the limit of an infinite number of stages. For a finite-time passage of a resource fluid between two given thermodynamic states, an optimal process is shown to be irreversible. Its optimal intensity is characterized well by the Hamiltonian H. Characteristic functions which describe extremal work are found numerically in terms of final states, process duration and number of stages. An extension of classical exergy to nonisothermal separation systems with a finite number of stages and finite holdup time of the resource fluid is one of the main results. This extended exergy simplifies to the classical thermal exergy in the limit of infinite duration and an infinite number of stages. The extended exergy exhibits a hysteretic property as a decrease of maximum work received from a multistage engine system and an increase of minimum work added to a heat-pump system, two properties which are particularly important in high-rate regimes. This work is a significant step towards a realistic theory of nonisothermal chemical engines.

The validity of the double layer compression as the mechanism which governs the stability of a non-aqueous suspension has been checked. Positively charged polystyrene latexes have been used as model colloids. Another stability mechanism is claimed.

It is shown how one can derive the impedance of a polarized electrode surface from irreversible thermodynamics. The oxygen electrode is studied as an example. A Nyquist diagram is constructed for the case that the electrode conducts by electrons only, and the electrolyte conducts by oxygen ions or vacancies. The electrode surface contributes to the diagram with two semi-circles. One semi-circle is due to production of dipoles from adsorbed oxygen atoms. The other is due to the dipole moment of the ion-electron hole pair.

We derive two versions of Clausius inequality for open discrete systems, one formulated for the non-equilibrium system itself using contact quantities, the other one using equilibrium quantities belongs to the system's environment. Consequently, Bhalekar's conjecture that there is no Clausius inequality for open systems is disproved.