Coupled transport processes

With respect to the driving forces and the modes of energy coupling, transport processes can be divided in four major classes ... 

If the cations of variable valency (e.g., Fe2+/Fe3 + ) are present in not too low concentrations, the crystals will be semiconductors. In non-equilibrium vermiculites, the internal electric field is then strongly influenced by their electronic conductivity, as explained in Section 4.4.2. If we start with an equilibrium crystal and change either pH, ae, aor a, (where i designates any other component), coupled transport processes are induced. The coupling is enforced firstly by the condition of electroneutrality, secondly by the site conservation requirements in the T-O-T blocks (Fig. 15-3), and thirdly by the available free volume in the (van der Waals) interlayer. It is in this interlayer that the cations and the molecules are the more mobile species. However, local ion exchange between the interlayer and the relatively rigid T-O-T blocks is also possible. 

The results obtained on coupled transport processes stress the role of cocarrier systems capable of transporting several substrates and driven by physical and chemical energy sources. 

Carrier facilitated transport processes often achieve spectacular separations between closely related species because of the selectivity of the carriers. However, no coupled transport process has advanced to the commercial stage despite a steady stream of papers in the academic literature. The instability of the membranes is a major technical hurdle, but another issue has been the marginal improvements in economics offered by coupled transport processes over conventional technology such as solvent extraction or ion exchange. Major breakthroughs in performance are required to make coupled transport technology commercially competitive. 

An alternative approach is to make the simplification that the rate of chemical reaction is fast compared to the rate of diffusion that is, the membrane diffusion is rate controlling. This approximation is a good one for most coupled transport processes and can be easily verified by showing that flux is inversely proportional to membrane thickness. If interfacial reaction rates were rate controlling, the flux would be constant and independent of membrane thickness. Making the assumption that chemical equilibrium is reached at the membrane interfaces allows the coupled transport process to be modeled easily [9], The process is... 

Thermodynamics for non-equilibrium processes is referred to as irreversible thermodynamics. The scientific field of irreversible thermodynamics was established during the early 1900 s. There are three major reasons why irreversible thermodynamics is important for non-equilibrium systems. In the first place special attention is paid to the validity of the classical thermodynamic relations outside equilibrium (i.e., simple systems). In the second place the theory gives a description of the coupled transport processes (i.e., the Onsager reciprocal relations). In the third place the theory quantifies the entropy that is produced during transport. Irreversible thermodynamics can also be used to assess the second law efficiency of how valuable energy resources are exploited. 

Apart from ammonia, some other inorganic species extracted by hquid membranes are strong acids like nitric acid and thiocyanate ions from aqueous solutions using carrier-mediated coupled transport process. 

Facilitated or carrier-mediated transport is a coupled transport process that combines a (chemical) coupling reaction with a diffusion process. The solute has first to react with the carrier to fonn a solute-carrier complex, which then diffuses through the membrane to finally release the solute at the permeate side. The overall process can be considered as a passive transport since the solute molecule is transported from a high to a low chemical potential. In the case of polymeric membranes the carrier can be chemically or physically bound to the solid matrix (Jixed carrier system), whereby the solute hops from one site to the other. Mobile carrier molecules have been incorporated in liquid membranes, which consist of a solid polymer matrix (support) and a liquid phase containing the carrier [2, 8], see Fig. 7.1. The state of the art of supported liquid membranes for gas separations will be discussed in detail in this chapter. 

The coupled transport process is illustrated in Figure 9.1 for Cu2+ and H ions and a complexing agent denoted by RH. The water-immiscible agent fills the pores of a microporous membrane, thus forming a liquid organic membrane, The equilibrium that exists at the two membrane-solution interfaces is ... 

A number of reviews on various aspects of liquid membranes and coupled transport processes have also appeared.52-55... 

Coupled transport processes can be divided into two categories, depending on the type of reaction occurring between complexing agent and permeant. The first type is called counter transport (shown in Figure 9.6). The key feature of counter transport is that the fluxes of the two permeating ions move counter to each other across the membrane. The reaction in this case is ... 

The principal applications of coupled transport have been the separation and concentration of metals from hydrometallurgical feeds or industrial effluent streams. These streams and the membranes used are briefly described below. In general, the application of a coupled transport process to mining operations involves the installation of a very large plant, and mine operators are reluctant to risk this type of investment in as yet unproven processes. Thus, the first commercial applications of coupled transport are likely to be smaller plants installed in pollution control applications. 

Figure 9.29 An integrated coupled transport processing scheme using membranes containing LIX 54, Kelex 100 and XI-51.62...

Theoretical studies of catalytic conversion in a flow reactor reveal that a compensation effect will be observed under certain restrictive conditions. It appears that the compensation effect is observed when two or more coupled transport processes are involved and consequently may be a general law. Compensation effects have been observed in electronic conductivity in semiconductors, diffusion of atoms in solids, etc however, more work is needed to establish its generality. 

The driving force in this case is the difference between the concentration of the carrier-extracted species complex at the membrane/feed solution interface and the practically zero concentration of the complex at the membrane/receiver solution interface. In the case of extracted ionic species, the driving force for the uphill transport can be the potential gradient generated by the coupled transport of another ionic species across the membrane. The extracted ionic species, in this case, is transported to satisfy the electroneutrality condition within the membrane system. This coupled transport process can be countertransported (Figure 27.5b,c) and cotransporled (Figure 27.5a,d) with respect to the extracted ionic species. 

The model presented here is a comprehensive full three-dimensional, non-isothermal, singlephase, steady-state model that resolves coupled transport processes in the membrane, eatalyst layer, gas diffusion eleetrodes and reactant flow channels of a PEM fuel cell. This model accounts for a distributed over potential at the catalyst layer as well as in the membrane and gas diffusion electrodes. The model features an algorithm that allows for a more realistie representation of the loeal activation overpotentials which leads to improved prediction of the local current density distribution. This model also takes into aeeount convection and diffusion of different species in the channels as well as in the porous gas diffusion layer, heat transfer in the solids as well as in the gases, electrochemical reactions and the transport of water through the membrane. 

In conclusion to this introduction it may be remarked that a new branch of thermodynamics has developed during the past few decades which is not limited in its applications to systems at equilibrium. This is based on the use of the principle of microscopic reversibility as an auxiliary to the information contained in the laws of classical thermodynamics. It gives useful and interesting results when applied to non-equilibrium systems in which there are coupled transport processes, as in the thermo-electric effect and in thermal diffusion. It does not have significant applications in the study of chemical reaction or phase change and for this reason is not included in the present volume.f... 

Temperature jumps from coupled transport processes. /. Electrochem. Soc. Vol. 143, 767-779. 

Coupled Transport Processes An Approach 83 which we substitute for Ts in the linear problem to obtain the excess work... 

Coupled Transport Processes An Approach to Thermodynamics and Fluctuations in Hydrodynamics... 

We present a brief introduction to coupled transport processes described macroscopically by hydrodynamic equations, the Navier-Stokes equations [4]. These are difficult, highly non-linear coupled partial differential equations they are frequently approximated. One such approximation consists of the Lorenz equations [5,6], which are obtained from the Navier-Stokes equations by Fourier transform of the spatial variables in those equations, retention of first order Fourier modes and restriction to small deviations from a bifurcation of an homogeneous motionless stationary state (a conductive state) to an inhomogeneous convective state in Rayleigh-Benard convection (see the next paragraph). The Lorenz equations have been applied successfully in various fields ranging from meteorology to laser physics. 

Modeling has increased understanding of the complex coupled transport processes in all types of fuel cells and on different scales. For design purposes, modeling today is used in fuel cell development where standard, established... 

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