Description of transport processes

Whereas the general linear transport equation (11) usually provides an adequate description of transport processes, there are cases of practical interest where a generalization is needed Since the transport coefficient is a constant, equation (11) implies that the response— the flux J— momentarily follows the driving force T, which is not always the case. Consider, for example, the response of a viscoelastic material (such as a gel) to an applied stress or the response of a dielectric material to an applied electric field, both of which generally lag behind the driving force. Such delayed responses may be interpreted as... 

A later paper [47] gives the appropriate equation for the case of a spherical, radially directing source of sodium vapour where a complete description of transport processes depends only upon the radial coordinate and where a more exact definition of streaming effects is possible. No further studies of this type have appeared. It is of particular interest that the values appear to be in good agreement with values obtained by the life period technique. 

This equation replaces Eq. (8) in the description of transport processes. Though it is customary to use the equal symbol in Eq. (9), the electric charge density is not strictly zero, and the Poisson equation cannot be reduced to the Laplace equation = 0. 

When the supporting electrolyte is elec-troinactive (and chemically inert), its presence can be totally ignored in the description of transport processes. The absence of migration and the zero flux condition for the inactive species impUes that these species have an approximately uniform concentration throughout the DEL, which... 

We saw above that non-equilibrium thermodynamics is required for a proper description of transport processes in many common cases, because coupling coefScients cannot be neglected. Coupling leads to reversible contributions in processes and plays, therefore, an important role in problems that address energy efSciency. 

In the description of transport processes in homogenous systems, investigators often adopt linear phenomenological equations of the form... 

It seems probable that a fruitful approach to a simplified, general description of gas-liquid-particle operation can be based upon the film (or boundary-resistance) theory of transport processes in combination with theories of backmixing or axial diffusion. Most previously described models of gas-liquid-particle operation are of this type, and practically all experimental data reported in the literature are correlated in terms of such conventional chemical engineering concepts. In view of the so far rather limited success of more advanced concepts (such as those based on turbulence theory) for even the description of single-phase and two-phase chemical engineering systems, it appears unlikely that they should, in the near future, become of great practical importance in the description of the considerably more complex three-phase systems that are the subject of the present review. 

As far as modeling of transport phenomena in porous media is concerned, the task is to provide a generic description which is applicable to as broad a class of materials as possible. The models should to some extent be idealized, allowing them to capture a broad class of phenomena without the need to model all geometric details of the pore space and allowing for a fundamental understanding of transport processes in porous media. 

Studies of the effect of permeant s size on the translational diffusion in membranes suggest that a free-volume model is appropriate for the description of diffusion processes in the bilayers [93]. The dynamic motion of the chains of the membrane lipids and proteins may result in the formation of transient pockets of free volume or cavities into which a permeant molecule can enter. Diffusion occurs when a permeant jumps from a donor to an acceptor cavity. Results from recent molecular dynamics simulations suggest that the free volume transport mechanism is more likely to be operative in the core of the bilayer [84]. In the more ordered region of the bilayer, a kink shift diffusion mechanism is more likely to occur [84,94]. Kinks may be pictured as dynamic structural defects representing small, mobile free volumes in the hydrocarbon phase of the membrane, i.e., conformational kink g tg ) isomers of the hydrocarbon chains resulting from thermal motion [52] (Fig. 8). Small molecules can enter the small free volumes of the kinks and migrate across the membrane together with the kinks. 

Of the three general categories of transport processes, heat transport gets the most attention for several reasons. First, unlike momentum transfer, it occurs in both the liquid and solid states of a material. Second, it is important not only in the processing and production of materials, but in their application and use. Ultimately, the thermal properties of a material may be the most influential design parameters in selecting a material for a specific application. In the description of heat transport properties, let us limit ourselves to conduction as the primary means of transfer, while recognizing that for some processes, convection or radiation may play a more important role. Finally, we will limit the discussion here to theoretical and empirical correlations and trends in heat transport properties. Tabulated values of thermal conductivities for a variety of materials can be found in Appendix 5. 

Because the quantitative analysis of transport processes in terms of the microscopic description of turbulence is difficult, Kdrmdn suggested (K2) the use of a macroscopic quantity called eddy viscosity to describe the momentum transport in turbulent flow. This quantity, which is dimensionally and physically analogous to kinematic viscosity in the laminar motion of a Newtonian fluid, is defined by... 

The complex nature of heterogeneous catalytic reactions, which consist of a sequence of at least three steps (adsorption, surface reaction and desorption), the possible intervention of transport processes and the uncertainty about the actual state of the surface makes every attempt to obtain a complete formal kinetic description without simplifying assumptions futile. In this situation, some authors prefer fully empirical equations of the type... 

Transport Processes. The velocity of electrode reactions is controlled by the charge-transfer rate of the electrode process, or by the velocity of the approach of the reactants, to the reaction site. The movement or trausport of reactants to and from the reaction site at the electrode interface is a common feature of all electrode reactions. Transport of reactants and products occurs by diffusion, by migration under a potential field, and by convection. The complete description of transport requires a solution to the transport equations. A full account is given in texts and discussions on hydrodynamic flow. Molecular diffusion in electrolytes is relatively slow. Although the process can be accelerated by stirring, enhanced mass transfer... 

Following oral administration of a lipophilic drug, the main route for the drug to access into the intestinal lymphatics is transcellular, by tracking the same pathway as the lipidic nutrients in food, which use the physiological intestinal lipid transport system. Hence, a brief description of this process is described. 

We consider a system made of a solid phase (denoted by s) containing a liquid phase (denoted by L). The latter is composed by water (denoted by e) and by two kinds of ions (denoted by + and —). An electric field is applied. The methods of the linear thermodynamics of irreversible processes permits the description of transport phenomena by linear relations. For the liquid phase [9] (in this paper, the indices or exponents k and m refer to cartesian coordinates) ... 

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