Material transport macroscopic

Sherwood was one of the early workers to recognize the importance of turbulence (S15, S16, S17) in material transport. He summarized the progress in this field some years ago (S13) and contributed additional experimental work (L7, M2, M3). Kirkwood and Crawford (K7) set forth the relationships for transport in homogeneous phases with particular emphasis upon the interrelation of material and thermal flux. These contributions have laid a satisfactory basis for work in the field which has been well summarized from a macroscopic standpoint by Sherwood and Pigford (S14). 

The influence of turbulence was studied somewhat earlier by Bag-otskaya (Bl). Local coefficients of transport of water into an air jet were evaluated experimentally by Spielman and Jakob (S20). These essentially macroscopic studies supplement the investigations reported elsewhere in this discussion and contribute to the background of experimental information concerning material transport in fluid systems. 

Material transport is usually associated with thermal transport except in situations involving homogeneous phases which can be treated as ideal solutions (L4). For this reason it is necessary to consider the behavior of combined thermal and material transport in turbulent flow. The evaporation of liquids under macroscopic adiabatic conditions is a typical example of such a phenomenon. Under such circumstances the behavior in the boundary layer is similar to that found in the field of aerodynamics in a blowing boundary layer (S4). However, it is not... 

Satterfield (S2, S3) carried out a number of interesting macroscopic studies of simultaneous thermal and material transfer. This work was done in connection with the thermal decomposition of hydrogen peroxide and yielded results indicating that for the relatively low level of turbulence experienced the thermal transport did not markedly influence the material transport. However, the results obtained deviated by 10 to 20 from the commonly accepted macroscopic methods of correlating heat and material transfer data. The final expression proposed by Satterfield (S3), neglecting the thermal diffusion effect (S19) in the boundary layer, was written as... 

Equation (57) applies to material transport in tubes and yields an average deviation of 9.5% from the experimental data. An expression of similar form yielded an average deviation of 14.8% for the thermal transport. The ratio of thermal to material transport was found to be 1.09 with an average deviation of 13.7% (S3). Somewhat better agreement with predicted behavior was encountered for the studies on packed beds (S2). These data serve to illustrate the uncertainties which presently exist in the prediction of simultaneous material and thermal transfer under a variety of conditions. Satterfield s work has made a distinct contribution to understanding the macroscopic influences of combined thermal and material transport. Some of the discrepancy he noted may relate to assumptions concerning the nature of the chemical reaction associated with the decomposition of hydrogen peroxide. 

In macroscopic reactors, knowledge of the velocity profile in the channel cross-section is a necessary and sufficient prerequisite to describe the material transport. In microscopic dimensions down to a few micrometers, diffusion also has to be considered. In fact, without the influence of diffusion, extremely broad residence time distributions would be found because of the laminar flow conditions. Superposition of convection and diffusion is called dispersion. Taylor [91] was among the first to notice this strong dominating effect in laminar flow. It is possible to transfer his deduction to rectangular channels. A complete fluid dynamic description has been given of the flow, including effects such as the influence of the wall, the aspect ratio and a chemical wall reaction on the concentration field in the cross-section [37]. 

We now consider the transport of these charge carriers across the material. Transport along a macroscopic distance involves different processes, which reflect the structure of the material at different scales. Let us look at the various levels in the conduction process. We will follow the theorist s approach, which considers a pure and ideal one-dimensional system isolated from the rest of the world, going on to the point of view of the experimentalist, who has to deal with real matter assemblies of macro-molecular compounds with all kinds of imperfections, packed together in very complicated ways. 

All of the conduction mechanisms so far described assume that the material is macroscopically uniform. Both the hopping conductivity and the models of transport at the mobility edge take into account the randomness of an amorphous material, but this is done without any consideration of large scale inhomogeneity. Structural non-uniformity and Coulomb potentials are examples of inhomogeneity in a-Si H which may influence the conductivity. Investigations of the a-Si H... 

The aim here is not to go into thorough detail about mass transport in porous materials. We will merely describe these phenomena in macroscopic terms using the effective mass transport parameters (diffusion coefficients and mobilities) denoted by the index m and adapted to the material s macroscopic geometry. 

According to the conventional interpretation, the mechanisms of the material transport entail both pressure flow and drag flow [55]. Material transport through the gap between the rotor tip and the chamber wall is affected by the drag flow and a part of the pressure flow, i.e., in the through direction. However, the pressure also pushes the material backwards. The latter does not contribute to effective mixing, except perhaps in macroscopic homogenisation. 

The theory on the level of the electrode and on the electrochemical cell is sufficiently advanced [4-7]. In this connection, it is necessary to mention the works of J.Newman and R.White s group [8-12], In the majority of publications, the macroscopical approach is used. The authors take into account the transport process and material balance within the system in a proper way. The analysis of the flows in the porous matrix or in the cell takes generally into consideration the diffusion, migration and convection processes. While computing transport processes in the concentrated electrolytes the Stefan-Maxwell equations are used. To calculate electron transfer in a solid phase the Ohm s law in its differential form is used. The electrochemical transformations within the electrodes are described by the Batler-Volmer equation. The internal surface of the electrode, where electrochemical process runs, is frequently presented as a certain function of the porosity or as a certain state of the reagents transformation. To describe this function, various modeling or empirical equations are offered, and they... 

The macroscopic properties of a material are related intimately to the interactions between its constituent particles, be they atoms, ions, molecules, or colloids suspended in a solvent. Such relationships are fairly well understood for cases where the particles are present in low concentration and interparticle interactions occur primarily in isolated clusters (pairs, triplets, etc.). For example, the pressure of a low-density vapor can be accurately described by the virial expansion,1 whereas its transport coefficients can be estimated from kinetic theory.2,3 On the other hand, using microscopic information to predict the properties, and in particular the dynamics, of condensed phases such as liquids and solids remains a far more challenging task. In these states... 

For applications where only mechanical properties are relevant, it is often sufficient to use resins for the filling and we end up with carbon-reinforced polymer structures. Such materials [23] can be soft, like the family of poly-butadiene materials leading to rubber or tires. The transport properties of the carbon fibers lead to some limited improvement of the transport properties of the polymer. If carbon nanotubes with their extensive propensity of percolation are used [24], then a compromise between mechanical reinforcement and improvement of electrical and thermal stability is possible provided one solves the severe challenge of homogeneous mixing of binder and filler phases. For the macroscopic carbon fibers this is less of a problem, in particular when advanced techniques of vacuum infiltration of the fluid resin precursor and suitable chemical functionalization of the carbon fiber are applied. 

PAH chemistry is of practical as well as theoretical interest. PAHs can be regarded as well defined subunits of graphite, an important industrial material, which is so far not totally understood at the macroscopic level. In this context, it is our aim to delineate the molecular size at which the electronic properties of PAHs converge to those of graphite. Furthermore, alkyl substituted derivatives of hexabenzocoronene (HBC) form discotic mesophases and, therefore, provide opportunities for materials which allow one-dimensional transport processes along their columnar axis [83,84]. Their application for photovoltaics and Xerox processes is also of current interest. 

The last comprehensive review covering proton conductivity and proton conducting materials was written by one of the authors (dating back to 1996) since then, there have been several other review articles of similar scope (e.g., see Colomban ). There are also many reviews available on separator materials used for fuel cells (see articles in refs 3 and 4 and references therein, recent review-type articles, " and a literature survey ), which, more or less, address all properties that are relevant for their functioning in a fuel cell. The transport properties are usually described in these articles however, the treatments are frequently restricted to macroscopic approaches and handwaving arguments about the transport mechanisms. The purpose of the present review is to combine a few recently published results in the context of a discussion of transport phenomena in proton-conducting separator materials, which have some relevance in fuel cell applications (for a more complete list of the comprehensive literature in the field, the interested reader is referred to the aforementioned references). 

Apart from mechanistic aspects, we have also summarized the macroscopic transport behavior of some well-studied materials in a way that may contribute to a clearer view on the relevant transport coefficients and driving forces that govern the behavior of such electrolytes under fuel cell operating conditions (Section 4). This also comprises precise definitions of the different transport coefficients and the experimental techniques implemented in their determination providing a physicochemical rational behind vague terms such as cross over , which are frequently used by engineers in the fuel cell community. Again, most of the data presented in this section is for the prototypical materials however, trends for other types of materials are also presented. 

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