Mass transport phenomena

In order to determine the various diffusion-controlled rate coefficients, monomer and polymer diffusivities were estimated. In general, the free-volume theory is the accepted model for the determination of these quantities. In this model, diffusion is 

Using the free-volume theory, the following polymer diffiisivity expression attributed to Achillas and Kiparissides (1992) was used, which in turn was based on the scaling theory predications of De Gennes (1979) 

The self-diffusion coefficient of the polymer in the limit of zero polymer concentration can be used to cancel the 0 2 pre-exponential constant 

It is possible to estimate the self-diffusion coefficient at zero polymer concentration (iD2)a)i i) using the Stokes-Einstein equation as 

The hydraulic radius of the polymer molecule (/ h) was estimated using the mean end-to-end distance calculations for a polymer globule as (Strobl, 1997) 

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In principle, TPD can also be applied to high-surface area catalysts in plug-flow reactors. Often, however, the curves are seriously broadened by mass-transport phenomena. Hence, the use of single crystals or particles on planar supports offers great advantages for these investigations. 

Estimation of parameters. Model parameters in the selected model are then estimated. If available, some model parameters (e.g. thermodynamic properties, heat- and mass-transfer coefficient, etc.) are taken from literature. This is usually not possible for kinetic parameters. These should be estimated based on data obtained from laboratory expieriments, if possible carried out isothermal ly and not falsified by heat- and mass-transport phenomena. The methods for parameter estimation, also the kinetic parameters in complex organic systems, and for discrimination between models are discussed in more detail in Section 5.4.4. More information on parameter estimation the reader will find in review papers by Kittrell (1970), or Froment and Hosten (1981) or in the book by Froment and Bischoff (1990). 

GL Flynn, SK Yalkowsky, TJ Roseman. Mass transport phenomena and models theoretical concepts. J Pharm Sci 63 479- 510, 1974. 

A continuous oxygen supply is thus achieved, which is limited only by the mass transport phenomena between the gas and aqueous phases this is the main advantage of air sparging over the alternative of water circulation systems. 

Hydration can be an important factor in diffusion and mass transport phenomena in pharmaceutical systems. It may alter the apparent solubility or dissolution rate of the drug, the hydrodynamic radii of permeants, the physicochemical state of the polymeric membrane through which the permeant is moving, or the skin permeability characteristics in transdermal applications. 

Mass transport phenomena between phases present in the bioreactor (gas, liquid and solids)... 

The models proposed by Wu et al. [36] and by Lin and Leu [45] refer to continuous conversion processes by immobilized bacteria the first to a fixed mixed culture entrapped into PVA beads operated in a fluidized bed, and the second to BAC of P. luteola operated in a packed bed. Results of these models highlight the role of mass transport phenomena and biophase granule size on reactor performance. 

FIG. 1 Mass transport phenomena during the osmotic process. 

Mass transport phenomena usually are effective on distance scales much larger than cell wall and double layer dimensions. Thicknesses of steady-state diffusion layers in mildly stirred systems are in the order of 10 5m. Thus one may generally adopt a picture where the local interphasial properties define the boundary conditions, while the actual mass transfer processes take place on a much larger spatial scale. 

The HTE characteristics that apply for gas-phase reactions (i.e., measurement under nondiffusion-limited conditions, equal distribution of gas flows and temperature, avoidance of crosscontamination, etc.) also apply for catalytic reactions in the liquid-phase. In addition, in liquid phase reactions mass-transport phenomena of the reactants are a vital point, especially if one of the reactants is a gas. It is worth spending some time to reflect on the topic of mass transfer related to liquid-gas-phase reactions. As we discussed before, for gas-phase catalysis, a crucial point is the measurement of catalysts under conditions where mass transport is not limiting the reaction and yields true microkinetic data. As an additional factor for mass transport in liquid-gas-phase reactions, the rate of reaction gas saturation of the liquid can also determine the kinetics of the reaction [81], In order to avoid mass-transport limitations with regard to gas/liquid mass transport, the transfer rate of the gas into the liquid (saturation of the liquid with gas) must be higher than the consumption of the reactant gas by the reaction. Otherwise, it is not possible to obtain true kinetic data of the catalytic reaction, which allow a comparison of the different catalyst candidates on a microkinetic basis, as only the gas uptake of the liquid will govern the result of the experiment (see Figure 11.32a). In three-phase reactions (gas-liquid-solid), the transport of the reactants to the surface of the solid (and the transport from the resulting products from this surface) will also... 

However, in contrast to the production know-how , the scientific knowledge on the details of phase equilibria, kinetics, mechanisms, catalysis and mass-transport phenomena involved in polycondensation is rather unsatisfactory. Thus, engineering calculations are based on limited scientific fundamentals. Only a few high-quality papers on the details of esterification and transesterification in PET synthesis have been published in the last 45 years. The kinetic data available in the public domain are scattered over a wide range, and for some aspects the publications even offer contradicting data. 

This review contains a great deal of information about the thermochemical conversion chemistry. The reader is referred to the original paper (Appendix B) for details. Here follows some of the most important findings on the heat and mass transport phenomena in a packed bed during thermochemical conversion. 

Appendix B includes a review and a classification of conversion concepts. It also investigates the potentials to develop an all-round bed model or CFSD code simulating the conversion system. This review also contains a great deal of information on the heat and mass transport phenomena taking place inside a packed bed in the context of PBC of biomass. The phenomena include conversion regimes, pyrolysis chemistry, char combustion chemistry, and wood fuel chemistry. The main conclusions from this review are ... 

Below is a review of some of the most important conceptual models applied to describe the heat and mass transport phenomena and chemistry with respect to the thermochemical conversion of solid fuels in general and biofuels in particular, in the context of the three-step model. 

Here follows a section outlining the heat and mass transport phenomena of the thermochemical conversion on both the micro- and the macro-scale of the fuel bed. Knowledge about the heat and mass transport phenomena on micro-scale is very important to be able to understand and model, for example, the mass flow of conversion gas. 

Figure 42 shows an overview of the heat and mass transport phenomena in the extraparticle and intraparticle phase during the thermochemical conversion of a single particle in one dimension. Several excellent reviews have been presented on this subject [22,23,39,54,55],... 

The heat and mass transport phenomena of the char gasification is not described in the literature as much as for the char combustion [11,28,78]. There are good reasons to believe that it is quite analogous to the char combustion phenomenology [79]. However, the heterogeneous gasification reactions are overall endothermic which results in some differences with respect to the intraparticle heat transport [79]. 

From an engineering perspective, deep-fat frying can be defined as a unit operation where heat and mass transport phenomena occur simultaneously. Convective heat is transferred from the frying media to the surface of the product, which is thereafter conducted within the food. Mass transfer is characterized by the loss of water from the food as water vapor and the movement of oil into the food (Singh, 1995). 

Figure 19.1 gives an overview of some of the most common membrane separation techniques, their application range and their denotation. It should be pointed out that the terminology for membrane separation processes is partly traditional. The kind of membrane-solute interactions and the respective mass-transport phenomena can therefore not necessarily be derived from the designation of the membrane separation, and should always be evaluated for the individual application envisaged. 

In a follow-up study, Koptyug et al. 115) reported images of both liquid and gas flow and mass transport phenomena in two different cylindrical monolith catalysts (one with triangular channels, the other with square channels) at various axial locations within the monolith. Heibel et al. 116,117) addressed two-phase flow in the film flow regime and reported investigations of liquid distributions in the plane perpendicular to the direction of superficial flow, in particular, addressing the accumulation of liquid in the corners of the square channels of the monolith. 

The void volume will become an important factor when we begin to discuss reaction rates in the environmental sections of this book. Void volume also exerts an effect on the inhibition of flow through the foam, not to mention turbulence and other mass transport phenomena. 

Besides these positive effects, a major disadvantage is introduced a liquid barrier to direct access of gaseous H2 to the catalyst particle The rheological properties of the fluid are also deeply modified, because the viscosity of liquids is many orders of magnitude higher than for gases. Finally, properties such as solubility, molecular diffusivity, etc., of H2 in organic mixtures, difficult to measure and even to estimate, have a vital influence on the mass transport phenomena, which can be schematized as follows ... 

Other low-temperature studies have been motivated by the desire to characterize and understand processes occurring in unusual media. For example, the use of liquid ammonia [8-10] and liquid sulfur dioxide [11-13] naturally requires reduced temperatures unless high pressures are used, as is done for electrochemistry in supercritical fluids [14]. Frozen media are interesting systems in terms of mass transport phenomena and microstructural effects. Examples include glasses of acetonitrile and acetone [15], frozen dimethyl sulfoxide solutions [16,17], and the solid electrolyte HC104 5.5 H20 [18-20]. 

Like CVD units, plasma etching and deposition systems are simply chemical reactors. Therefore, flow rates and flow patterns of reactant vapors, along with substrate or film temperature, must be precisely controlled to achieve uniform etching and deposition. The prediction of etch and deposition rates and uniformity require a detailed understanding of thermodynamics, kinetics, fluid flow, and mass-transport phenomena for the appropriate reactions and reactor designs. 

Flynn, G.L., et al., Mass transport phenomena and models theoretical conteiptajm. Sci., 63,... 

This brief review attempts to summarize the salient features of chemically modified electrodes, and, of necessity, does not address many of the theoretical and practical concepts in any real detail. It is clear, however, that this field will continue to grow rapidly in the future to provide electrodes for a variety of purposes including electrocatalysis, electrochromic displays, surface corrosion protection, electrosynthesis, photosensitization, and selective chemical concentration and analysis. But before many of these applications are realized, numerous unanswered questions concerning surface orientation, bonding, electron-transfer processes, mass-transport phenomena and non-ideal redox behavior must be addressed. This is a very challenging area of research, and the potential for important contributions, both fundamental and applied, is extremely high. 

In order to clarify the meaning of the concentration losses, Figure 3.5 represents, in a 2D domain, the mass transport phenomena within an SOFC. 

Flynn, G., Yalkowsky, S., and Roseman T. Mass transport phenomena and models Theoretical concepts. J. Pharm. Sci. 63 479—510, 1974. 

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