Balanced transport theory

An alternative theory to explain the improved scale adhesion as a result of water presence in the oxidizing atmosphere is the balanced transport theory developed by Hultquist etal [50,51]. In this theory, it was proposed that the presence of hydrogen in some oxide scales would modify their transport mechanisms to improve the balance between oxygen-ion and metal-ion transports so that the tendency for scale spallation or scale cracking can be lowered. 

In summary, it has been observed that the presence of water vapour in air or oxygen improves the scale adhesion formed at high temperatures. When voids or pores are generated in the scale, the void migration theory proposed by Rahmel and Tobolsk [38] can be used to explain the improved scale adhesion. However, when voids or pores are not present in the scale, the void migration mechanism is invalid. Two other promising theories have been proposed to explain the improved scale-steel adhesion in this latter case. One is the traditional theory of improved plasticity as a result of improved dislocation mobility in the wustite scale due to the presence of hydrogen in certain forms in the scale. The other is the balanced transport theory recently developed by Hultquist et al. However, the actual mechanisms by which these proposed theories work are still not clear. 

Expressions of the conservation of mass, a particular chemical species, momentum, and energy are fundamental principles which are used in the analysis and design of any separation device. It is appropriate to formulate these laws first without specific rate expressions so that a clear distinction between conservation laws and rate expressions is made. Some of these laws contain a source or generation term, for example, for a particular chemical species, so that the particular quantity is not actually conserved. A conservation law for entropy can also be formulated which contributes to a useful framework for a generalized transport theory. Such a discussion is beyond the scope of this chapter. The conservation expressions are first presented in their macroscopic forms, which are applicable to overall balances on energy, mass, and so on, within a system. However, such macroscopic formulations do not provide the information required to size equiprrwnt. Such analyses usually depend on a differential formulation of the conservation laws which permits consideration of spatial variations of composition, temperature, and so on within a system. 

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 transport equations for the turbulent kinetic energy, k, and the turbulence dissipation, e, in the RNG k-s model are again defined similar to the standard k-s model, now utilizing the effective viscosity defined through the RNG theory. The major difference in the RNG k-s model from the standard k-s model can be found in the e balance where a new source term appears, which is a function of both k and s. The new term in the RNG k- s model makes the turbulence in this model sensitive to the mean rate of strain. The result is a model that responds to the effect of strain and the effect of streamline curvature,... 

Concentrated Solution "Theory. For an electrolyte with three species, it is as simple and more rigorous to use concentrated solution theory. Concentrated solution theory takes into account all binary interactions between all of the species. For membranes, this was initially done by Bennion ° and Pintauro and Bennion. ° They wrote out force balances for the three species, equating a thermodynamic driving force to a sum of frictional interactions for each species. As discussed by Fuller,Pintauro and Bennion also showed how to relate the interaction parameters to the transport parameters mentioned above. The resulting equations for the three-species system are... 

Rapid evaporation introduces complications, for the heat and mass transfer processes are then coupled. The heat of vaporization must be supplied by conduction heat transfer from the gas and liquid phases, chiefly from the gas phase. Furthermore, convective flow associated with vapor transport from the surface, Stefan flow, occurs, and thermal diffusion and the thermal energy of the diffusing species must be taken into account. Wagner 1982) reviewed the theory and principles involved, and a higher-order quasisteady-state analysis leads to the following energy balance between the net heat transferred from the gas phase and the latent heat transferred by the diffusing species ... 

The rate-based models usually use the two-film theory and comprise the material and energy balances of a differential element of the two-phase volume in the packing (148). The classical two-film model shown in Figure 13 is extended here to consider the catalyst phase (Figure 33). A pseudo-homogeneous approach is chosen for the catalyzed reaction (see also Section 2.1), and the corresponding overall reaction kinetics is determined by fixed-bed experiments (34). This macroscopic kinetics includes the influence of the liquid distribution and mass transfer resistances at the liquid-solid interface as well as dififusional transport phenomena inside the porous catalyst. 

The formulation of linear nonequilibrium thermodynamics is based on the combination of the first and second laws of thermodynamics with the balance equations including the entropy balance. These equations allow additional effects and processes to be taken into account. The linear nonequilibrium thermodynamics approach is widely recognized as a useful phenomenological theory that describes the coupled transport without the need for the examination of the detailed coupling mechanisms of complex processes. 

You are expected to set up a simple theory of the stmcture of your product, and of what happens with your product. You may need to set up balances and transport equations as you have learned in Transport Phenomena or Process Engineering. For some assignments the Notes on Colloids may help. Our experience is that many teams find this job difficult, so start early. 

Chapter 4 is devoted to the description of stochastic mathematical modelling and the methods used to solve these models such as analytical, asymptotic or numerical methods. The evolution of processes is then analyzed by using different concepts, theories and methods. The concept of Markov chains or of complete connected chains, probability balance, the similarity between the Fokker-Plank-Kolmogorov equation and the property transport equation, and the stochastic differential equation systems are presented as the basic elements of stochastic process modelling. Mathematical models of the application of continuous and discrete polystochastic processes to chemical engineering processes are discussed. They include liquid and gas flow in a column with a mobile packed bed, mechanical stirring of a liquid in a tank, solid motion in a liquid fluidized bed, species movement and transfer in a porous media. Deep bed filtration and heat exchanger dynamics are also analyzed. 

Adopting the dusty gas model(DGM) for the description of gas phase mass transfer and a Generalized Stefon-Maxwell(GSM) theory to quantify surface diffusion, a combined transport model has been applied. The tubular geometry membrane mass balance is given in equation (1). 

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