Mass transfer diffusive

An industrial chemical reacdor is a complex device in which heat transfer, mass transfer, diffusion, and friction may occur along with chemical reaction, and it must be safe and controllable. In large vessels, questions of mixing of reactants, flow distribution, residence time distribution, and efficient utilization of the surface of porous catalysts also arise. A particular process can be dominated by one of these factors or by several of them for example, a reactor may on occasion be predominantly a heat exchanger or a mass-transfer device. A successful commercial unit is an economic balance of all these factors. 

The Hatta criterion compares the rates of the mass transfer (diffusion) process and that of the chemical reaction. In gas-liquid reactions, a further complication arises because the chemical reaction can lead to an increase of the rate of mass transfer. Intuition provides an explanation for this. Some of the reaction will proceed within the liquid boundary layer, and consequently some hydrogen will be consumed already within the boundary layer. As a result, the molar transfer rate JH with reaction will be higher than that without reaction. One can now feel the impact of the rate of reaction not only on the transfer rate but also, as a second-order effect, on the enhancement of the transfer rate. In the case of a slow reaction (see case 2 in Fig. 45.2), the enhancement is negligible. For a faster reaction, however, a large part of the conversion occurs in the boundary layer, and this results in an overall increase of mass transfer (cases 3 and 4 in Fig. 45.2). 

Chemical reactions may be classified by the number of phases involved in the reaction. If the reaction takes place inside one single phase, it is said to be a homogeneous reaction. Otherwise, it is a heterogeneous reaction. For homogeneous reactions, there are no surface effects and mass transfer usually does not play a role. Heterogeneous reactions, on the other hand, often involve surface effects, formation of new phases (nucleation), and mass transfer diffusion and convection). Hence, the theories for the kinetics of homogeneous and heterogeneous reactions are different and are treated in different sections. 

Diffusion is ubiquitous in nature whenever there is heterogeneity, there is diffusion. In liquid and gas, flow or convection is often present, which might be the dominant means of mass transfer. However, inside solid phases (minerals and glass), diffusion is the only way of mass transfer. Diffusion often plays a major role in solid-state reactions, but in the presence of a fluid dissolution and recrystallization may dominate. 

Limitation of a reaction by translational diffusion in solution is a rather rare case. Much more frequently the limitation of the observed overall reaction rate is by external mass transfer (through a laminar film around a solid macroscopic carrier) (Chapter 5, Section 5.5.1) or internal mass transfer (diffusion of substrate or product through the pores of a solid carrier or a gel network to an enzyme molecule in the interior of the carrier) (Chapter 5, Section 5.5.2). 

Enhanced Mass Transfer, Diffusivity Supercritical fluids share many of the advantages of gases, including lower viscosities and higher diffusivities relative to liquid solvents, thereby potentially providing the opportunity for faster rates, particularly for diffusion-limited reactions. 

Low-rate processes are active at low frequencies, such as mass transfer (diffusion)... 

It is important to note that the preparative separation is carried out at a low flow rate to allow for mass transfer, diffusion and column wall effects discussed previously. 

Equilibrium partitioning and mass transfer relationships that control the fate of HOPs in CRM and in different phases in the environment were presented in this chapter. Partitioning relationships were derived from thermodynamic principles for air, liquid, and solid phases, and they were used to determine the driving force for mass transfer. Diffusion coefficients were examined and those in water were much greater than those in air. Mass transfer relationships were developed for both transport within phases, and transport between phases. Several analytical solutions for mass transfer were examined and applied to relevant problems using calculated diffusion coefficients or mass transfer rate constants obtained from the literature. The equations and approaches used in this chapter can be used to evaluate partitioning and transport of HOP in CRM and the environment. 

Ash fouling appears to be initiated by the formation of a layer of sodium sulfate on the boiler tube. It is thought that thermal decomposition of sodium salts of carboxylic functional groups in the coal is the start of a sequence of reactions leading ultimately to the formation of sodium sulfate in the flame or flue gas. The convective mass transfer diffusion of the sodium-containing species through a boundary layer around the tube results in deposition of sodium sulfate on the tube surface. 

The general approach for modelling catalyst deactivation is schematically organised in Figure 2. The central part are the mass balances of reactants, intermediates, and metal deposits. In these mass balances, coefficients are present to describe reaction kinetics (reaction rate constant), mass transfer (diffusion coefficient), and catalyst porous texture (accessible porosity and effective transport properties). The mass balances together with the initial and boundary conditions define the catalyst deactivation model. The boundary conditions are determined by the axial position in the reactor. Simulations result in metal deposition profiles in catalyst pellets and catalyst life-time predictions. 

MULTICOMPONENT MASS TRANSFER DIFFUSION MODEL FOR THE ADSORPTION OF ACID DYES ON ACTIVATED CARBON... 

Mass transfer (diffusion) of the reactant(s) (e.g., species A) from the bulk fluid to the external surface of the catalyst pellet... 

When thinking of any electrochemical reaction, it is important to remember that the very act of electron transfer takes place at a surface, whereas the material to be reduced or oxidized is dispersed in a volumetric phase. Thus mass transfer from the bulk of the solution (or to the bulk solution, for the products) plays a central role in electrochemical processes. As such the physical processes of mass transfer (diffusion, migration, and... 

The diffusion coefficient D(y) is a fimction of temperature, and it varies with position near the electrode according to the local temperature variation. However, as the thermal layer thickness is about five times larger than the diffusion layer thickness, the dif ion coefficient has in fact a variation that can be assumed to be negligible within the mass-transfer diffusion layer corresponding to the integration domain of equation (14.51). Thus, in the following development, D(y) = D, and dD/dy = 0. 

Dry deposition of air particles Mass transfer (diffusion and advection) downward to groundwater... 

H has the dimensions of a length and has been called the height of a reactor unit, by analogy with heights of transfer units and equivalent theoretical plates. Interpret Eq. (6.5.4) to show that H is the sum of a height for external mass transfer HTU) and a term dependent on the reaction, the so-called height of a catalytic unit (HCU). Examine the contribution of these terms when the mass transfer, diffusion, and kinetic regimes are dominant. 

Taylor, R. and Krishnamurthy, R., Film Models for Multicomponent Mass Transfer.—Diffusion in Physiological Gas Mixtures, Bull. Math. Biol., 44, 361-376 (1982). 

Step 1 Open FEMLAB and choose Chemical Engineering, ID, Mass Transfer, Diffusion. The variable c is a stand-in for velocity, v. (You can change the variable name if desired.)... 

In some situations, the oxygen or proton reduction reaction during metal corrosion will be mass transfer (diffusion) controlled, due to poor fluid agitation and/or a low concentration of H or dissolved oxygen in solution (this is especially trae for O2, which has a low solubility in water at... 

Since mass transfer (diffusion) resistance is typically geometry-dependent (just like the ohmic resistance), it promotes non-uniform distribution. The activation (kinetics) resistance, on the other hand, is geometry independent and tends to level the distribution. A large value for L (L > > 1) implies, therefore, kinetics resistance dominance with a uniform current distribution on the micro-scale. L may therefore be viewed as a micro-leveling parameter, in analogy with the Wagner number on the macroscopic scale. 

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