Diffusion resistance reaction

This Choice of 0 and k gives a raiher low total conversion. Since diffusion-reaction resistance is the larges by far, W coefficient is almost linear in it. 

The model postulates two significant resistances in series diffusion through the growing shell ( R.jyp) and polymerization at the catalyst surface (R(jat catalytic reaction resistance,... 

Equation (1) consists of various resistance terms. l/Kj a is the gas absorption resistance, while 1/ K,a corresponds to the maleic anhydride diffusion resistance and l/i k represents the chemical reaction resistance. The reaction rate data obtained under the reaction conditions of 250°C and 70 atm were plotted according to equation (1). Although catalytic reaction data with respect to time on stream were not shown here, a linear correlation between reaction rate data and catalyst loading was observed as shown in Fig. 2. The gas absorption resistance (1/ a) was -1.26 h, while the combined reaction-diffusion resistance (lJK,a + 1 T]k) was determined to be 5.57 h. The small negative value of gas absorption resistance indicates that the gas-liquid diffusion resistance was very small and had several orders of magnitude less than the chanical reaction resistance, as similarly observed for the isobutene hydration over Amberlyst-15 in a slurry reactor [6]. This indicates that absorption of malei c anhydride in solvent was a rapid process compared to the reaction rate on the catalyst surface. 

Equation (6.42) is a generalization of Eqs. (6.25) and (6.30) it shows that the formal resistance is the sum of reaction resistance (the first term in parentheses) and diffusion resistance (the second and third terms). Equation (6.40) yields directly the important relation... 

Figure 7. (A, top) Simple battery circuit diagram, where Cdl represents the capacitance of the electrical double layer at the electrode—solution interface (cf. discussion of supercapacitors below), W depicts the Warburg impedance for diffusion processes, Rj is the internal resistance, and Zanode and Zcathode are the impedances of the electrode reactions. These are sometimes represented as a series resistance capacitance network with values derived from the Argand diagram. This reaction capacitance can be 10 times the size of the double-layer capacitance. The reaction resistance component of Z is related to the exchange current for the kinetics of the reaction. (B, bottom) Corresponding Argand diagram of the behavior of impedance with frequency, f, for an idealized battery system, where the characteristic behaviors of ohmic, activation, and diffusion or concentration polarizations are depicted.

Let us finally comment on the morphological stability of the boundaries during metal oxidation (A + -02 = AO) or compound formation (A+B = AB) as discussed in the previous chapters. Here it is characteristic that the reaction product separates the reactants. 1 vo interfaces are formed and move. The reaction resistance increases with increasing product layer thickness (reaction rate 1/A J). The boundaries of these reaction products are inherently stable since the reactive flux and the boundary velocity point in the same direction. The flux which causes the boundary motion pushes the boundary (see case c) in Fig. 11-5). If instabilities are occasionally found, they are not primarily related to diffusional transport. The very fact that the rate of the diffusion controlled reaction is inversely proportional to the product layer thickness immediately stabilizes the moving planar interface in a one-... 

The following can be concluded from Eq. (8.21) (1) A large particle has very large diffusion resistance and (2) An increase in Ts yields reduced reaction resistance. The inference made by Tamir in Ref. [5] on the influence of T is incorrect. 

O. Thomas, C.S. Petersson, F.M. d Heurle. The reaction of scandium thin films with silicon diffusion, nucleation, resistivities // Appl.Surf.Sci.- 1991.- V.53.- P.138-146. 

Figure 3.4 Different diffusion-related resistances in a gas—liquid—solid reaction. (Diffusion from bulk gas to the gas—liquid interface is represented by 1 movement through the gas—liquid film is 2, etc.)...

Let us consider a shallow fluidized bed combustor with multiple coal feeders which are used to reduce the lateral concentration gradient of coal (11). For simplicity, let us assume that the bed can be divided into N similar cylinders of radius R, each with a single feed point in the center. The assumption allows us to use the symmetrical properties of a cylindrical coordinate system and thus greatly reduce the difficulty of computation. The model proposed is based on the two phase theory of fluidization. Both diffusion and reaction resistances in combustion are considered, and the particle size distribution of coal is taken into account also. The assumptions of the model are (a) The bed consists of two phases, namely, the bubble and emulsion phases. The voidage of emulsion phase remains constant and is equal to that at incipient fluidization, and the flow of gas through the bed in excess of minimum fluidization passes through the bed in the form of bubbles (12). (b) The emulsion phase is well mixed in the axial... 

Model accounted for external phase mass transfer resistance, the interfacial reaction resistance, diffusion within the emulsion globule as well as leakage of the internal phase due to membrane breakage. 

For more complex reactions, the effect of intraparticle diffusion resistance on rate, selectivity, and yield depends on the particulars of the network. Also, the use of the Thiele modulus-effectiveness factor relationships is not as easily applicable, and numerical solution of the diffusion-reaction equations may be required. 

Intraparticle Diffusion and External Mass-Transfer Resistance For typical industrial conditions, external mass transfer is important only if there is substantial intraparticle diffusion resistance. This subject has been discussed by Luss, Diffusion-Reaction Interactions in Catalyst Pellets, in Carberry and Varma (eds.), Chemical Reaction and Reactor Engineering, Dekker, 1987. This, however, may not be the case for laboratory conditions, and care must be exerted in including the proper data interpretation. For instance, for a spherical particle with both external and internal mass-transfer limitations and first-order reaction, an overall effectiveness factor r, can be derived, indicating the series-of-resistances nature of external mass transfer followed by intraparticle diffusion-reaction ... 

Consider the diffusion reaction problem (problem 1) with a mass transfer resistance at the surface.[6] [11] The governing equation and boundary conditions for dimensionless concentration are ... 

This model is applicable to the reactions of nonporous pellets and to porous pellets when the global rate is controlled by pore diffusion. Reaction is limited to a surface separating the solid reactant at the core of the pellet surrounded by a porous layer of solid product. It occurs initially on the external surface of the pellet, and the thickness of the product layer increases as the reaction proceeds, as illustrated in Fig. 1. The global reaction rate is determined by three resistances— mass transfer from bulk gas to particle surface, diffusion... 

Eq. (11) shows the relationship between the three reaction resistances. The first term represents the external mass transfer resistance, the second the resistance associated with diffusion through the product layer, and the third the chemical reaction resistance at the reactant-product interface. 

Costa and Smith " studied the hydrofiuorination of nonporous uranium dioxide pellets under conditions where external mass transfer resistance was negligible. The global rate was initially controlled by the surface chemical reaction resistance, but switched to product layer diffusion as the reaction progressed and the product layer thickness increased. 

These components of are transition concentration diffusion reaction crystallization and resistance. 

Photochemically generated acid must diffuse in resist film to catalyze desired reactions and to provide a gain mechanism for amplification. However, excessive diffusion (into the unexposed areas) destroys the linewidth control and eventually the resolution. Thus, as the minimum feature size becomes smaller and smaller, the control of acid diffusion plays a more important and difficult role. Therefore, investigation of acid diffusion in chemical amplification resist film is one of the most active areas of research today. A number of experimental procedures to measure acid diffusion length have been reported [67-88] ... 

If we can set up a system in which the reaction is not controlled by either diffusion or resistance,the rate of the reaction will be determined by the activation over-potential. This follows from the Arrhenius equation which states that... 

In the film diffusion region, r-eff increases slowly with increasing temperature because the diffusion has only a slight temperature dependence. There is practically no reaction resistance, and the gas already undergoes complete conversion on the outer surface of the catalyst. 

An interesting limiting case correspond to negligible resistance from gas to liquid (large Sherwood number values) and negligible diffusion resistance within the liquid with respect to reaction resistance then equations (14 - 18) reduce to ... 

We have been so far conducting the research of varietal difference of apparent photosynthetic rate per unit leaf area (APS) in rice plants, aiming to clarify the mechanism of APS determination. APS is limited by the following two C02 diffusion resistances, stomatal (Rs), and mesophyll (Rm) one. However, the process limited by Rm involves so many different kinds of physical and chemical processes. The purpose of this paper is to divide Rm further to two resistances. One is the physical C02 diffusion resistance from the stomatal cavity to the C02 fixation site in the chroloplasts, and the other is the chemical reaction resistance at the site of ribulose-1,5-bisphosphate carboxylase/oxygenase (RuBisCO). 

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