Effect diffusion

Ahn C B and Cho Z H 1989 A generalized formulation of diffusion effects in pm resolution nuclear magnetic-resonance imaging Med. Rhys. 16 22-8... 

Thermal transpiration and thermal diffusion effects have been neglected in developing the dusty gas model, and will be neglected throughout the rest of the text. The physics of these phenomena and the justification for neglecting them are discussed in some detail in Appendix I. 

Thermal diffusion effects will be neglected throughout, so the flux relations are given by equations (3.17) - (3.19), which are repeated here for convenience ... 

Synthesis ofp-Ethyltoluene. j )i7n7-Ethyltoluene, the feedstock for j )-methylstyrene, is difficult to separate from the products of toluene alkylation with ethane using conventional acidic catalysts. The unique configurational diffusion effect of ZSM-5 permits -dialkylbenzenes to be produced in one step. In the alkylation of toluene with ethene over a chemically modified ZSM-5, -ethyltoluene is obtained at 97% purity (58). 

A second type of apparatus based on the pressure diffusion effect is the separation nozzle. Pressure gradients in a curved expanding jet produce an isotopic separation similar to that in a centrifuge. The separation effect obtained with a single jet is relatively small, and separation nozzle stages, similar to gaseous diffusion stages, must be used in a cascade to realize most of the desired separations. 

Mass Transport. An expression for the diffusive transport of the light component of a binary gas mixture in the radial direction in the gas centrifuge can be obtained directly from the general diffusion equation and an expression for the radial pressure gradient in the centrifuge. For diffusion in a binary system in the absence of temperature gradients and external forces, the general diffusion equation retains only the pressure diffusion and ordinary diffusion effects and takes the form... 

Binary Electrolyte Mixtures When electrolytes are added to a solvent, they dissociate to a certain degree. It would appear that the solution contains at least three components solvent, anions, and cations, if the solution is to remain neutral in charge at each point (assuming the absence of any applied electric potential field), the anions and cations diffuse effectively as a single component, as for molecular diffusion. The diffusion or the anionic and cationic species in the solvent can thus be treated as a binary mixture. 

Driven by the concentration gradient, solutes naturally diffuse when contained in a fluid. Thus, a discrete solute band will diffuse in a gas or liquid and, because the diffusion process is random in nature, will produce a concentration curve that is Gaussian in form. This diffusion effect occurs in the mobile phase of both packed GC and LC columns. The diffusion process is depicted in Figure 6. 

Diffusion effect The capture of particles due to Brownian motion. 

Diffusion effects can be expected in reactions that are very rapid. A great deal of effort has been made to shorten the diffusion path, which increases the efficiency of the catalysts. Pellets are made with all the active ingredients concentrated on a thin peripheral shell and monoliths are made with very thin washcoats containing the noble metals. In order to convert 90% of the CO from the inlet stream at a residence time of no more than 0.01 sec, one needs a first-order kinetic rate constant of about 230 sec-1. When the catalytic activity is distributed uniformly through a porous pellet of 0.15 cm radius with a diffusion coefficient of 0.01 cm2/sec, one obtains a Thiele modulus y> = 22.7. This would yield an effectiveness factor of 0.132 for a spherical geometry, and an apparent kinetic rate constant of 30.3 sec-1 (106). 

Accumulatory pressure measurements have been used to study the kinetics of more complicated reactions. In the low temperature decomposition of ammonium perchlorate, the rate measurements depend on the constancy of composition of the non-condensable components of the product mixture [120], The kinetics of the high temperature decomposition [ 59] of this compound have been studied by accumulatory pressure measurements in the presence of an inert gas to suppress sublimation of the solid reactant. Reversible dissociations are not, however, appropriately studied in a closed system, where product readsorption and diffusion effects within the product layer may control, or exert perceptible influence on, the rate of gas release [121]. 

The relative magnitudes of the thermal diffusion and diffusion effects are represented by the dimensionless ratio ... 

If a local concentration of solute is placed at the midpoint of a tube filled with either a liquid or a gas, the solute will slowly diffuse to either end of the tube. It will first produce a Gaussian distribution with a maximum concentration at the center and finally, when the solute reaches the end of the tube, end effects occur and the solute will continue to diffuse until there is a constant concentration throughout the length of the tube. This diffusion effect occurs in the mobile phase of a packed LC column but the end effects are never realized. The diffusion process is depicted in figure 2. 

Weisz, P. B. and Hicks, J. S., The behaviour of porous catalyst particles in view of internal mass and heat diffusion effects, Chem. Eng. Sci., 17, 265-275 (1962). 

It has been reported by Lewis et al. [1] that the equivalence ratio where the minimum ignition energy has a minimum is dependent on the fuel property for hydrocarbon fuel and air mixtures, and that it moves to the rich side as the molecular weight of the fuel increases. This equivalence ratio dependency has been explained by the preferential diffusion effect. 

When both hydrodynamic and thermo-diffusive effects are simultaneously taken into account, it is found that the growth rate a of wrinkling is given by the roots of the dispersion relation [11,12] ... 

Bechtold, J.K. and Matalon, M., Hydrodynamic and diffusion effects on the stability of spherically expanding flames. Combust. Flame, 67, 77,1987. 

In order to eliminate the possibility that the observed FRC signal was due to diffusion effects or other experimental artifacts, two types of blank runs were performed with each catalyst. In one set of experiments, Ife was used as the "adsorbing" gas with a reduced catalyst while in a second set, H2 was used with a non-reduced catalyst. Neither type or experimental led to any observable FRC signal. 

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