Relative diffusion

Identification of the pollutant source and installation of the local exhaust is critically important. For example, an improperly designed local exhaust can draw other contaminants through the occupied space and make the problem worse. The physical layout of grilles and diffusers relative to room occupants and pollutant sources can be important. If supply diffusers are all at one end of a room and returns are all at the other end, the people located near the supplies may be provided with relatively clean air while those located near the returns breathe air that has already picked up contaminants from all the sources in the room that are not served by local exhaust. 

In many cases, metal silicides may very well be the catalysts. For example, FeSi2 is being considered to be the catalyst in Fe-assisted nanowire synthesis. This is similar to the silicon mono-oxide case, although it is much easier to understand the mechanisms in the FeSi2 case. It is also possible that during the catalytic processes that silicon diffuses relatively freely through the metal catalyst and consequently, the observed silicides at the end of reaction may be different from those during the catalytic reaction. No direct evidence is available to show whether metal or metal silicide nanoparticles are the tme catalyst. 

In analysing the behaviour of a tubular reactor, the simplest assumption to make is that plug flow occurs. In plug flow, there is negligible diffusion relative to bulk flow and, over any cross-section normal to the fluid motion, the mass flow rate and fluid properties are uniform. This situation is quite closely approached in many industrial reactors and it means that... 

The theoretical curve for Ds/Ds0 in Fig. 16a has been drawn using Eq. (67) with Di0/Dlj0 = 0.622, and agrees fairly well with the simulation data. The longitudinal diffusion relative to the total translational diffusion becomes more important at higher concentrations. 

A major complication exists for constructing the Lagrangian density of a pair of particles diffusing relative to each other. The diffusion (Euler) equation is dissipative and the density of the diffusing species is not conserved. The Euler density, p, would lead to a space—time invariant, Sfr, which would not be constant. This difficulty requires the same approach as that used to handle the Schrodinger equation. Morse and Feshbach [499] define a reverse or backward diffusion equation where time goes backwards compared with that in eqn. (254)... 

Although there is considerable scatter in the diffusivity values for the treated samples, the major effect is a large increase in diffusivity, relative to the original H-mordenite, on either acid extraction or NH4NO3 exchange. On this basis we would conclude that the sodium rather than the aluminum content appears to be the factor of greatest importance. 

Because the adatoms diffuse relatively rapidly along the surface and the ledges to the kinks, many more atoms reach the kinks by these routes than by direct impingement from the vapor. Note the close similarity between this crystal growth process on a vicinal surface and the climb of dislocations depicted in Fig. 11.2. 

The fact that uncouplers are lipophilic weak acids (see above) explains their ability to collapse transmembrane pH gradients. Their lipophilic character allows uncouplers to diffuse relatively freely through the phospholipid bilayer. Because they are weak acids, uncouplers can release a proton to the solution on one side of the membrane and then diffuse across the membrane to fetch another proton. The chemiosmotic theory thus provides a simple explanation of the effects of uncouplers on oxidative phosphorylation. 

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. 

Fick s law of molecular diffusion states that, for a binary mixture of components A and B, the molar flux of component A by ordinary molecular diffusion relative to the molar average velocity of the mixture in the positive z direction, is proportional to the concentration gradient dcA/dz, which is negative in the direction of ordinary molecular diffusion ... 

When the viscosity of a sample is high, the reactive chain ends, which are attached to fairly large molecules, diffuse relatively slowly compared to the monomer and growth occurs primarily by diffusion of the latter to react with the relatively immobile free radicals. It is frequently desirable to form images in samples which are somewhat viscous and depleted of inhibitors. 

Lewis number is a measure of heal diffusion relative to mass diffusion. 

Dialysis and Gas Diffusion Dialysis is often used in continuous-flow methods to separate inorganic ions, such as chloride or sodium, or small organic molecules, such as glucose, from high-molecular-weight species, such as proteins. Small ions and molecules diffuse relatively rapidly through hydrophilic membranes of cellulose acetate or nitrate while large molecules do not. Dialysis usually precedes the determination of ions and small molecules in whole blood or serum. 

To adopt the conventional Pick s law of binary diffusion we assume that in both media one of the components present moves by diffusion relative to the zi and Z2 coordinates and is transfered from one medium to the other. The concentration of the diffusing component at time t is denoted by ci at and by C2 at Z2. 

FIGURE 18.5 The mechanistic basis of the dispersion element. The three dispersion element parameters are a nondimensional dispersion number that measures the rate of signal diffusion relative to convection t, the apparent mean residence time and a, the signal-to-transcript conversion parameter. For the mRNA and protein compartments in the Hargrove-Schmidt model element, kx, kM, and kp are rate constants for translation, mRNA degradation, and protein degradation, respectively. The gray line indicates that information rather than mass is transferred from the TAT mRNA to the TAT protein compartment (140). 

Light hydrocarbons, particularly methane, can diffuse relatively rapidly through imperfect seals. Because reservoir seals are usually not perfect the gases are likely to become depleted over geological time periods. Because diffusion is related to molecular mass, methane containing the 12C isotope diffuses more rapidly than that containing 13C, so there is an isotopic fractionation effect, with the residual gas becoming isotopically heavier (see Section 5.8.6b). 

Calculating Steady State Diffusion Relative Fluxes W, and J Diffusion Through a Stagnant Gas Measuring Gas-Pha.se Ditfusivilies... 

Thermal Diffusion Relative motion of the various molecular species of the given mixture under temperature gradient. 

Equation 8.26 includes two dimensionless parameters that govern the importance of molecular diffusion relative to convection. The parameters are t/R for diffusion in the radial direction and <3 111 for diffusion in the axial direction. They differ in magnitude by a factor of Expressed in terms of the dimensionless variables... 

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