Sources diffuse

V. Point Source Diffusion Formulas Based on a Gaussian Distribution. 233... 

The presumption of a Gaussian distribution for the mean concentration from a point source, although demonstrated only in the case of stationary, homogeneous turbulence, has been made widely and, in fact, is the basis for many of the atmospheric diffusion formulas in common use. Based on the developments of Section IV, we present in this section the Gaussian point source diffusion formulas that have been used for practical calculations. 

Diffusion systems are based upon the ability of the antibiotic to diffuse through agar and cause the inhibition of the sensitive assay strains. Since the substrate to be assayed is applied in a "point source," diffusion occurs radially. A circular zone of inhibition forms and the size of the zone is a function of the concentration. This function is expressed as a linear relationship between the size of the zone of inhibition and the logarithm of the concentration. 

Figure 1-7 Evolution of concentration profiles for (a) one-dimensional point-source diffusion and (b) 3-D point-source diffusion. This calculation is made for M= 100 kg/m, and Oeddy lO " ui /s (eddy diffusivity). in the 3-D case, C was much higher at the center at smaller times because initial mass distribution was at a point instead of a plane but at greater times, the concentration dissipates much more rapidly.

The mathematical translation of the plane-source problem is as follows. Initially, there is a finite amount of mass M but very high concentration at a = 0, i.e., the density or concentration at a = 0 is defined to be infinite (which is unrealistic but merely an abstraction for the case in which initially the mass is concentrated in a very small region around a = 0). The initial condition is not consistent with that required for Boltzmann transformation. Hence, other methods must be used to solve the case of plane-source diffusion. Because this is the classical random walk problem, the solution can be found by statistical treatment as the following Gaussian distribution ... 

For two-dimensional (line-source) diffusion, the mean square displacement is 4Dt. For three-dimensional (point-source) diffusion, the mean square distance is 6Dt. 

Figure 4.5 One-dimensional diffusion into an infinite domain, (a) Point source diffusing into a line, (b) Line source diffusing into a plane, (c) Planar source diffusing into a volume.

For various instantaneous localized sources diffusing out into an infinite medium, the solution is a spreading Gaussian distribution ... 

The form of the solution for one-dimensional diffusion is illustrated in Fig. 5.3. The solution c(x,t) is symmetric about x = 0 (i.e., c(x,t) = c(—x,t)). Because the flux at this location always vanishes, no material passes from one side of the plane to the other and therefore the two sides of the solution are independent. Thus the general form of the solution for the infinite domain is also valid for the semi-infinite domain (0 < x < oo) with an initial thin source of diffusant at x = 0. However, in the semi-infinite case, the initial thin source diffuses into one side rather than two and the concentration is therefore larger by a factor of two, so that... 

Diffusion of PCBs from highly contaminated surficial sediments in areas of concern may be an important net source to the Great Lakes. In fact, PCB diffusion from the porewaters of heavily contaminated coastal and riverine sediments may justify the removal of those sediments. Porewater diffusion in open lake sediments is not a major source. Diffusion of PCBs from porewater is governed by an effective diffusion or mass transfer coefficient and the... 

As the ions from the instantaneous plane source diffuse into the solution, their concentration at various distances will change with time. The problem is to calculate the distance and time variation of this concentration. 

The occurrence of etch rate reduction on highly boron doped materials appears to be independent of doping methods, whether by solid-source diffusion, epitaxial growth, or ion implantation. However, the boron concentration at which significant reduction occurs is different for different methods of doping. The critical boron concentration for etch rate reduction to occur is affected by the defect density in different doped materials. It is found that for similar boron concentrations the amount of etch rate reduction in KOH solutions decreases with increasing defect densityIn... 

No. DiWusion path routes Diffusion source Diffusion sink Densifi cation... 

Summary of Gaussian Point Source Diffusion Formulas... 

The various point source diffusion formulas we have derived are summarized in Table 18.2. 

SUMMARY OF GAUSSIAN POINT SOURCE DIFFUSION FORMULAS 923... 

Ion exchange, or ionic inter diffusion, occurs when a glass containing one mobile ion. A, is exposed to a source of a different mobile ion, B. Ions from the glass diffuse out of the sample, while ions from the source diffuse into the sample. Since these ions have different sizes, their mobilities in the glass are different. The faster ion will tend to outrun the slower ion, which will cause an electric field to develop within the glass. This field will act to slow the faster ion and to accelerate the slower ion, until the fluxes of the two ions are identical The overall process can be described by an interdiffusion coefficient, D, which is given by ... 

Impurities caused by diffusion from other sources. Diffusion rate is evaluated to be about 50 g 02/day. Total amount of impurities is about 720 kg. 

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