Diffusion coefficients agglomerate

For z = hja 1 (prolate or cigar-shaped ellipsoid), the diffusion coefficient is 

The diffusion coefficient of the ellipsoid is always less than that of a sphere of equal volume. However, over the range 10 z 0.1, the coefficient for the ellipsoid is always greater than 60% of the value for the sphere. These results are not directly applicable to the diffusion of particles suspended in a shear field, because all orientations of the particle are no longer equally likely. 

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Figure 4.10 A schematic model for tracer diffusion in a compacted nanocrystalline sample. Dg isthe bulk lattice diffusion coefficient, Dg/, is the grain boundary diffusion coefficient, Da is the inter-agglomerate diffusion coefficient, tf is the grain size, 5 is the width ofthe grain boundary, and 5a is the separation between agglomerates.

Turbulent agglomeration. Far turbulent agglomeration two cases should be considered. First, if the inertia of the aerosol particles is approximately the same as that of the medium, the particles will move about with the same velocities as associated air parcels and can be characterized by a turbulence or eddy diffusion coefficient DT. This coefficient can have a value 104 to 106 times greater than aerosol diffusion coefficients. Turbulent agglomeration processes can be treated in a manner similar to conventional coagulation except that the larger diffusion coefficients are used. 

In general, primary panicle size increased with volume loading, solid-state diffusion coefficient, and maximum temperature. Larger panicles were also obtained by decreasing the jet velocity. The number of particles per agglomerate increased with volume loading and decreased with solid-state diffusion coefficient and maximum temperature. 

The further development of mathematical representations of estuarine processes should proceed simultaneously with investigations of both specific sedimentary processes and regional sedimentary systems. For the model proposed here some of the specific processes that deserve attention in the future include the processes that control the rate of formation of marine mud at the base of the surficial layer of agglomerates and the relationship between the eddy-diffusion coefficient for sand transport and fluctuations in the water velocity. The study of specific processes tell us little about the long-term manifestations of these processes. For this there is the need to develop comprehensive descriptions of estuarine sedimentary systems and to begin to contrast and compare sediment budgets in different coastal areas. 

We use Bruggemann formula to relate the effective diffusion coefficient of protons in micropores, to the relative volume portion of micropores in agglomerates and the proton diffusion coefficient in water. 

The fractal dimension of an agglomerate is not the only number that characterizes the morphology. There are other numbers, related to the fractal dimension, that characterize properties such as diffusion coefficients and mechanical strength. In the case of nonfractal objects or sets, these numbers are equal to the dimension d of the topological space (d = 3 mostly). 

If we now postulate that the mechanism of crystal inhibition is related to the hindering of the growth of agglomerates to their critical size, we can say that this will happen if one or more poljmaer molecules can diffuse into the volume Vi and reach the then subcritical agglomerate faster than the molecules of the dissolved salt present in the same volume. One possible use of the equation is therefore to calculate the concentration of the polymer needed in the solution to stop the nuclei from growing, once the diffusion coefficients are known or measured and die concentrations of the scaling salts are also known. 

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