Rectangular channel, diffusion

An aerosol size distribution can, therefore, be described in terms of the count median diameter, d, and the geometric standard deviation, a These parameters were obtained from experimental data using a diffusion battery method (Busigin et al., 1980). A diffusion battery is an assembly of a number of cylindrical or rectangular channels. The relative penetration of aerosols through different sizes of diffusion batteries at specified flow rates allows the aerosol size distribution to be calculated. 

In macroscopic reactors, knowledge of the velocity profile in the channel cross-section is a necessary and sufficient prerequisite to describe the material transport. In microscopic dimensions down to a few micrometers, diffusion also has to be considered. In fact, without the influence of diffusion, extremely broad residence time distributions would be found because of the laminar flow conditions. Superposition of convection and diffusion is called dispersion. Taylor [91] was among the first to notice this strong dominating effect in laminar flow. It is possible to transfer his deduction to rectangular channels. A complete fluid dynamic description has been given of the flow, including effects such as the influence of the wall, the aspect ratio and a chemical wall reaction on the concentration field in the cross-section [37]. 

This effect is more distinct in a very flat rectangular channel and even more so in a liquid system, as shown in Fig. 4.33 for the water-acetone system at 25 °C. Diffusion coefficients of liquids are close to 1(T5 cm2 s a value four orders of magnitude smaller than the diffusion coefficients of gases. In consequence, the dispersion... 

A more general case was studied in Refs. 4 and 5, where different initial solute distributions were examined, including the distributions describing the syringe inlet with and without the stop-flow relaxation. The 3D generalized dispersion theory was used to solve the 3D diffusion-convection equation. Unlike Refs. 2 and 3, the exact equation for flow profile in the rectangular channel was used ... 

Several published works have been devoted to the mathematical solution of the problems of penetration of aerosols through a diffusion battery, which is essentially a bundle of identical circular or rectangular channels in parallel [11]. The deposited matter is characterized only by its diffusion coefficient it means that the derived formulae hold for aerosol particulates, as well as for molecular entities. 

Based on their abihty to convert reactants to products via first-order irreversible chemical kinetics, in rectangular channels with various aspect ratios at large Damkohler numbers (i.e., p = 1000) in the diffusion-limited regime. Reactant molar density vs. channel length follows a single exponential decay for those deposition profiles that are not underlined. 

Chatwin PC, Sullivan PJ (1982) The effect of aspect ratio on longitudinal diffusivity in rectangular channels. J Fluid Mech 120 347-358... 

Anderson JL, Moldoveanu S (1984) Numerical simulation of convective diffusion at a rectangular channel flow electrode. 

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