Eddy dispersion

The eddy dispersion coefficient has been measured and correlated empirically as... 

Axial and radial dispersion or non-ideal flow in tubular reactors is usually characterised by analogy to molecular diffusion, in which the molecular diffusivity is replaced by eddy dispersion coefficients, characterising both radial and longitudinal dispersion effects. In this text, however, the discussion will be limited to that of tubular reactors with axial dispersion only. Otherwise the model equations become too complicated and beyond the capability of a simple digital simulation language. 

In the above case, D is an eddy dispersion coefficient and Z is the axial distance along the reactor length. When combined with an axial convective flow contribution, and considering D as constant, the equation takes the form... 

Here the nomenclature is the same as in Sec. 4.4.2 and in addition, Dq is the effective eddy dispersion coefficient for the organic or extract phase (m / s) and Dl is the effective eddy dispersion coefficient for the aqueous or feed phase (m / s). The above equations are difficult to solve analytically (Lo et al., 1983) but are solved with ease, using digital simulation. 

As previously indicated, this discussion is organized for chromatograms from very narrow polymer standards for which we can consider that the effect of molecular weight distribution is negligible and for which the unique separation process is size exclusion. With these limitations, the contribution to band broadening is conveniently separated into extra column effects, eddy dispersion, static dispersion, and mass transfer. In the most classical chromatographic interpretation, extra-column effects are not discussed and the three other contributions are considered as Gaussian, so there is simply the addition of their variances. The number of theoretical plates is defined as N = VJaY and the influence of v, the linear velocity of the eluent, is summarized by the so-called Van Deemter equation ... 

Eddy dispersion coefficient Inverse residence time Inverse dispersion time Fractional phase holdup Superficial phase velocity... 

The A term depends on eddy dispersion and is proportional to tbe diameter of the punicles, df. Tbe axial diffusion constant B is proportional to the molecular diffusivity DM of the solute. The mase tieasfer effect, the C terms, iocludes mass transfer outside the purticles—C proportional to dpD, and mass transfer in the solid or the conled liquid phase—Q proportioanl to d /Ds, where df is the film thickness and is the diffesion coefficieni in the stationaty phase,... 

Movement of a soluble chemical throughout a water body such as a lake or river is governed by thermal, gravitational, or wind-induced convection currents that set up laminar, or nearly frictionless, flows, and also by turbulent effects caused by inhomogeneities at the boundaries of the aqueous phase. In a river, for example, convective flows transport solutes in a nearly uniform, constant-velocity manner near the center of the stream due to the mass motion of the current, but the friction between the water and the bottom also sets up eddies that move parcels of water about in more randomized and less precisely describable patterns where the instantaneous velocity of the fluid fluctuates rapidly over a relatively short spatial distance. The dissolved constituents of the water parcel move with them in a process called eddy diffusion, or eddy dispersion. Horizontal eddy diffusion is often many times faster than vertical diffusion, so that chemicals spread sideways from a point of discharge much faster than perpendicular to it (Thomas, 1990). In a temperature- and density-stratified water body such as a lake or the ocean, movement of water parcels and their associated solutes will be restricted by currents confined to the stratified layers, and rates of exchange of materials between the layers will be slow. 

For conventional packings and linear isotherms Van Deemter et al. [10] developed the well-known equation for HETP including contributions from eddy dispersion (A-term), molecular diffusion (B-term) and intraparticle kinetics (C-term). 

Bubble columns are used for liquid aeration and gas-liquid reactions. Thus, finely suspended bubbles produce large interfacial areas for effective mass transfer, where the contact area per unit volume of emulsion is calculated from the expression a 6e/dg, where e is the volume fraction of injected gas. While simple to design and construct, bubble columns sustain rather large eddy dispersion coefficients, and this must be accounted for in the modeling process. For cocurrent operation, liquid of... 

A final value needed to solve the complete set of equations is the eddy dispersion coefficient, Eq. The Chung and Wen (1968) correlation is commonly used to determine Eq. 

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