Axial dispersion contribution

The elimination or estimation of the axial dispersion contribution presents a more difficult problem. Established correlations for the axial dispersion coefficient are notoriously unreliable for small particles at low Reynolds number(17,18) and it has recently been shown that dispersion in a column packed with porous particles may be much greater than for inert non-porous particles under similar hydrodynamic conditions(19>20). one method which has proved useful is to make measurements over a range of velocities and plot (cj2/2y ) (L/v) vs l/v2. It follows from eqn. 6 that in the low Reynolds number region where Dj. is essentially constant, such a plot should be linear with slope Dj, and intercept equal to the mass transfer resistance term. Representative data for several systems are shown plotted in this way in figure 2(21). CF4 and iC io molecules are too large to penetrate the 4A zeolite and the intercepts correspond only to the external film and macropore diffusion resistance which varies little with temperature. 

Axial dispersion contributes to the broadening of the adsorption front due to flow in the void spaces between particles. Similar to diffusion phenomena, dispersion effect in the bed is expressed in terms of the following dispersion model ... 

Neglecting flow nonuniformities, the contributions of molecular diffusion and turbulent mixing arising from stream sphtting and recombination around the sorbent particles can be considered additive [Langer et al., Int. ]. Heat and Mass Transfer, 21, 751 (1978)] thus, the axial dispersion coefficient is given by ... 

They convert the initial value problem into a two-point boundary value problem in the axial direction. Applying the method of lines gives a set of ODEs that can be solved using the reverse shooting method developed in Section 9.5. See also Appendix 8.3. However, axial dispersion is usually negligible compared with radial dispersion in packed-bed reactors. Perhaps more to the point, uncertainties in the value for will usually overwhelm any possible contribution of D. ... 

Kang, Fan and Kim(96) measured coefficients for heat transfer from a cone-shaped heater to beds of glass particles fluidised by water. They also found that the heat transfer coefficient passed through a maximum as the liquid velocity was increased. The heat transfer rate was strongly influenced by the axial dispersion coefficient for the particles, indicating the importance of convective heat transfer by the particles. The region adjacent to the surface of the heater was found to contribute the greater part of the resistance to heat transfer. 

It has been demonstrated that radial dispersion contributes more significantly to the dilution of the sample in the flow than does axial dispersion. This type of fluid movement, termed secondary flow by Tijssen [43], results in a washout effect accounting for the low mutual contamination of samples successively injected into a carrier stream. TTiis advantageous feature is a result of the use of low flow rates and small tubing bores, and results in decreased peak-width and hence to increased sampling rate. 

Axial dispersion can affect measurements of decay and growth rates of transients of interest. In Figure 5 is sketched the concentration of a transient, initially formed as a square wave by a light pulse of uniform intensity from — L < x < L and zero elsewhere. As shown in Figure 6, at later times the profile becomes smoothed by diffusion. As the purge flow pushes reactive species past the pinhole at x = 0, the spatial dependence of the concentration becomes a time-varying concentration that will contribute to any time variation caused by kinetics. 

Axial dispersion. An axial (longitudinal) dispersion coefficient may be defined by analogy with Boussinesq s concept of eddy viscosity ". Thus both molecular diffusion and eddy diffusion due to local turbulence contribute to the overall dispersion coefficient or effective diffusivity in the direction of flow for the bed of solid. The moles of fluid per unit area and unit time an element of length 8z entering by longitudinal diffusion will be - D L (dY/dz)t, where D L is now the dispersion coefficient in the axial direction and has units ML T- (since the concentration gradient has units NM L ). The amount leaving the element will be -D l (dY/dz)2 + S2. The material balance equation will therefore be ... 

This study, which contributes towards the understanding of hydrodynamic behaviour of gas-liquid reactors at elevated pressure, has shown the influence of pressure on the gas flow in a packed column through the axial dispersion coefficient. The gas flow diverges from plug flow when the pressure increases. As for the gas hold-up, an important parameter for the calculation of the reactional volume of a reactor, the pressure has no effect on this parameter in the studied range. This result allows to extrapolate gas hold-up values obtained... 

Equation 5.29 shows that the variance of the response curve is separable into contributions from the axial dispersion, and from the external and internal mass transfer. Measurements at different velocities lead to an estimate of all transport coefficients. 

The total axial dispersion coefficient of the emulsion phase calculated from Eq. (4-16) is shown in Figs. 40 and 41 as a function of Dt and C/q, in reasonable agreement with experimental data. The 25 shown here are for particles of good fluidity. Also, note in Figs. 40 and 41 that the second term in the right-hand side of Eq. (4-16) tends to be significant as Dt increases. At Uq = 20 cm/sec the contribution of this term to is 10% for Dt = 100 cm and 22% for Dt = 300 cm. At C/g = 50 cm/sec the contribution decreases down to about 0.75 times the mentioned levels. 

Most chromatographic production systems use particulate adsorbents with defined pore structures due to the higher loadability of mesoporous adsorbents compared with non-porous adsorbents. Adsorption of the target molecules on the inner surface of a particle has a tremendous influence on the efficiency of a preparative separation. Several factors with regard to mass transfer that contribute to the total band broadening effect in addition to axial dispersion can be distinguished (Fig. 2.10) ... 

However, the definitions related to specific processes have to be kept in mind. In chromatography the plate height is a measure that lumps together the contribution of the fluid dynamic non-idealities (axial dispersion) and the mass transfer resistance... 

Sufficient sensitivity (need not to be too sensitive, as no trace detection is the goal in preparative chromatography, but the sensitivity should be high enough to keep the flow cell volume, which contributes to the axial dispersion, small)... 

Column Length and diameter Flow distribution and collection Adjust to the needs of the separation Secure low contributions to the axial dispersion... 

The axial dispersion coefficient D ix depends only on the quality of the packing and represents any deviation of the fluid dynamics from plug flow. The contribution of molecular diffusion is generally negligible (Section 6.5.6.2). 

The axial dispersion coefficient is determined from the concentration profile of a non-penetrating tracer (Tl). A reasonable approximation for its velocity dependence goes back to van Deemter et al. (1956). The axial dispersion coefficient is the sum of the contributions of eddy diffusion and molecular diffusion (Chapter 2.3.4) ... 

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