Mass transfer contribution

To minimize the multiple path and mass transfer contributions to plate height (equations 12.23 and 12.26), the packing material should be of as small a diameter as is practical and loaded with a thin film of stationary phase (equation 12.25). Compared with capillary columns, which are discussed in the next section, packed columns can handle larger amounts of sample. Samples of 0.1-10 )J,L are routinely analyzed with a packed column. Column efficiencies are typically several hundred to 2000 plates/m, providing columns with 3000-10,000 theoretical plates. Assuming Wiax/Wiin is approximately 50, a packed column with 10,000 theoretical plates has a peak capacity (equation 12.18) of... 

The aim of this example is to demonstrate the use of the simplified model for reactions other than first order with respect to the gas reactant and zero order to the liquid one, and more specifically to demonstrate the case of first order with respect to the gas reactant and half order to the liquid one, which may have, under specific operating conditions, an analytic solution. For example, if the liquid mass superficial velocity was higher, say 10 kg/m2 s, the wetting efficiency is 1 and the mass transfer contribution lower than 4.07%. At the same time, there is no contribution of the unwetted part of the catalyst. Under these conditions, the approximate model is expected to exhibit a better performance. The same result can be achieved for smaller particles. 

Longitudinal diffusion is the major source of diffusion. Eddy diffusion and resistance to mass transfer contribute only to packed columns. 

Sunderland (1974) showed that for a frequency of reciprocation of 50 cps, the reactor demonstrated nonideal macromixing only for amplitudes of reciprocation approaching zero. Experiments with the oxidation of o-xylene indicated that the reactor effectively minimized heat and mass transfer contributions to overall reaction rate, but the proper evaluation of extent of effectiveness requires further experimental measurements of heat and mass transfer coefficients (fluid-solid) for varying rates of reciprocation of the piston. 

Originally, Houghton [13] derived his equation with the assumption that the mass transfer kinetics is infinitely fast but that axial dispersion caimot be neglected. In view of the previous discussion (Section 10.1), we can extend the validity of the Houghton approach to the case of a finite rate of mass transfer, by lumping axial dispersion and mass transfer contributions into an apparent dispersion coefficient. 

There is no convective (i.e., mass transfer) contribution to the energy flux for the coolant E ... 

Particle nucleation generates a contribution similar to the mass-transfer term involving i inEq. (4.105). It is also important to recognize that the model for [Pg.126]

Santacesaria deduced a unique rate expression for PO consumption, considering both chemical and mass transfer contributions (Equation 4.21) [62-67] ... 

Mass transfer, contribution to HETP, 103 Mercuric ion, as adsorbent additive, 177 Molecular areas, see A, values Molecular orbital theory, see Pi electronic properties... 

Prominent models for estimating peak profiles carry out a differentiation of the equilibrium isotherm with approximations for the mass transfer contribution. The equilibrium-dispersive model, above, assumes that all contributions due to nonequilibrium can be lumped into an apparent axial dispersion term. It further assumes that the apparent dispersion coefficient of the solutes remain constant, independent of the concentration of the sample components. For small particles, these approximations are reasonable for many applications. The ideal model assumes that the column efficiency is infinite. There is no axial diffusion, and the two phases are constantly at equilibrium. The band profiles obtained as solutions are in good agreement with experimental chromatograms for columns with N > 1000 having high loading factors. On the other... 

The importance of external mass transfer can be judged by comparing kgU and kt] or their reciprocals, which are resistances. For example, if kga = 10 and krj = 2 (any consistent units), Kq = 1.67 and external mass transfer contributes 0.1/0.6 or 17 percent of the overall resistance to the process of mass transfer plus reaction. 

The major difficulty in the analysis of chromatographic data is separating the axial dispersion and mass-transfer contributions since, except for gaseous systems at very low flow rates, the axial dispersion coefficient (Dl) is velocity dependent. For liquid systems Dl varies essentially linearly with velocity so a plot of HETP vs. superficial velocity (ev) should be linear with the mass-transfer resistance directly related to the slope (Fig. 6). For gaseous systems at a high Reynolds number this same plot can be used, but in the low Reynolds number region a plot oiH/v vs. 1 /v may be more convenient since in this region Dl is essentially constant and the intercept thus yields the mass-transfer resistance [43-45]. 

A second difference, between gas and liquid chromatography, lies in the mode of solute dispersion. In the first instance, virtually all LC columns are packed (not open tubes) which introduces a dispersion process into the column that is not present in the GC capillary column. In a packed column the solute molecules will describe a tortuous path through the interstices between the particles and obviously some will travel shorter paths than the average, and some longer paths. Consequently, some molecules will move ahead of the average and some will lag behind, thus causing band dispersion. This type of dispersion is called multipath dispersion and is an additional contribution to longitudinal diffusion, and the two resistance to mass transfer contributions, to the overall peak variance. 

For the mass transfer contribution in the Taylor flow regime, the film thickness is of particular importance and many studies have been concerned with its characterization (see Chapter 11). 

Figure 9.9 Schematic of Taylor flow showing the definitions of the unit cell, gas bubble length Lb and the liquid slug length L,. The lengths of the nose L ose and tail L,aii sections of the gas bubble are also indicated. Mass transfer contributions in the Taylor flow are indicated with the numbers (i) bubble to wall through film, (2) bubble to slug, and (3) slug to wall.

In comparison to isothermal membrane processes, little attention has been paid to date to polarisation phenomena in non-isothermal processes. In non-isothermal processes such as membrane distillation and thermo-osmosis, transport through the membrane Occurs when a temperature difference is applied across the membrane. Temperature polarisation will occur in both membrane processes although both differ considerably in membrane structure, separation principle and practical-application. In a similar manner to concentration polarisation in pressure-driven membrane processes, coupled heat and mass transfer contribute towards temperature polarisation. 

Besides masking, elemental transfer can occtir between two dissimilar materials in contact with the same liquid metal (even isothermally) due to an activity gradient. Again, experiments with only one solid material in contact with the liquid metal would avoid this complication. However, if this type of system cannot be used, careful surface analysis of as-exposed specimens shordd be used to try and understand mass transfer contributions from dissimilar material driving forces. 

Ammons, Dougharty, and Smith have studied the adsorption of methyl-mercuric chloride from aqueous solution by activated carbon by both batch and flow techniques. The data were analysed to investigate the factors that control the breakthrough curves. Axial dispersion was found to contribute no more than 15% to the second moment of the breakthrough curve, while liquid-to-particle mass transfer contributed about 60%. On a similar topic Benediktov, Vlasov, and Yurkevich in a paper of which only the title is abstracted, discuss the determination of the degree of exhaustion of active carbon with respect to organic substances during adsorption from aqueous solutions. 

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