C terms resistance to mass transfer

In open tubular columns dp is replaced by the internal diameter of the column, dc- Diffusion rates in a gas are much higher than in a liquid, therefore in GC the mobile phase effects. Cm, are much smaller than the corresponding effects in the stationary phase, Cs- In HPLC, Gm and Cs are of comparable significance. 

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The curves represent a plot of log (h ) (reduced plate height) against log (v) (reduced velocity) for two very different columns. The lower the curve, the better the column is packed (the lower the minimum reduced plate height). At low velocities, the (B) term (longitudinal diffusion) dominates, and at high velocities the (C) term (resistance to mass transfer in the stationary phase) dominates, as in the Van Deemter equation. The best column efficiency is achieved when the minimum is about 2 particle diameters and thus, log (h ) is about 0.35. The optimum reduced velocity is in the range of 3 to 5 cm/sec., that is log (v) takes values between 0.3 and 0.5. The Knox... 

When u E, this interstitial mixing effect was considered complete, and the resistance to mass transfer in the mobile phase between the particles becomes very small and the equation again reduces to the Van Deemter equation. However, under these circumstances, the C term in the Van Deemter equation now only describes the resistance to mass transfer in the mobile phase contained in the pores of the particles and, thus, would constitute an additional resistance to mass transfer in the stationary (static mobile) phase. It will be shown later that there is experimental evidence to support this. It is possible, and likely, that this was the rationale that explains why Van Deemter et al. did not include a resistance to mass transfer term for the mobile phase in their original form of the equation. 

It is seen that the Van Deemter equation predicts that the total resistance to mass transfer term must also be linearly related to the reciprocal of the solute diffusivity, either in the mobile phase or the stationary phase. Furthermore, it is seen that if the value of (C) is plotted against 1/Dni, the result will be a straight line and if there is a... 

In Figure 7, the resistance to mass transfer term (the (C) term from the Van Deemter curve fit) is plotted against the reciprocal of the diffusivity for both solutes. It is seen that the expected linear curves are realized and there is a small, but significant, intercept for both solutes. This shows that there is a small but, nevertheless, significant contribution from the resistance to mass transfer in the stationary phase for these two particular solvent/stationary phase/solute systems. Overall, however, all the results in Figures 5, 6 and 7 support the Van Deemter equation extremely well. 

Katz et al. [1] also examined the effect of particle diameter on resistance to mass transfer constant (C). They employed columns packed with 3.2 im, 4.4 p,m, 7.8 pm, and 17.5 pm, and obtained HETP curves for the solute benzyl acetate in 4.3%w/w of ethyl acetate in n-heptane on each column. The data were curve fitted to the Van Deemter equation and the values for the A, B and C terms for all four columns extracted. A graph relating the value of the (C) term with the square of the particle diameter is shown in Figure 8. 

Oxygen transfer rate (OTR) The product of volumetric oxygen transfer rate kj a and the oxygen concentration driving force (C - Cl), (ML T ), where Tl is the mass transfer coefficient based on liquid phase resistance to mass transfer (LT ), a is the air bubble surface area per unit volume (L ), and C and Cl are oxygen solubility and dissolved oxygen concentration, respectively. All the terms of OTR refer to the time average values of a dynamic situation. 

B, molecular diffusion term C, resistance to mass transfer term D summation for gas chromatography and E, summation for liquid chromatography. 

The B term represents longitudinal diffusion and is proportional to D ). The C term represents resistance to mass transfer and is proportional to... 

For isocratic analysis, flow rate has no impact on k or a, since flow has the same effect on % and tg- Both operating pressnre and analysis time are inversely proportional to flow rate. Flow rate also has a significant effect on N, as efficiency is reduced (with H increasing) at higher flow rate dne the higher resistance to mass transfer (the van Deemter C term). 

In figure 7 the Resistance to Mass Transfer term (the (C) term from the Van Deemter curve fit) is plotted against the reciprocal of the diffusivity for both solutes. 

Figure 8 shows the predicted linear relationship between the resistance to mass transfer term and the square of the particle diameter. The linear correlation is extremely good and it is seen that there is, indeed an intercept on the (C) term axis, at zero particle diameter, which confirms the existence of a small, but significant, contribution from the resistance to mass transfer in the stationary phase. 

C resistance to mass transfer term in the Van Deemter equation... 

The terms in the brackets represent the complex series-parallel resistances to mass transfer and reaction. The parameter c is... 

The last term accounts for the resistance to mass transfer in the gas phase. Low-loaded liquid coatings cause the Cg term to be significant. Equation 2.82 was further extended to account for velocity distributions due to retarded gas flow in the layers (C ) and the interaction of the two types of gas resistance (C2) ... 

In Eq. (1.11) the C terms represents the contributions to zone broadening from resistance to mass transfer in the stationary phase and the mobile phase, respectively. 

C. Resistance to Mass Transfer In the plate theory, it was assumed that the transfer of solute molecules between the mobile phase and the stationary phase was instantaneous. In the rate theory, it is accepted that there is a finite rate of mass transfer. In addition, molecules of the same species may spend different lengths of time in the stationary and mobile phases (Fig. 1.15). Resistance to mass transfer is represented by the C term of the van Deemter equation. 

Constant Pattern Behavior. In a real system the finite resistance to mass transfer and axial mixing in the column lead to departures from the idealized response predicted by equilibrium theory. In the case of a favorable isotherm the shock wave solution is replaced by a constant pattern solution. The concentration profile spreads in the initial region until a stable situation is reached in which the mass transfer rate is the same at all points along the wave front and exactly matches the shock velocity. In this situation the fluid-phase and adsorbed-pliase profiles become coincident, as illustrated in Figure 13. This represents a stable situation and the profile propagates without further change in shape—lienee the term constant pattern. The form of the concentration profile under constant pattern conditions may be easily deduced by integrating the mass transfer rate expression subject to the condition c/c0 = q/qQy where qfj is the adsorbed phase concentration in equilibrium with c(y... 

Although the B and C terms exhibit opposite relationships with analyte diffusion, the C-term relationship is mainly of interest because resistance to mass transfer is the dominant form of band-spreading at the faster velocities that are desired. Equations (17-9) and (17-10) imply that speeding up diffusion will increase mass transfer and help decrease plate height. The Wilke-Chang equation [9] shows that diffusivity is directly proportional to temperature and inversely proportional to viscosity ... 

The third term, C, is a measure of the resistance to mass transfer between the stationary and the mobile phase. It includes ihe contributions by both the stationary phase and the stagnant mobile phase in the pores of the particles in the column bed. This term is complex, but, to a first approximation, it is inversely proportional to the diffusion coefficient, D, and directly proportional to the second power of the distance a solute molecule should travel to get from the mobile phase to the interaction site in the particle. For a totally porous particle, this distance is proportional to the mean particle diameter. 

The C term relates to resistance to mass transfer which arises from the non-instanta-neous rate of equilibrium of solute between the particles and the liquid flowing outside them. This has been discussed by Knox and Scott 119) and becomes increasingly smaller as the particle diameter decreases. Knox concluded that the ultimate performance from CEC would be obtained using sub-micron particles (4), but this has yet to be fully demonstrated owing to difficulty in obtaining and packing such particles. 

At velocities above // , the C term controls H and relates to nonequilibrium resulting from resistance to mass transfer in the stationary and mobile phases [6],... 

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