Resistance-to-mass transfer

Resistance to mass transfer describes the band broadening caused by transporting the analytes by diffusion and convection from one phase to the other. 

Resistance to mass transfer is, in general, inversely proportional to the diffusion constants in either phase. 

In the mobile phase, there is an additional link to eddy diffusion. The contribution to the plate height can be described by band broadening taking place in the mobile phase, stagnant mobile phase, and stationary phase. 

In packed columns, Hm should be coupled with the eddy diffusion and the coupled term Hme = l/(l/fJe + 1/Hm). 

Note The plate height in a packed column is independent of the column inner diameter. 

When one considers the effects of chemical interactions (carbohydrate aroma) on sensory perception, one would expect that aroma character and/or intensity will be altered. This is because the various polysaccharides will interact with different aroma compounds to varying degrees, i.e., change the balance of aroma compounds liberated from a food. However, the effect of carbohydrates on limiting mass transfer would be expected to likely affect flavor intensity and not character. This is because mass transfer effects would be more uniform across aroma compounds. 

---

Though the case of constant matrix elements and the example investigated by Hite are the only situations for which Che stoichiometric relations have been fully established in pellets of arbitrary shape, it is worth mentioning situations in which these relations are known not to hold. When the composition and pressure at the surface of the pellet may vary in an arbitrary way from point to point it seems unlikely on intuitive grounds that equations (11.3) will be satisfied, and Hite and Jackson [77] confirmed by direct computation that there are, indeed, simple situations in which they are violated. Less obviously, direct computation [75] has also shown them to be violated even when the pressure and composition of the environment are the same everywhere, in the case where finite resistances to mass transfer exist at the surface of Che pellet. 

Expressions similar to equations 6 and 7 may be derived in terms of an overall Hquid-phase driving force. Equation 7 represents an addition of the resistances to mass transfer in the gas and Hquid films. The analogy of this process to the flow of electrical current through two resistances in series has been analyzed (25). 

As illustrated ia Figure 6, a porous adsorbent ia contact with a fluid phase offers at least two and often three distinct resistances to mass transfer external film resistance and iatraparticle diffusional resistance. When the pore size distribution has a well-defined bimodal form, the latter may be divided iato macropore and micropore diffusional resistances. Depending on the particular system and the conditions, any one of these resistances maybe dominant or the overall rate of mass transfer may be determined by the combiaed effects of more than one resistance. 

The time constant R /D, and hence the diffusivity, may thus be found dkecdy from the uptake curve. However, it is important to confirm by experiment that the basic assumptions of the model are fulfilled, since intmsions of thermal effects or extraparticle resistance to mass transfer may easily occur, leading to erroneously low apparent diffusivity values. 

In certain adsorbents, notably partially coked 2eohtes and some carbon molecular sieves, the resistance to mass transfer may be concentrated at the surface of the particle, lea ding to an uptake expression of the form... 

Catalyst Particle Size. Catalyst activity increases as catalyst particles decrease in size and the ratio of the catalyst s surface area to its volume increases. Small catalyst particles also have a lower resistance to mass transfer within the catalyst pore stmcture. Catalysts are available in a wide range of sizes. Axial flow converters predorninanfly use those in the 6—10 mm range whereas the radial and horizontal designs take advantage of the increased activity of the 1.5—3.0 mm size. 

Transfer of material between phases is important in most separation processes in which two phases are involved. When one phase is pure, mass transfer in the pure phase is not involved. For example, when a pure liqmd is being evaporated into a gas, only the gas-phase mass transfer need be calculated. Occasionally, mass transfer in one of the two phases may be neglec ted even though pure components are not involved. This will be the case when the resistance to mass transfer is much larger in one phase than in the other. Understanding the nature and magnitudes of these resistances is one of the keys to performing reliable mass transfer. In this section, mass transfer between gas and liquid phases will be discussed. The principles are easily applied to the other phases. 

Mass-Transfer Principles Dilute Systems When material is transferred from one phase to another across an interface that separates the two, the resistance to mass transfer in each phase causes a concentration gradient in each, as shown in Fig. 5-26 for a gas-hquid interface. The concentrations of the diffusing material in the two phases immediately adjacent to the interface generally are unequal, even if expressed in the same units, but usually are assumed to be related to each other by the laws of thermodynamic equihbrium. Thus, it is assumed that the thermodynamic equilibrium is reached at the gas-liquid interface almost immediately when a gas and a hquid are brought into contact. 

Solution. For TGE in water, the Henry s law coefficient may he taken as 417 atm/mf at 20°G. In this low-concentration region, the coefficient is constant and equal to the slope of the eqnihhrinm hne m. The solnhility of TGE in water, based on H = 417, is 2390 ppm. Because of this low solnhility, the entire resistance to mass transfer resides in the liquid phase. Thus, Eq. (14-25) may he used to obtain Nql, the nnmher of overall hqnid phase transfer units. 

While the carbon dioxide/caiistic test method has become accepted, one should use the results with caution. The chemical reaction masks the effect of physical absorption, and the relative values in the table may not hold for other cases, especially distillation applications where much of the resistance to mass transfer is in the gas phase. Background on this combination of physical and chemical absorption may Be found earher in the present section, under Absorption with Chemical Reaction. ... 

The contribution to the height of a transfer unit overall based on the raffinate-phase compositions is the sum of the contribution from the resistance to mass transfer in the raffinate phase plus the contribution from the resistance to mass transfer in the extract phase divided bythe extraction factor [Eq. (15-31)]. 

Prediction methods attempt to quantify the resistances to mass transfer in terms of the raffinate rate R and the extract rate E, per tower cross-sectional area Af, and the mass-transfer coefficient in the raffinate phase and the extract phase times the interfacial (droplet) mass-transfer area per volume of tower a [Eqs. (15-32) and (15-33)]. 

Saturation of the oil with hydrogen is maintained by agitation. The rate of reaction depends on agitation and catalyst concentration. Beyond a certain agitation rate, resistance to mass transfer is eliminated and the rate oecomes independent of pressure. The effect of catalyst concentration also reaches hmiting values. The effects of pressure and temperature on the rate are indicated by Fig. 23-34 and of catalyst concentration by Fig. 23-35. Reaction time is related to temperature, catalyst concentration, and IV in Table 23-13. 

The dispersion of a solute band in a packed column was originally treated comprehensively by Van Deemter et al. [4] who postulated that there were four first-order effect, spreading processes that were responsible for peak dispersion. These the authors designated as multi-path dispersion, longitudinal diffusion, resistance to mass transfer in the mobile phase and resistance to mass transfer in the stationary phase. Van Deemter derived an expression for the variance contribution of each dispersion process to the overall variance per unit length of the column. Consequently, as the individual dispersion processes can be assumed to be random and non-interacting, the total variance per unit length of the column was obtained from a sum of the individual variance contributions. 

Dispersion Due to Resistance to Mass Transfer Resistance to Mass Transfer in the Mobile Phase... 

Dispersion caused by the resistance to mass transfer in the stationary phase is exactly analogous to that in the mobile phase. Solute molecules close to the surface will leave the stationary phase and enter the mobile phase before those that have diffused further into the stationary phase and have a longer distance to diffuse back to the surface. Thus, as those molecules that were close to the surface will be swept along in the moving phase, they will be dispersed from those molecules still diffusing to the surface. The dispersion resulting from the resistance to mass transfer in the stationary phase is depicted in Figure 8. 

Quantitative Treatment of Resistance to Mass Transfer Dispersion... 

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. 

In 1967, Huber and Hulsman [2] introduced yet another HETP equation having a very similar form to that of Giddings. Their equation included a modified multipath term somewhat similar in form to that of Giddings and a separate term describing the resistance to mass transfer in the mobile phase contained between the particles. The form of their equation was as follows ... 

The composite curve from the Huber equation is similar to that obtained from that of Van Deemter but the individual contributions to the overall variance are different. The contributions from the resistance to mass transfer in the stationary phase and... 

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... 

Substituting for (h ) the expression for the resistance to mass transfer in the stationary phase,... 

It is seen that equations (13) and (15) are very similar to equation (10) except that the velocity used is the outlet velocity and not the average velocity and that the diffusivity of the solute in the gas phase is taken as that measured at the outlet pressure of the column (atmospheric). It is also seen from equation (14) that the resistance to mass transfer in the stationary phase is now a function of the inlet-outlet pressure ratio (y). 

It is a common procedure to assume certain conditions for the chromatographic system and operating conditions and, as a result, simplify equations (20) and (21). However, in many cases the assumptions can easily be over-optimistic, to say the least. It is necessary, therefore, to carefully consider the conditions that may allow such simplifying procedures and take steps to ensure that such conditions are carefully met when such expressions are used in practice. Now, the relative magnitudes of the resistance to mass transfer terms will vary with the type of columns (packed or capillary), the type of chromatography (GC or LC) and the type of particle, i.e., porous or microporous (diatomaceous support or silica gel). 

The ratio of the resistance to mass transfer in the mobile phase to that in the stationary phase (Rms) will indicate whether the expressions can be simplified or not. Now, (Rms) will be given by. 

---