Mobile phase velocity interstitial

HETP can be related to the experimental parameters through the Van Deemter [59] or Knox [60] equations. It is possible to describe the dependence of H on u since H is a. function of the interstitial mobile phase velocity u. In the case of preparative chromatography, where relatively high velocities are used, these equations can very often be simplified into a linear relation [61, 62]. 

By definition, the e]q>erlmentally determined average mobile phase velocity Is equal to the ratio of the column length to the retention time of an unretalned solute. The value obtained will depend on the ability of the unretalned solute to probe the pore volume. In liquid chromatography, a value for the Interstitial velocity can be obtained by using an unretalned solute that Is excluded from the pore volume for the measurement (section 4.4.4). The Interstitial velocity Is probably more fundamentally significant than the chromatographic velocity in liquid chromatography (39). 

Where u, is the mobile phase velocity at the column outlet, Fg the column volumetric flow rate, and Ag the column cross-sectional area available to the mobile phase. In a packed bed only a fraction of the column geometric cross-sectional area is available to the mobile phase, the rest is occupied by the solid (support) particles. The flow of mobile phase in a packed bed occurs predominantly through the interstitial spaces the mobile phase trapped within the porous particles is largely stagnant (37-40). 

The lumped kinetic model can be obtained with further simplifications from the lumped pore model. We now ignore the presence of the intraparticle pores in which the mobile phase is stagnant. Thus, p = 0 and the external porosity becomes identical to the total bed porosity e. The mobile phase velocity in this model is the linear mobile phase velocity rather than the interstitial velocity u = L/Iq. There is now a single mass balance equation that is written in the same form as Equation 10.8. 

In addition to the enhanced diffusivity effect, another issue needs to be taken into account when considering stationary-phase mass transfer in CEC with porous particles. The velocity difference between the pore and interstitial space may be small in CEC. Under such conditions the rate of mass transfer between the interstitial and pore space cannot be very important for the total separation efficiency, as the driving mechanism for peak broadening, i.e., the difference in mobile-phase velocity within and outside the particles, is absent. This effect on the plate height contribution II, s has been termed the equilibrium effect [35], How to account for this effect in the plate height equation is still open to debate. Using a modified mass balance equation and Laplace transformation, we first arrived at the following expression for Hc,s, which accounts for both the effective diffusivity and the equilibrium effect [18] ... 

Care must be taken with the definition of the velocity. S ne part of the obstruction factor can be explained by an inappropriate definition of the velocity. We must keep in mind that it refers to the residence time in the mobile phase of the sample compound whose diffusion is measured. This residence time is not necessarily identical to the residence time of an unretained sample compound, which is used to measure the linear velocity. Also, we implicitly assimied that the diffusion coefficient in the pores is the same as the diffusion coefficient in the interstitial mobile phase. This is also not necessarily the case. If me pore size is less than about 10 times larger than the size of the molecule, the diffusion coefficient depends on the ratio of the size of the sample molecule to w pore size of the packing. 

Here uR is the velocity at which the solute band moves along the column and u is the velocity of the mobile phase that is, u = (superficial velocity)/e, where superficial velocity is volumetric flow rate divided by cross-sectional area of column and s is the fractional volume of column occupied by mobile phase. Most column packings are porous, in which case s includes both interstitial and pore (intraparticle) voidage, as defined in the note to Table 19.1, and here u is less than the interstitial velocity. 

C is the concentration of the analyte in the bnlk mobile phase is the interstitial velocity of the mobile phase... 

As the first term of the right-hand side of Equation 11.20 is independent of fluid velocity and is proportional to the radius fg (m) of particles packed as the stationary phase under usual conditions in chromatography separation, Hs (m) will increase linearly with the interstitial velocity of the mobile phase u (m s ), as shown in Figure 11.9. With a decrease in the effective diffusivities of solutes (m s ), Hs for a given velocity will increases, while the intercept of the straight lines on the y-axis, which corresponds to the value of the first term of Equation 11.20, is constant for different solutes. The value ofthe intercept will depend on the radius of packed particles, but does not vary with the effective diffusivity of the solute. 

In a gel chromatography column packed with particles of average radius 22 pm at an interstitial velocity of 1.2 cm min- of the mobile phase, two peaks show poor separation characteristics, that is, =0.85. 

From a correlation similar to Figure 14.7, the velocity of the mobile phase for the scaled up column to obtain the equal value of can be determined. In the case where particles with a smaller radius are used, an operation with a higher interstitial velocity will be possible to attain the same resolution with the same column height, and thus this increases the productivity. The resolution between a target and a contaminant can be estimated by Equation 11.23 to calculate the purity and recovery of the target. 

The irony is that both velocities are derived directly from data easily acquired using the conventional methods of the field in which they are used but that, unfortunately, neither informs well on the actual kinetics of the band convection, which is the primary concern in mass transfer investigations. Since, for all practical purposes, the stream of mobile phase flows only through the macropores, a more useful definition of the velocity is the interstitial velocity... 

The mathematical model for the mass transfer of an adsorbate in the LC column packed with the silicalite crystal particles is based on the assumptions of (1) axial—dispersed plug—flow for the mobile phase with a constant interstitial flow velocity (2) Fickian diffusion in the silicalite crystal pore with an intracrystalline diffus— ivity independent of concentration and pressure and (3) spherical silicalite crystal particles with a uniform particle size distribution. A detailed discussion of these assumptions can be found in (13). The differential mass balances over an element of the LC column and silicalite crystal result in the following two partial differential equations ... 

After having defined above the accumulation terms of the general mass balances (Equations 6.1-6.6), the transport and source terms can be evaluated as follows. Mass transport in the mobile phase occurs due to convection with the interstitial velocity Uim (Equation 2.9)... 

Degree of peak asymmetry Velocity in the empty column Interstitial velocity in the packed column Effective velocity (total mobile phase)... 

Changing the temperature of the feed to a sorption column will cause a thermal wave to pass through the column. The velocity of this thermal wave can be calculated by a procedure analogous to that used for solute waves. The thermal wave velocity will be the fraction of the change in thermal energy in the mobile phase multiplied by the interstitial velocity. 

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