Mobile phase velocity definition

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). 

A definite problem may be the appearance of some secondary fronts. One possibility is the so-called front of the total wetness, that may occur when the mobile phase velocity... 

In general (there are many exceptions), chemists and chemical engineers tend to use two different definitions for the mobile phase velocity and for the internal or particle porosity, and different units for the concentrations in the liquid and solid phases (see Section 2.3), hence different expressions for the equilibrium constant. While most papers dealing with the simple models derived from Eq. 2.2 do not need to distinguish between internal and external porosities (there is no... 

Velocity There are three different definitions of the mobile phase velocity, the chromatographic, the interfacial, and the superficial velocity They are all defined as the ratio of the mobile phase flow rate to an estimate of the column volume and differ by the estimate of the column volume used. The chromatographic velocity uses the total volume in the column that is available to the mobile phase the superficial velocity, the geometrical column tube volume and the intersticial velocity the external or extra-particle volume. See Chapter 2, Section 2.3.3. 

A considerable amount of work has been published on optimizing the experimental conditions for minimum analysis time under various constraints [52]. One complication arises from the definition of reduced mobile-phase velocity. The actual mobile-phase velocity depends largely on the molecular-diffusion coefficient of the analyte. Thus, very small particles can be used for the analysis of high molecular mass compounds, which have low values. The actual flow rate required will remain compatible with pressure constraints despite the resulting high pneumatic or hydraulic resistance. Detailed results obviously depend greatly on the mode of chromatography used. 

H is the plate height (cm) u is linear velocity (cm/s) dp is particle diameter, and >ni is the diffusion coefficient of analyte (cm /s). By combining the relationships between retention time, U, and retention factor, k tt = to(l + k), the definition of dead time, to, to = L u where L is the length of the column, and H = LIN where N is chromatographic efficiency with Equations 9.2 and 9.3, a relationship (Equation 9.4) for retention time, tt, in terms of diffusion coefficient, efficiency, particle size, and reduced variables (h and v) and retention factor results. Equation 9.4 illustrates that mobile phases with large diffusion coefficients are preferred if short retention times are desired. 

In the Mint model, we have to take into account the following considerations (i) the initial filtration coefficient Xq, which is a parameter, presents a constant value after time and position (ii) the detachment coefficient, which is another constant parameter (iii) the quantity of the suspension treated by deep filtration depends on the quantity of the deposited solid in the bed this dependency is the result of the definition of the filtration coefficient (iv) the start of the deep bed filtration is not accompanied by an increase in the filtration efficiency. These considerations stress the inconsistencies of the Mint model 1. valid especially when the saturation with retained microparticles of the fixed bed is slow 2. unfeasible to explain the situations where the detachment depends on the retained solid concentration and /or on the flowing velocity 3. unfeasible when the velocity of the mobile phase inside the filtration bed, varies with time this occurrence is due to the solid deposition in the bed or to an increasing pressure when the filtration occurs with constant flow rate. Here below we come back to the development of the stochastic model for the deep filtration process. 

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... 

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. 

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