Extraparticle diffusional effects in gel permeation chromatography. II. Experimental results

Experiments coupled with a systems analysis were conducted on chromatogram dispersion, or zone broadening, in gel permeation chromatography (GPC). Three components of a Waters Associates Model 200 chromatograph, each of which is a potential cause of dispersion, were considered; these are: the packed column, with extraparticle dispersion only; the empty tubing, between pump and columns, columns and detector, etc.; and the detection system, viz., the differential refractometer cell. Toluene solvent was used and the solutes whose dispersion was studied included orthodichlorobenzene (ODCB) and narrow-molecular-weight polystyrene standards having molecular weights of 900, 20,400, 51,000, 97,200, and 160,000. Nonporous glass beads, 50 μ in diameter, were used as column packing. Two diameters, 1 mm and 0.5 mm, of stainless steel tubing were studied. In addition to the usual rectangular pulse sample injection, a step input mode for solute introduction was also used. The empty tubing was found to contribute significantly to the degree of dispersion and to skewness of elution curves. Anomalous bimodal characteristics of the elution curves were also observed which could only be ascribed to the empty tubing. These phenomena depended markedly on parameters such as tube diameter and length, and solute concentration and molecular weight. Dispersion in the packed column, although important, was found to be symmetrical (Gaussian) and less sensitive to these parameters than in the empty tubing, especially with respect to molecular weight. Dispersion in the cell was believed to be insignificant relative to the packed column and empty tubing.     

Impact of retention on trans‐column velocity biases in packed columns

The heights equivalent to a theoretical plate of a weakly and strongly retained compounds were measured on two packed columns having different average mesopore sizes. The measurements were carried out in two different cases, with access to the mesopores by the sample molecules blocked (filled with n‐nonane) or not. The experimental results demonstrate that the eddy dispersion terms of both columns are significantly smaller for porous than for nonporous particles. Two simultaneous phenomena explain this observation. First, packed columns are radially heterogeneous which causes significant trans‐column velocity biases warping the bands. Second, radial dispersion contributes to mass transfer across the column, relaxing the radial concentration gradients that are caused by these velocity biases. The impact of these biases is minimized when the pores of the particles are not blocked; it decreases with increasing residence time and radial dispersion coefficient of the solutes. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

Flüssigphase-Rückvermischung in gepackten Blasensäulen

Liquid phase backmixing in packed bubble columns . Correlations for the axial liquid phase dispersion coefficient in bubble columns packed with metal Raschig rings and Pall rings are given as Pe_g = f (Ga, Re_g, H/D). The dependencies on physical and operational properties are discussed in detail with the aid of diagrams. Pall rings are not able to completely suppress greater turbulences and backmixing in columns of diameters D > 20 cm. A rule of thumb is also given for the apparent dispersion coefficient in this range. Raschig rings, however, are well suited for suppressing backmixing. The problems of adequate fulfilling of the model and undisturbed measurement of the backmixing behaviour are dealt with in detail.     

A structured catalytic bubble column reactor: hydrodynamics and mixing studies

This paper reports the results of a comprehensive experimental study of the hydrodynamics and mixing in two bubble column reactors of 0.1 and 0.24 m in diameter with KATAPAK-S^® as packing material. Total gas hold up and axial dispersion coefficients were measured in the structured bubble columns and the values were compared with experimental results obtained in the same work with empty bubble columns. The results reveal that the gas hold up in structured bubble columns is practically the same as in empty bubble columns when compared at the same superficial gas velocity based on open area available for gas–liquid dispersion. The presence of the structured elements in the bubble column reactor reduces the liquid phase backmixing by one order of magnitude.     

High performance g.p.c. with crosslinked polystyrene gels: influence of particle size distribution

Spherical crosslinked polystyrene gel particles have been separated by air classification into fractions having average particle diameters in the range 10–40 μm. The particle size distributions have been shown to be narrow by Coulter Counter measurements. G.p.c. column performance improves as the average particle diameter decreases and columns packed with gel fractions having a number-average particle diameter below 20 μm give plate counts in excess of 3000 plates per foot. Plate height results as a function of eluent flow rate suggest that chromatogram broadening due to mobile phase dispersion is reduced in columns packed with spherical particles having a narrow size distribution.     

Absorption in packed bubble columns

The mass transfer characteristics of packed bubble columns were studied by employing various packings of different sizes and shapes in 10–38·5 cm i.d. columns. The theory of absorption accompanied by pseudo-mth order reaction was used to obtain the values of effective interfacial area. The values of liquid side mass transfer coefficient were obtained by using the theory of absorption accompanied by slow chemical reaction. The superficial gas velocity was varied from 5 to 25 cm/sec. The packed bubble columns showed a considerable improvement in the performance over empty bubble columns. A criterion for the scale-up of these columns has been suggested.     

Open tubular columns for gas liquid chromatography: Cleaning and recoating procedures

Procedures have been developed that permit the routine reuse of open tubular columns for the analysis of fatty acid methyl esters. Cleaning techniques are given that permit essentially endless recycling of the expensive capillary tubing with nearly 100% success in obtaining excellent columns upon recoating when using polyester liquid phases. Cost, including preparation of column, is equal to or less than the usual conventional packed column. These procedures make it both practical and economical to take advantage of the improved resolution and the reduced time for an analysis obtained with the open tubular column.     

Axial dispersion in a rectangular bubble column

This paper presents the results of an experimental study on the gas holdup and the liquid phase axial dispersion coefficient in a narrow packed and unpacked rectangular bubble column. In both cases the gas and liquid flow rates were varied and the data were obtained by employing standard tracer technique. The gas holdup and the axial dispersion coefficient for both the packed and unpacked columns were found to be dependent on the gas and liquid flow rates. For given gas and liquid velocities and a given packing size in the case of the packed column, the rectangular column gave significantly higher dispersion coefficients than a cylindrical column of the equivalent cross sectional area. This result agrees very well with the one predicted by the velocity distribution model. The correlations for the Peclet number, the axial dispersion coefficient, and the fluid holdup for both the unpacked and packed bubble columns are presented.     

Inline Measurement of the Residence Time Distribution in High-Pressure Extraction Columns

Axial backmixing lowers the efficiency of packed countercurrent high-pressure extraction columns. To quantify backmixing, a method of measuring the residence time distribution and calculating the axial dispersion coefficient in high-pressure extraction columns is introduced. Using a design of experiments, the effect of supercritical and liquid mass flow rates as well as the pressure at a constant temperature on the mean residence time and the axial dispersion coefficient are evaluated for the system water/supercritical CO₂. The experimental data is correlated to the Reynolds and Schmidt number.     

A Comparison of Mobile-Phase Peak Dispersion in Gas and Liquid Chromatography

Abstract

The field of axial and radial dispersion of unsorbed bands in columns or beds packed with spherical particles is reviewed and it is shown that there is broad agreement between various workers: at low reduced velocities both axial and radial dispersion occur by obstructed molecular diffusion. At higher velocities the processes are more complex but at very high velocities and at Reynolds numbers in excess of about 10 the reduced plate height becomes independent of velocity and has a value for axial dispersion of about 2 and for radial dispersion of about 0.2. In the intervening region the dispersion process is complex and shows dependence upon the column-to-particle-diameter ratio. The most inefficient columns appear to be formed when this ratio is between 10 and 30. It is therefore suggested that efforts be made to design and construct columns with greater trans-column uniformity. When trans-column packing inequalities are unimportant, the reduced plate height in the high-velocity region is only slightly affected by fluid velocity, in strong contrast to the situation in open tubes. With gases the reduced plate height does not rise much above 2 for well-constructed columns, whereas with liquids it rises to about 4 before turbulence becomes important and again limits the dispersion, so that it falls to about 2.     

Exact Analysis of Field-Flow Fractionation

Abstract

A rigorous convective diffusion theory is formulated for the predictive modeling of field-flow fractionation (FFF) columns used for the separation of colloidal mixtures. The theory is developed for simulating the behavior of a colloid introduced into fluid in time-dependent flow in a parallel plate channel across which a transverse field is applied. The methodology of generalized dispersion theory is used to solve the model equations. The theoretical results show that the cross-sectional average concentration of the colloid satisfies a dispersion equation with time-dependent coefficients. The results of this work, in principle, are valid for all values of time since the introduction of the colloid. It is shown that these results asymptotically approach those of the nonequilibrium theory formulated by Giddings for large values of time.

Illustrative numerical results are obtained for the case of steady laminar flow and a uniform initial distribution. The behavior of the coefficients in the dispersion equation is explained on physical grounds. Of particular interest is the fact that at large values of the transverse Peclet number P, Taylor dispersion in the FFF column is very small. Under these conditions, axial molecular diffusion as well as Taylor dispersion in the connecting tubing could make a substantial contribution to the axial dispersion observed in practical FFF columns.

The theoretical predictions are compared with the experimental data of Caldwell et al. and Kesner et al. on electrical FFF columns. The comparisons indicate that the theory has potential in predicting the performance of such systems.     

Minimizing axial dispersion in narrow packed column using superhydrophobic wall

The scope of minimizing dispersion in narrow packed column using superhydrophobic (SH) wall is assessed experimentally with implications in analytical techniques such as liquid chromatography. The study includes devising a packed column (7-19 mm) with lotus leaf pasted on the inner wall and establishing a gravity driven flow through it. The flow dispersion is characterized based on the residence time distribution study of the column. The results are compared against similar flow through smooth packed column. Experimental results reveal the influence of two factors: column diameter as well as the wall features, superhydrophobic or smooth. For similar surface features, the axial dispersion reduces with decrease in column diameter due to the increase in voidage, which leads to plug flow. For the same diameter, between smooth and superhydrophobic, effects of slip in the latter reduce the dispersion significantly. Thus, the introduction of superhydrophobic narrow columns can play a crucial role in minimizing dispersion in analytical techniques.     

Analysis of pseudo-continuum mass transfer in media with spatially periodic boundaries

The theories developed by Taylor, Aris, and Gill for convective dispersion of soluble matter in nonuniform flow are extended to systems with spatially periodic boundaries. More specifically the generalized theory explains solute retardation and dispersion in columns packed with a regular array of permeable particles, and is thus applicable to most chromatographic processes.The general theory is then specialized to the case of solute dispersion in creeping flow through a body-center-cubic array of impermeable, spherical particles. Preliminary calculations indicate that the present theory predicts correctly solute dispersion at the zero-flow limit. However numerical difficulties are encountered in the calculations for convective dispersion which seriously limit the utility of the theory.     

Liquid dispersion,gas holdup and frictional pressure drop in a packed bubble column at elevated pressures

The gas holdup, frictional pressure drop and liquid dispersion have been investigated in a packed bubble column at elevated pressures for the air–water system. The bubble column, which had an internal diameter of 0.15 m and which was packed with 15 mm plastic Pall rings was operated in the semibatch mode. The operating pressures ranged from 0.1 to 0.66 MPa. It was found that increasing the pressure increases both the gas holdup and the dispersion coefficient. In contradiction to the results obtained from packed bubble columns fed with a continuous net flow of liquid, a maximum point of the frictional pressure drop was observed at the transition point between bubble and pulse flow region.     

Experimental determination of longitudinal dispersion in two-phase flow through packing

Experimental correlations for the parameters of the plug-flow model with imposed longitudinal dispersion, i.e. the longitudinal dispersion coefficient and the real mass-transfer coefficient, have been derived. Assuming that the dispersion takes place only on the gas side, concentration profiles of the component being transferred have been measured. From the experimental data correlations were derived allowing to compute the gas-phase Peclet number and the real mass transfer coefficient. The correlations are then used in the further analysis of the influence of longitudinal dispersion on mass transfer in packed columns.     

The evaluation in time domain of mass transfer parameters from chromatographic peaks

Impulse response experiments have been carried out in packed beds in order to determine parameters as interstitial velocities, dispersion coefficients, internal diffusion coefficients and film transfer coefficients. The transfer function of the Kubín-Kucera model is solved in the Fourier domain. Two types of beds are considered, viz. long columns (about 6 m), packed with small particles and a short tube (1 m), packed with particles with a diameter in the order of the tube diameter. Moment analysis, Fourier analysis and fitting in the time domain are applied. It is shown that for Gaussian curves Fourier analysis has no advantage with respect to the method of moments. Moreover, for asymmetric curves a combination of Fourier analysis and time domain fitting is to be preferred. This is exemplified with a system where internal diffusion is the most important process. By applying Fourier analysis and fitting in the time domain, the interstitial velocity, axial dispersion coefficient and internal diffusion coefficient could be determined from a single experimental run with an accuracy better than 10 percent. For the experiments, performed in this work, the contribution of the film resistance compared with internal resistance proved to be negligible. The values obtained for the internal tortuosity factor and for the Péclet number agree with literature.     

A continuum model for gas–liquid flow in packed towers

Gas–liquid flow in packed towers is commonly encountered in the chemical and processing industry. A continuum model is developed based on the volume-and-time averaging of multiphase flows in isotropic rigid porous media/packed columns. Closures are presented for the evaluations of the extra surface/intrinsic phase integral terms. Both inertia and inter-phase interactions are retained in the volume averaged (Navier–Stokes) equations. These governing equations are solved for fully-developed axi-symmetric single and gas–liquid two phase flows in highly porous packed towers. It is found that the dispersion term is present in the continuity equation as well as the momentum equations. Numerical simulations with the models show that the volume-and-time averaged equations can predict the velocity, phase hold-up and pressure drop quite well for up to the loading point for gas–liquid counter-current flows.     

TUM–WelChem cell model for the prediction of liquid distribution in random packed columns

Liquid maldistribution is one of the main deficiencies in random packed column design. Therefore, the knowledge of liquid distribution and its model-based prediction is of great interest. This work aims to further develop and validate the TUM–WelChem Cell Model for random packed columns. First, cell dimension calculations and the determination of random packing element orientations are standardized. The original WelChem Cell Model applies a liquid distribution mechanism based on liquid spread factors derived by virtual 3D irrigation experiments. An extension of the model involves the implementation of liquid and gas load related distribution mechanisms, considering dispersion effects caused by liquid loading and the countercurrent gas flow. The wall flow is refined by an increase of packing porosity at the column wall. Liquid distribution profiles provided by the TUM–WelChem Cell Model are validated against experimental data and show good agreement for both uniform and point source initial liquid distribution.