Mathematics of Adsorption in Beds. VI. The Effect of Longitudinal Diffusion in Ion Exchange and Chromatographic Columns

Lapidus, Leon; Amundson, Neal R.

doi:10.1021/j150500a014

Cited by 908 publications

(304 citation statements)

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“… accounts for the equilibrium linear adsorption process, where n p is the porosity of the medium and K 1 is an empirical constant (Cherry et al, 1984;Lapidus and Amundson, 1952).…”

Section: Y T R DX T U X T Cxy T T X X C X Y T D Y T V Y T C X Y T Ymentioning

confidence: 99%

Explicit finite-difference solution of two-dimensional solute transport with periodic flow in homogenous porous media

Djordjevich

Savović

Janićijević

2017

Journal of Hydrology and Hydromechanics

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Abstract:The two-dimensional advection-diffusion equation with variable coefficients is solved by the explicit finitedifference method for the transport of solutes through a homogenous two-dimensional domain that is finite and porous. Retardation by adsorption, periodic seepage velocity, and a dispersion coefficient proportional to this velocity are permitted. The transport is from a pulse-type point source (that ceases after a period of activity). Included are the firstorder decay and zero-order production parameters proportional to the seepage velocity, and periodic boundary conditions at the origin and at the end of the domain. Results agree well with analytical solutions that were reported in the literature for special cases. It is shown that the solute concentration profile is influenced strongly by periodic velocity fluctuations. Solutions for a variety of combinations of unsteadiness of the coefficients in the advection-diffusion equation are obtainable as particular cases of the one demonstrated here. This further attests to the effectiveness of the explicit finite difference method for solving two-dimensional advection-diffusion equation with variable coefficients in finite media, which is especially important when arbitrary initial and boundary conditions are required.

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“… accounts for the equilibrium linear adsorption process, where n p is the porosity of the medium and K 1 is an empirical constant (Cherry et al, 1984;Lapidus and Amundson, 1952).…”

Section: Y T R DX T U X T Cxy T T X X C X Y T D Y T V Y T C X Y T Ymentioning

confidence: 99%

Explicit finite-difference solution of two-dimensional solute transport with periodic flow in homogenous porous media

Djordjevich

Savović

Janićijević

2017

Journal of Hydrology and Hydromechanics

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“…Moreover certain physical features of the fibers such as fiber porosity and fiber radius were ignored. Lapidus and Amundson [7] also followed two adsorption isotherms; one implies that equilibrium is established at each point in the bed while the other assumes the rate of adsorption is finite. Washing models of pulp based on axial dispersion and particle diffusion along with adsorption isotherms for sodium and lignin are fairly established and also solved by earlier workers such as Arora et al The accuracy of the analytic solution undoubtedly exceeds the limit of applicability of the theory to real situations.…”

Section: Introductionmentioning

confidence: 99%

Mathematical Model of Pulp Washing Using Mathematica

Kumar¹,

Kukreja

2016

MATEC Web of Conferences

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Good washing is the key to a successful closure of the water system in a pulp production line. An improved understanding of associated phenomena, particularly those related to the removal of the very last impurities, is therefore desirable. Therefore a mathematical model describing the desorption phenomenon. The system of governing partial differential equations is solved using Mathematica. Model is simulated using the industrial data. The output thus obtained is compared with the analytic and numerical results of earlier workers. Present technique is simple, elegant and convenient for solving two point boundary value problems with varying range of parameters.

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“…Given the above, this study aimed at investigating whether a practically useful expression for the band broadening in PACs cannot be obtained by starting from the general plate height expression of LC originally derived by Lapidus and Amundson [13] for packed bed columns, and to verify whether this expression also applies to the case of PACs. If this is indeed the case, investigate how the geometrical parameters appearing in the expression need to be tuned to faithfully represent the observed band broadening.…”

Section: Introductionmentioning

confidence: 99%

Modelling the relation between the species retention factor and the C‐term band broadening in pressure‐driven and electrically driven flows through perfectly ordered 2‐D chromatographic media

Wilde

Detobel

Billen

et al. 2009

J of Separation Science

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The band broadening that can be expected in perfectly ordered cylindrical pillar arrays has been calculated for a wide range of intra-particle diffusion coefficients (D sz ) and zone retention factors (0ok 00 o10) using an in-house-developed computational fluid dynamicsalgorithm. Both pressure-driven and electrically driven (PD and ED) flows are considered. In the case of a large intra-pillar diffusion coefficient (D sz /D mol 5 0.5), the minimal reduced plate height varies between h 5 0.8 (low k 00 ) and h 5 1.2 (high k 00 ), while the C-term range of the Van Deemter curve depends only slightly on k 00 . In the case of a small intra-pillar diffusion coefficient (D sz /D mol 5 0.1), h is nearly independent of k 00 and approximately equals h min 5 1.1, while the C-term band broadening decreases strongly with increasing k 00 . The difference between ED and PD flows in perfectly ordered porous pillar arrays is much smaller than in packed beds, generally only 3% difference around the minimum of the plate-height curve and maximally 10% at high-reduced velocities. The generated data sets were also ideal to verify the accuracy of k 00 and D sz dependency of the general plate height model of chromatography. Determining the values of the geometrical parameters appearing in the model through curve fitting, the average fitting error can be reduced to a value of about 1%.

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Mathematics of Adsorption in Beds. VI. The Effect of Longitudinal Diffusion in Ion Exchange and Chromatographic Columns

Cited by 908 publications

References 0 publications

Explicit finite-difference solution of two-dimensional solute transport with periodic flow in homogenous porous media

Explicit finite-difference solution of two-dimensional solute transport with periodic flow in homogenous porous media

Mathematical Model of Pulp Washing Using Mathematica

Modelling the relation between the species retention factor and the C‐term band broadening in pressure‐driven and electrically driven flows through perfectly ordered 2‐D chromatographic media

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