General solution of the dispersion model for a one-dimensional stirred flow system using Danckwerts’ boundary conditions

Kudrna, Vladimı́r; Jahoda, M.; Siyakatshana, Njabulo; Čermáková, Jiřina; Machoň, Václav

doi:10.1016/j.ces.2004.01.068

Cited by 9 publications

(5 citation statements)

References 5 publications

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“…[7] Equation (7) was solved with Danckwerts' boundary conditions by Fourier's method and the solution is published in dimensionless form (option 2 in Table 1, column IX), [7] …”

Section: Description Of the Input Concentration Functionmentioning

confidence: 99%

Influence of the Non‐Perfect Step Input Concentration at the Feed Side of the Membrane Surface on the Diffusion Coefficient Evaluation

Čermáková

Fialová

Petrychkovych

et al. 2006

Macro Theory & Simulations

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Summary: Vapor diffusion coefficients in polymeric membranes were evaluated from dynamic permeation experiments. A membrane separated the diffusion cell into two parts – upstream and downstream. At the start of the experiment the concentration change in the upstream part (feed side) was made by substituting the input stream of pure nitrogen by the stream of permeant vapors. The solution of the Fick's second law with the step input concentration function is used for the evaluation of diffusion coefficients. The realization of the step input function can be difficult and its imperfection can negatively influence the evaluation process. This contribution deals with the description of the experimentally obtained input function and the study of its influence on evaluated values of diffusion coefficients. The mathematical model, which includes the non‐perfect step input concentration function and the transport through a polymer was developed. The results of this study enable the estimation of diffusion coefficient evaluation errors as dependence on the experimental arrangements and on the membrane transport properties.Diffusion apparatus for measurement of the steady‐state permeation process.magnified imageDiffusion apparatus for measurement of the steady‐state permeation process.

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“…[7] Equation (7) was solved with Danckwerts' boundary conditions by Fourier's method and the solution is published in dimensionless form (option 2 in Table 1, column IX), [7] …”

Section: Description Of the Input Concentration Functionmentioning

confidence: 99%

Influence of the Non‐Perfect Step Input Concentration at the Feed Side of the Membrane Surface on the Diffusion Coefficient Evaluation

Čermáková

Fialová

Petrychkovych

et al. 2006

Macro Theory & Simulations

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“…Most of the RTD studies done up to now are dealing with the influence of different design features or operating conditions on the flow pattern (Lee & Singh, 1993;Chandarana & Unverferth, 1996;Alhamdan & Sastry, 1997, 1998 but, as said before, do not give information on the temperature profile in the exchanger. The most used model to represent residence type distributions with or without reaction in tubular reactors or exchangers is the plug flow model with axial dispersion (Roetzel & Balzereit, 2000;Kudrna, Jahoda, Siyakatshana, Cermakova & Machon, 2004;Castelain & Legentilhomme, 2006), but also in less classical geometries such as Taylor-Poisseuille vortex flow (Giodano, Giordano, Prazares & Cooney, 2000) or torus reactor (Benkhelifa, Legrand, Legentilhomme & Montillet, 2000). RTD measurements in scraped surface heat exchangers have also been handled in our laboratory (Mabit, Loisel, Fayolle & Legrand, 2004;.…”

Section: Introductionmentioning

confidence: 99%

Development of a time temperature integrator for quantification of thermal treatment in scraped surface heat exchangers

Mabit

Belhamri

Fayolle

et al. 2008

Innovative Food Science & Emerging Technologies

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“…The other semi-opened axial dispersion models (ADM) are also included in this paper. These models differ in the left boundary condition according to [7].…”

Section: Model Descriptionmentioning

confidence: 99%

“…The one-dimensional axial flow dispersion model [1,7,8] is considered. The traditional mathematical expression of such a model is [7] …”

Section: Model Descriptionmentioning

confidence: 99%

“…[1,4,7,8,12,13] and natural sciences (medicine, ecology, metrology, etc.). All the applications are based on the following simple presumptions: the first and the second Fick's diffusion laws in one-dimensional system; absence of radial mixing; inclusion of turbulent behavior into diffusion process; constant diffusion coefficient and flow velocity; and idealized mathematical expression of boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

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Generalized semi-opened axial dispersion model

Bartova¹,

Jakeš²,

Kukal³

2012

Archives of Control Sciences

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The axial dispersion model (ADM) is studied and then generalized by a new form of the left boundary condition of semi-open flow system. The resulting parameter driven model covers the traditional axial models: axial closed-opened dispersion model with enforced input concentration (AEO), axial closed-opened dispersion model with input Danckwerts' condition (ACO), and axial opened-opened model (AOO). It also enables development of the degraded axial model (ADO). The research is concerned with both modeling and mathematical solution. Also, many numerical aspects of computer realization are discussed.

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General solution of the dispersion model for a one-dimensional stirred flow system using Danckwerts’ boundary conditions

Cited by 9 publications

References 5 publications

Influence of the Non‐Perfect Step Input Concentration at the Feed Side of the Membrane Surface on the Diffusion Coefficient Evaluation

Influence of the Non‐Perfect Step Input Concentration at the Feed Side of the Membrane Surface on the Diffusion Coefficient Evaluation

Development of a time temperature integrator for quantification of thermal treatment in scraped surface heat exchangers

Generalized semi-opened axial dispersion model

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