Numerical approximation of a two-dimensional non-equilibrium model of non-isothermal liquid chromatography considering core-shell particles

Ahmad, Abdulaziz Garba; Perveen, Sadia; Qamar, Shamsul

doi:10.1080/10826076.2020.1812641

Cited by 4 publications

(7 citation statements)

References 56 publications

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“…A high-resolution finite volume method is proposed with flux limitation in this section to construct the estimated results to examine the one-dimensional general rate model with a response of the heterogeneous reaction in the particle-phase equation. In prior publications, 3,14,15 we validated the order of accuracy for this method numerically analytically. The system is secondorder precise in both axial and radial coordinates.…”

Section: Numerical Schemementioning

confidence: 98%

“…The backward difference scheme is used in estimating the concentration fluxes at the interfaces of every cell; a first-order efficient method can be created , c normall , m + 1 / 2 = c normall , m , 0.25em c normall , m − 1 / 2 = c normall , m − 1 c pl , m , n + 1 / 2 = c pl , m , n , 0.25em c pl , m , n − 1 / 2 = c normall , m , n − 1 …”

Section: Numerical Schemementioning

confidence: 99%

“…To avoid division by zero, a tiny value γ = 10 –10 is utilized here. φ and ϕ are employed to maintain the scheme’s local monotonicity (positivity), which is defined as , φ ( α l , m ) = max ( 0 , min true( 2 α normall , m , min ( 1 3 + 2 3 α l , m , 2 ) true) ) ϕ ( β m , n ) = max ( 0 , min true( 2 β m , n , min ( 1 3 + 2 3 β m , n , 2 ) true) ) The proposed method is inapplicable at the border intervals. Thus, the backward approximation of first order is utilized for the boundary of cell fluxes, whereas the high-resolution approach is employed for all internal cell interface fluxes.…”

Section: Numerical Schemementioning

confidence: 99%

See 2 more Smart Citations

Analysis of Liquid Chromatography Considering a Linear Single-Component Heterogeneous-Type Reactive General Rate Model

Alharbi,

Bashir,

Ramzan

et al. 2023

ACS Omega

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This paper elaborates on the significance of liquid chromatography for a single-component reactive linear general rate model. The model equations consist of a set of two coupled partial differential equations, which include diffusion, interfacial mass transfer, axial dispersion, external and intraparticle pore diffusivity, and heterogeneous chemical reaction of the first order with two sets of boundary conditions. The model equations are solved by the Laplace transformation. The actual time domain solution is obtained by numerical Laplace inversion, as analytical inversion cannot be obtained. The graphical sketch of different physical parameters is presented to analyze the dynamics of the elution profiles. The result indicates that the chromatographic reactor works more efficiently on increasing the value of the heterogeneoustype first-order reaction. To check the analytical results, a second-order high-resolution finite volume scheme is used. Both results are in good agreement and indicate the correctness of the numerical scheme. The current work is also compared with the previously available numerical schemes, which shows that the proposed numerical scheme is better for elaborating the chromatographic reactor performance. A comparison table is also presented to compute error analysis and computational run time for analyzing the efficiency of the reactor. A graphical sketch of the numerical temporal moment analysis is also presented, which gives significant information about the performance and the shape of the concentration profiles.

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Section: Numerical Schemementioning

confidence: 98%

Section: Numerical Schemementioning

confidence: 99%

Section: Numerical Schemementioning

confidence: 99%

See 1 more Smart Citation

Analysis of Liquid Chromatography Considering a Linear Single-Component Heterogeneous-Type Reactive General Rate Model

Alharbi,

Bashir,

Ramzan

et al. 2023

ACS Omega

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“…e utilization of core-shell particles has increasingly captivated the interest of many researchers in both the analytical and preparatory liquid chromatography separation processes [16][17][18]. ese were used to separate peptides as well as other molecules like nucleotides and proteins [12,16].…”

Section: Introductionmentioning

confidence: 99%

“…e most completed model, that is, the general rate model (GRM), was used to investigate and optimize the effects on multicomponent isocratic elution by using the core radius fraction by Gu et al [21]. Qamar et al and his fellow researchers have analyzed the effectiveness of fully porous particles and also some with the core-shell particles by developing and solving several chromatographic separation models [18,22].…”

Section: Introductionmentioning

confidence: 99%

A Novel Numerical Treatment of Nonlinear and Nonequilibrium Model of Gradient Elution Chromatography considering Core-Shell Particles in the Column

Ahmad¹,

Kaabar

Rashid

et al. 2022

Mathematical Problems in Engineering

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An extended method of semidiscrete high-resolution finite volume is used in this paper to obtain numerical solutions for a formulated nonlinear lumped kinetic model of liquid chromatographic process to examine the effect of chromatographic column overloading gradient elution considering core-shell particles. The model constitutes linear solvent strength (LSS), Henry’s constant, coefficient of nonlinearity, and coefficient of axial dispersion. The effects of modulator concentration changes for the elution of single and two components are analyzed. The advantages of introducing gradient elution against isocratic elution in terms of core radius fraction are investigated intensively. Numerical temporal moments are generated from the solutions obtained for a more in-depth examination of the considered model. Moreover, multiple forms of a single- and two-component mixture are generated to analyze the influences of core radius fractions on gradient elution. For example, the obtained results are utilized to investigate the effects of the slope of gradient, concentration of modulator, solvent strength parameter, coefficient of nonlinearity, coefficient of mass transfer, and coefficient of axial dispersion on the profiles of concentration in order to improve the process performance using optimal core radius fraction parameter values.

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Theoretical Analysis of Linearized Non-isothermal Two-dimensional Model of Liquid Chromatography Columns Packed with Core-Shell Particles

Uche¹,

Uche²

2021

Int. J. Appl. Comput. Math

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Numerical approximation of a two-dimensional non-equilibrium model of non-isothermal liquid chromatography considering core-shell particles

Cited by 4 publications

References 56 publications

Analysis of Liquid Chromatography Considering a Linear Single-Component Heterogeneous-Type Reactive General Rate Model

Analysis of Liquid Chromatography Considering a Linear Single-Component Heterogeneous-Type Reactive General Rate Model

A Novel Numerical Treatment of Nonlinear and Nonequilibrium Model of Gradient Elution Chromatography considering Core-Shell Particles in the Column

Theoretical Analysis of Linearized Non-isothermal Two-dimensional Model of Liquid Chromatography Columns Packed with Core-Shell Particles

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