Kinetic and dynamic chromatographic systems and models of mass transport: Behavior of multicomponent concentration waves

Kalinichev, A. I.

doi:10.1134/s2070205111060062

Cited by 5 publications

(20 citation statements)

References 6 publications

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“…4 The MMT NC "sink"-"source" mass transformation mechanism with the corresponding internal J k.m.p -fluxes (visually depicted in Figure 1 The propagating mode of the multi-component {X n (L,T}concentration waves behaviour together with their interferenceinteraction during the computerized simulation in the combined sorption NC media-matrix gives the fundamental understanding of the MMT NC theoretical problems. Previously the wave approach (here W-concept) has been used rather successfully by the simple previous MMT k (1)…”

Section: (S5 Below)mentioning

confidence: 99%

“…Model for the MMT NC kinetics with the three { m1 (Rp) + , (3,4) p + , 5 R 0 }-principal components in the NC Model for the k (1) 5-variance in the publications. 2,3…”

Section: (S5 Below)mentioning

confidence: 99%

“…The fundamental (W)-concept of "the multi-component waves" [1][2][3] is widely used in the theoretical description for many scientific fields of the multi-component transport for the various kinetic and dynamic MMT systems. The extensive review 3 presents the "multi-component waves" (W)-concept which has wide area for the applications in such various research fields as the percolation processes 5 , mechanics of liquids, gas dynamics, theory of burning and even the street traffic.…”

Section: Fundamental Wave (W)-concept For the Various Multicomponent mentioning

confidence: 99%

“…The author's computer simulation of the multi(n=6)-component mass transfer (MMT) NC kinetics is based on the irreversible thermodynamics approach with the mathematical approximate numerical solution of the multi-component mass balance described by the mass balance partial differential MMT n-Eqns (with k (2) =6variance) for the bi-functional MMT combined NC sorption system previously considered in publications. [1][2][3] One of the most important concept of the irreversible thermodynamics used here during the computer simulation proposed is the propagating mode of the multi(n=6)-component {X n (L,T)}-concentration waves (S. 4,[6][7][8] describing the MMT NC kinetics accordingly to the wave (W)concept. [1][2][3] The following notation "{2 p X 2 m } below emphasizes the noval expanded six(n=6)-component advanced bi-functional MMT NC Model mentioned with the k (2) (6)-variance comprising the two paired { (3,4) p X m 1,2 } (or else{2 p X 2 m }) principal sorption components participated in the MMT selective paired (I 1,2 )-MAL S reactions.…”

Section: Introductionmentioning

confidence: 99%

“…[1][2][3] One of the most important concept of the irreversible thermodynamics used here during the computer simulation proposed is the propagating mode of the multi(n=6)-component {X n (L,T)}-concentration waves (S. 4,[6][7][8] describing the MMT NC kinetics accordingly to the wave (W)concept. [1][2][3] The following notation "{2 p X 2 m } below emphasizes the noval expanded six(n=6)-component advanced bi-functional MMT NC Model mentioned with the k (2) (6)-variance comprising the two paired { (3,4) p X m 1,2 } (or else{2 p X 2 m }) principal sorption components participated in the MMT selective paired (I 1,2 )-MAL S reactions. The k (2) (6)-{2 p X 2 m } bi-functional NC Model concerned comprises the corresponding paired selective (I.K 1,2 )-MAL S relationships.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Concentration waves behaviour and displacement development in the nanocomposites during mass transfer kinetics on the basis of the author’s bi–functional multicomponent models

Ai¹

2018

MSEIJ

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The recent computer numerical simulation approach for the MMT NC kinetics considered here is based on the foundations of the irreversible thermodynamics such as: multi(n)-component (n=6) mass balance n-Eqns. mentioned; the k (2) (6)-variance (where k (2) is determined as "the degree of freedom" for the MMT NC sorption system considered here by the modeling); the fundamental wave concept (W) of the propagating mode of the multi-component {X n (L,T)}concentration waves; two Mass Action Laws (MAL S) with the {K S m1,2 }-two Selectivity parameters; the "sink-source" (or in other words "sorptiondesorption") mass transformation mechanism for various J k,m,p-mass fluxes, and including some others. The theoretical computer simulation is based on the recent advanced bifunctional NC Model developed. It comprises the various I, II-MMT co-routes for the two (3,4) p-principal sorbate components in the bi-functional NC matrix, i.e. (a) the paired (I 1,2)-selective MMT routes described by the MAL S (I.K 1,2)relationships which comprise the two selective paired "mass transformations" {namely (3,4) p⇌m 1,2 } onto the active fixed 6 R 0 ,"NP 0-nanosites" (i.e. the zero charged 6 R 0-principal 6th-component, namely "NP 0-nanosites" introduced into the consideration of the multicomponent kinetic process) together with (b) the D 3,4,5-multiDiffusion, (II)-MMT co-route for the diffusible (3,4) p-sorbate principals in the NC pores. The k (2) (6)-"variance" of the advanced recent k (2) (6)-bi-functional NC Model developed here (including the I&II-MMT coroutes) is one of the thermodynamic key parameter of the six(n)-component MMT NC sorption system considered. There is included here into the computer modelling the second MMT (II)-coroute with the realization of the {D 3-5 }-multi-Diffusion for the two diffusing (3,4) p +-principal sorbate components including additionally the 5th-anionic co-ions, (i.e. j-5-component intended for the maintaining of the electroneutrality condition) in the combined bi-functional MMT NC sorption system mentioned.. The conceptual schemes of the author's advanced k (2) (6)-NC Model. are displayed in the visual conceptual illustrations with the inclusion of the selective "sink-source" J k,m,p-mass fluxes mechanism mentioned. Further there is shown visually the interaction of the {X 1,2,6 (L,T)}-travelling concentration waves by the recent computer simulation developed which brings the Displacement Development (DD)-behavior of the two m 1,2-interactive X 1 (L,T)-displacer, and X 2 (L,T)-displaced concentration waves. The intensity of the DD-effect is estimated by the X 2 m-peak concentration with depending on the determinative two components' {K S m1,2 }-Selectivity factor.

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Section: (S5 Below)mentioning

confidence: 99%

“…Model for the MMT NC kinetics with the three { m1 (Rp) + , (3,4) p + , 5 R 0 }-principal components in the NC Model for the k (1) 5-variance in the publications. 2,3…”

Section: (S5 Below)mentioning

confidence: 99%

Section: Fundamental Wave (W)-concept For the Various Multicomponent mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Concentration waves behaviour and displacement development in the nanocomposites during mass transfer kinetics on the basis of the author’s bi–functional multicomponent models

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A macrokinetic model of redox sorption on metal–ion exchanger nanocomposites at electrochemical polarization

Polyanskii

Korzhov

Vakhnin

et al. 2016

Russ. J. Phys. Chem.

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New model of multicomponent masstransfer kinetics in bifunctional matrix of nanocomposites and results of simulation

Kalinitchev

2013

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Kinetic and dynamic chromatographic systems and models of mass transport: Behavior of multicomponent concentration waves

Cited by 5 publications

References 6 publications

Concentration waves behaviour and displacement development in the nanocomposites during mass transfer kinetics on the basis of the author’s bi–functional multicomponent models

Concentration waves behaviour and displacement development in the nanocomposites during mass transfer kinetics on the basis of the author’s bi–functional multicomponent models

A macrokinetic model of redox sorption on metal–ion exchanger nanocomposites at electrochemical polarization

New model of multicomponent masstransfer kinetics in bifunctional matrix of nanocomposites and results of simulation

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