Analysis of travelling wave equations in sorption processes

E. Barrab\'es; J. Anglada Lloveras; M. Aguareles

arxiv: 2507.16404 · v3 · submitted 2025-07-22 · 🧮 math-ph · math.MP

Analysis of travelling wave equations in sorption processes

J. Anglada Lloveras , M. Aguareles , E. Barrab\'es This is my paper

Pith reviewed 2026-05-19 03:42 UTC · model grok-4.3

classification 🧮 math-ph math.MP

keywords travelling wavessorption processessingular perturbationheteroclinic connectionadsorption columninverse Peclet numberPDE reduction

0 comments

The pith

Travelling waves persist in sorption processes for small inverse Péclet numbers, connecting clean downstream states to fully saturated upstream conditions.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper models contaminant transport and adsorption in a column using a system of PDEs. A travelling-wave ansatz reduces the system to an ODE parametrized by the inverse Péclet number. Treating this small parameter as a singular perturbation converts the problem into a slow-fast system whose leading-order equation admits a heteroclinic orbit between the clean and saturated equilibria. The authors prove that this orbit persists for small positive values of the parameter by means of analytical continuation. The persistence result justifies replacing the full PDE model with the reduced slow-fast system when predicting the propagation of a saturation front.

Core claim

The heteroclinic connection associated with the travelling wave persists for small values of the inverse Péclet number. By analytical continuation it follows that the concentration profile transitions from a clean downstream state of the adsorbent matrix to full upstream saturation.

What carries the argument

Persistence of the heteroclinic connection in the singularly perturbed travelling-wave ODE, established via analytical continuation.

If this is right

The leading-order slow-fast approximation accurately describes the saturation front for sufficiently small inverse Péclet numbers.
Sensitivity analysis shows the travelling-wave profile remains robust for moderate values of the inverse Péclet number.
Numerical simulations confirm both the persistence result and the accuracy of the reduced model.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Filter-design calculations can safely use the reduced model even when minor diffusive effects are present.
The same persistence technique may extend to other advection-dominated transport problems in porous media.
Time-dependent inlet concentrations or multi-species sorption could be analyzed by analogous continuation arguments.

Load-bearing premise

The inverse Péclet number is small enough that the singular-perturbation reduction remains valid and the heteroclinic orbit persists under analytical continuation.

What would settle it

Numerical integration of the original PDE system at a small but nonzero inverse Péclet number that shows whether the long-time concentration profile reaches full upstream saturation or deviates from the predicted travelling-wave shape.

Figures

Figures reproduced from arXiv: 2507.16404 by E. Barrab\'es, J. Anglada Lloveras, M. Aguareles.

**Figure 1.** Figure 1: Sketch of an adsorption column. pollution and toxicity in natural ecosystems (see, for instance, [13]). Furthermore, these models have been instrumental in the development of natural adsorbent materials, often derived from industrial waste, and in improving the efficiency of operating conditions in adsorption processes (see, for example, [14], [15] and [16]). Two types of curves are typically obtained from… view at source ↗

**Figure 2.** Figure 2: Evolution of the concentration c(x, t) and the adsorbed fraction q(x, t) inside of the column and breakthrough curve, c(L, t), obtained by solving system (5) using the parameter values given in (6), and with n = 1, m = 1, using a Péclet number Pe-1 = 0.1 and t ∈ [0, 1412]. 7 [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

**Figure 3.** Figure 3: Evolution of the concentration c(x, t) and the adsorbed fraction q(x, t) inside of the column and breakthrough curve, c(L, t), obtained by solving system (5) using the parameter values given in (6), and with n = 2, m = 1, using a Péclet number Pe-1 = 0.1 and t ∈ [0, 6354]. 8 [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗

**Figure 4.** Figure 4: Position (as the proportion of the column length) of points with a given concentration as [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗

**Figure 5.** Figure 5: Slow-fast dynamics in the configuration space system (17) for ϵ = 0. The fast dynamics take place along the “layers” x = x0. The blue curve corresponds to the slow-set (18). The dynamics along the slow set (18) is given by x ′ = qe + Da qe P(x, 0). Notice that for x ∈ (0, 1), x ′ < 0, that is, the curve is a heteroclinic connection from x = F = 1, y = 0 to x = F = 0, y = 0. In fact, the critical slow set (… view at source ↗

**Figure 6.** Figure 6: Heteroclinic connections of (14a) in the phase plane (left column) and travelling wave [PITH_FULL_IMAGE:figures/full_fig_p014_6.png] view at source ↗

**Figure 7.** Figure 7: Heteroclinic connections of (14a) in the phase plane (left column) and travelling wave [PITH_FULL_IMAGE:figures/full_fig_p015_7.png] view at source ↗

**Figure 8.** Figure 8: L 2 -norm provided in (21) of the difference between the travelling wave profiles obtained by solving the system (8) with F(0) = 1/2, as a function of the inverse Péclet number). See Section 4 for a description of the numerical resolutions. 17 [PITH_FULL_IMAGE:figures/full_fig_p017_8.png] view at source ↗

**Figure 9.** Figure 9: Relative error of the breakthrough time as a function of the inverse Péclet number, as defined [PITH_FULL_IMAGE:figures/full_fig_p018_9.png] view at source ↗

read the original abstract

This work presents a mathematical model of an adsorption column to study the evolution of contaminant concentration and adsorbed quantity along the longitudinal axis of the filter. The model is formulated as a system of partial differential equations (PDEs) and analysed using a travelling-wave approach, which reduces the system to a second-order ordinary differential equation depending on the inverse P\'eclet number, typically a small parameter. By neglecting this parameter, the model is simplified via a singular perturbation to a leading-order approximation, which can be interpreted as a slow-fast system. We rigorously justify this reduction by proving the persistence of the heteroclinic connection associated with the travelling wave. Using analytical continuation, we conclude that, at least for small values of the inverse P\'eclet number, the concentration profile transitions from a clean downstream state of the adsorbent matrix to fully upstream saturation. Numerical simulations are presented to validate the analytical results and to assess the accuracy of the reduced model. A sensitivity analysis demonstrates that the travelling-wave approximation remains remarkably robust for moderate values of the inverse P\'eclet number.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper proves that the heteroclinic travelling wave persists in this sorption model for small inverse Péclet numbers via analytical continuation, backed by numerics.

read the letter

The key point is that this paper takes a PDE model for contaminant transport and adsorption in a column, reduces it to a travelling wave ODE, and proves that the connecting orbit between the clean and saturated states persists when the inverse Péclet number is small. They use singular perturbation to get a reduced slow-fast system and then analytical continuation to show the heteroclinic stays intact. What stands out is the careful justification of the reduction. Travelling waves are common in these models, but pinning down the persistence with analysis rather than just numerics adds some rigor. The numerical simulations and sensitivity analysis are a plus; they show the approximation works reasonably even beyond the very small parameter regime. The math seems standard but executed properly for this application. On the downside, the result is quite specific to this sorption setup and doesn't introduce new methods or extend to broader classes of equations. The novelty is incremental, basically applying known techniques to justify an existing approximation. If the proof relies on particular properties of the adsorption isotherm or the form of the equations, that limits how far it travels. Also, while they mention validation, without seeing detailed error bounds or convergence rates in the full text, it's hard to gauge how sharp the result is. This kind of work is mainly for researchers in applied mathematics who deal with reduced models for filtration or adsorption processes. Someone looking for a concrete example of singular perturbation in a real-world PDE system might find it useful, especially the combination of analysis and computation. It has enough substance to warrant a serious referee. The central claim is well-defined and they back it with both proof and checks. I would send this to peer review rather than desk reject.

Referee Report

0 major / 3 minor

Summary. This paper models sorption processes in an adsorption column via a system of PDEs for contaminant concentration and adsorbed quantity. Assuming a travelling wave ansatz reduces the PDEs to a second-order ODE in the inverse Péclet number ε. The authors perform a singular perturbation analysis for small ε, interpreting it as a slow-fast system, and prove the persistence of the heteroclinic connection between the clean downstream and fully saturated upstream states using analytical continuation. They support this with numerical simulations validating the approximation and a sensitivity analysis showing robustness for moderate ε values.

Significance. The rigorous proof of heteroclinic persistence provides a solid mathematical justification for the reduced travelling-wave model in the small-ε regime, which is common in many sorption applications. The combination of analytical continuation for the persistence result and numerical validation, including sensitivity to moderate ε, enhances the reliability of the approximation for practical use. This contributes to the field by linking singular perturbation theory with concrete sorption models.

minor comments (3)

[Numerical validation / results] The abstract states that numerical simulations 'validate the analytical results and assess the accuracy of the reduced model,' but without explicit error norms, convergence rates as ε → 0, or comparison metrics in the results section, it is difficult to quantify how well the reduced model approximates the full ODE for small but nonzero ε.
[Sensitivity analysis] The sensitivity analysis claims the travelling-wave approximation 'remains remarkably robust for moderate values' of ε, yet the specific range tested, the quantitative measure of robustness (e.g., L2 deviation or wave speed error), and the corresponding figures or tables are not referenced, weakening the claim.
[Persistence proof / § on analytical continuation] Notation for the slow and fast variables in the reduced system and the precise statement of the transversality or non-degeneracy conditions used in the analytical continuation argument should be made explicit early in the persistence proof to improve readability.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive and accurate summary of our manuscript on travelling-wave analysis of sorption processes. We appreciate the recognition of the significance of the heteroclinic persistence result and the recommendation for minor revision. As no specific major comments were raised in the report, we will incorporate any minor editorial or presentational improvements in the revised version.

Circularity Check

0 steps flagged

No significant circularity; derivation is an independent persistence proof

full rationale

The paper reduces the sorption PDE system to a second-order travelling-wave ODE parametrized by the inverse Péclet number, then applies singular perturbation to obtain a slow-fast limit system whose heteroclinic orbit is continued analytically back to small positive values of the parameter. This persistence argument is presented as a self-contained mathematical construction relying on standard analytic-continuation techniques for heteroclinic orbits; it does not invoke fitted parameters, self-referential definitions, or load-bearing self-citations whose validity depends on the present work. The abstract and claim description contain no equations that equate a derived quantity to an input by construction, nor any renaming of known empirical patterns. The result is therefore externally verifiable against the stated assumptions on the reduced system and does not reduce to its own inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The analysis rests on standard existence and continuation results for ODEs together with the modelling assumption that the inverse Péclet number is small.

axioms (1)

domain assumption The inverse Péclet number is a small positive parameter
Invoked to justify singular perturbation and the persistence statement for small values.

pith-pipeline@v0.9.0 · 5717 in / 1249 out tokens · 34521 ms · 2026-05-19T03:42:00.892778+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/AbsoluteFloorClosure.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

We rigorously justify this reduction by proving the persistence of the heteroclinic connection associated with the travelling wave. Using analytical continuation, we conclude that, at least for small values of the inverse Péclet number...
IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

System (17) is a slow-fast system... Considering ϵ = 0 in system (17), we recover the leading-order approximation equation (15a).

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

27 extracted references · 27 canonical work pages

[1]

T. G. Myers, A. Cabrera-Codony, A. Valverde, On the development of a consistent math- ematical model for adsorption in a packed column (and why standard models fail), Inter- national Journal of Heat and Mass Transfer 202 (2023) 123660

work page 2023
[2]

S. Li, S. Deng, L. Zhao, R. Zhao, M. Lin, Y. Du, Y. Lian, Mathematical modeling and numerical investigation of carbon capture by adsorption: Literature review and case study, Applied Energy 221 (2018) 437–449

work page 2018
[3]

Patel, Fixed-bed column adsorption study: a comprehensive review, Applied Water Science 9 (3) (2019) 45

H. Patel, Fixed-bed column adsorption study: a comprehensive review, Applied Water Science 9 (3) (2019) 45

work page 2019
[4]

M. S. Shafeeyan, W. M. A. Wan Daud, A. Shamiri, A review of mathematical modeling of fixed-bed columns for carbon dioxide adsorption, Chemical Engineering Research and Design 92 (5) (2014) 961–988

work page 2014
[5]

Aguareles, E

M. Aguareles, E. Barrabés, T. Myers, A. Valverde, Mathematical analysis of a sips-based model for column adsorption, Physica D: Nonlinear Phenomena 448 (2023) 133690

work page 2023
[6]

ˇSivec, B

R. ˇSivec, B. Pomeroy, M. Hus, B. Likozar, M. Grilc, Modelling of transport, adsorption and surface reaction kinetics on ni, pd and ru metallic/acidic catalyst sites during hy- drodeoxygenation of furfural, Chemical Engineering Journal 483 (2024) 149284

work page 2024
[7]

Zhou, R.-C

B.-Q. Zhou, R.-C. Yang, H.-P. LI, Y.-J. Wang, C.-Y. Zhang, Z.-J. Xiao, Z.-Q. He, W.-H. Pang, Numeric and nonnumeric information input to predict adsorption amount, capac- ity and kinetics of tetracyclines by biochar via machine learning, Chemical Engineering Journal 471 (2023) 144636

work page 2023
[8]

M. Bos, T. Kreuger, S. Kersten, D. Brilman, Study on transport phenomena and intrinsic kineticsforco2adsorptioninsolidaminesorbent, ChemicalEngineeringJournal377(2019) 120374. 20

work page 2019
[9]

L. C. Auton, M. Aguareles, A. Valverde, T. G. Myers, M. Calvo-Schwarzwalder, An an- alytical investigation into solute transport and sorption via intra-particle diffusion in the dual-porosity limit, Applied Mathematical Modelling 130 (2024) 827–851

work page 2024
[10]

Myers, F

T. Myers, F. Font, M. Hennessy, Mathematical modelling of carbon capture in a packed column by adsorption, Applied Energy 278 (2020) 115565

work page 2020
[11]

Myers, F

T. Myers, F. Font, Mass transfer from a fluid flowing through a porous media, International Journal of Heat and Mass Transfer 163 (2020) 120374

work page 2020
[12]

Mondal, S

R. Mondal, S. Mondal, K. V. Kurada, S. Bhattacharjee, S. Sengupta, M. Mondal, S. Kar- makar, S. De, I. M. Griffiths, Modelling the transport and adsorption dynamics of arsenic in a soil bed filter, Chemical Engineering Science 210 (2019) 115205

work page 2019
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N. A. Sobolev, K. S. Larionov, D. S. Mryasova, A. N. Khreptugova, A. B. Volikov, A. I. Konstantinov, D. S. Volkov, I. V. Perminova, Yedoma permafrost releases organic matter with lesser affinity for cu2+ and ni2+ as compared to peat from the non-permafrost area: Risk of rising toxicity of potentially toxic elements in the arctic ocean, Toxics 11 (6) (2023)

work page 2023
[14]

Baraket, H

F.Z.Chajri, B.Meryem, B.Hatimi, A.Sanad, M.Joudi, A.Aarfane, M.Siniti, M.Bakasse, A. Baraket, H. Nasrellah, Study on wastewater treatment in the textile industry by ad- sorption of reactive red 141 dye using a phosphogypsum/vanadium composite developed from phosphate industry waste, Ecological Engineering & Environmental Technology 25 (2024) 46–62

work page 2024
[15]

Sadaiyan, R

B. Sadaiyan, R. Karunanithi, Y. Karunanithi, Adsorptive removal of orange g dye from aqueous solution by ultrasonic-activated peanut shell powder: isotherm, kinetic and ther- modynamic studies, Environmental Technology (United Kingdom) (2023) 1–15

work page 2023
[16]

Valverde, A

A. Valverde, A. Cabrera-Codony, M. Calvo-Schwarzwalder, T. G. Myers, Investigating the impact of adsorbent particle size on column adsorption kinetics through a mathematical model, International Journal of Heat and Mass Transfer 218 (2024) 124724

work page 2024
[17]

Arnaut, H

L. Arnaut, H. Burrows, Chemical kinetics: from molecular structure to chemical reactivity, Elsevier, 2006

work page 2006
[18]

Sips, On the structure of a catalyst surface, The Journal of Chemical Physics 16 (5) (1948) 490–495

R. Sips, On the structure of a catalyst surface, The Journal of Chemical Physics 16 (5) (1948) 490–495

work page 1948
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Danckwerts, Continuous flow systems

P. Danckwerts, Continuous flow systems. distribution of residence times, Chemical Engi- neering Sci. 2 (1953) 1–13

work page 1953
[20]

Danckwerts

J. Pearson, A note on the “Danckwerts”boundary conditions for continuous flow reactors, Chemical Engineering Sci. 10 (1959) 281–284

work page 1959
[21]

Cabrera-Codony, E

A. Cabrera-Codony, E. Santos-Clotas, C. O. Ania, M. J. Martin, Competitive siloxane adsorption in multicomponent gas streams for biogas upgrading, Chemical Engineering Journal 344 (2018) 565–573. 21

work page 2018
[22]

A. H. Sulaymon, S. A. Yousif, M. M. Al-Faize, Competitive biosorption of lead mercury chromium and arsenic ions onto activated sludge in fixed bed adsorber, Journal of the Taiwan Institute of Chemical Engineers 45 (2) (2014) 325–337

work page 2014
[23]

Dumortier, R

F. Dumortier, R. Roussarie, Canard Cycles and Center Manifolds, Vol. 121 (577) of Mem- oirs of the American Mathematical Society, American Mathematical Society, 1996

work page 1996
[24]

P. D. Maesschalck, J. Dumortier, R. Roussarie, Canard Cycles. From Birth to Transition., Vol.73ofErgebnissederMathematikundihrerGrenzgebiete.3.Folge/ASeriesofModern Surveys in Mathematics, Springer Cham, 2021

work page 2021
[25]

Myers, M

T. Myers, M. Calvo-Schwarzwalder, F. Font, A. Valverde, Modelling large mass removal in adsorption columns, International Communications in Heat and Mass Transfer 163 (2025) 108652

work page 2025
[26]

J. A. Delgado, M. A. Uguina, J. L. Sotelo, B. Ruíz, Fixed-bed adsorption of carbon diox- ide–helium, nitrogen–helium and carbon dioxide–nitrogen mixtures onto silicalite pellets, Separation and Purification Technology 49 (1) (2006) 91–100

work page 2006
[27]

T. G. Myers, A. Cabrera-Codony, A. Valverde, On the development of a consistent math- ematical model for adsorption in a packed column (and why standard models fail), Inter- national Journal of Heat and Mass Transfer 202 (2023) 123660. 22

work page 2023

[1] [1]

T. G. Myers, A. Cabrera-Codony, A. Valverde, On the development of a consistent math- ematical model for adsorption in a packed column (and why standard models fail), Inter- national Journal of Heat and Mass Transfer 202 (2023) 123660

work page 2023

[2] [2]

S. Li, S. Deng, L. Zhao, R. Zhao, M. Lin, Y. Du, Y. Lian, Mathematical modeling and numerical investigation of carbon capture by adsorption: Literature review and case study, Applied Energy 221 (2018) 437–449

work page 2018

[3] [3]

Patel, Fixed-bed column adsorption study: a comprehensive review, Applied Water Science 9 (3) (2019) 45

H. Patel, Fixed-bed column adsorption study: a comprehensive review, Applied Water Science 9 (3) (2019) 45

work page 2019

[4] [4]

M. S. Shafeeyan, W. M. A. Wan Daud, A. Shamiri, A review of mathematical modeling of fixed-bed columns for carbon dioxide adsorption, Chemical Engineering Research and Design 92 (5) (2014) 961–988

work page 2014

[5] [5]

Aguareles, E

M. Aguareles, E. Barrabés, T. Myers, A. Valverde, Mathematical analysis of a sips-based model for column adsorption, Physica D: Nonlinear Phenomena 448 (2023) 133690

work page 2023

[6] [6]

ˇSivec, B

R. ˇSivec, B. Pomeroy, M. Hus, B. Likozar, M. Grilc, Modelling of transport, adsorption and surface reaction kinetics on ni, pd and ru metallic/acidic catalyst sites during hy- drodeoxygenation of furfural, Chemical Engineering Journal 483 (2024) 149284

work page 2024

[7] [7]

Zhou, R.-C

B.-Q. Zhou, R.-C. Yang, H.-P. LI, Y.-J. Wang, C.-Y. Zhang, Z.-J. Xiao, Z.-Q. He, W.-H. Pang, Numeric and nonnumeric information input to predict adsorption amount, capac- ity and kinetics of tetracyclines by biochar via machine learning, Chemical Engineering Journal 471 (2023) 144636

work page 2023

[8] [8]

M. Bos, T. Kreuger, S. Kersten, D. Brilman, Study on transport phenomena and intrinsic kineticsforco2adsorptioninsolidaminesorbent, ChemicalEngineeringJournal377(2019) 120374. 20

work page 2019

[9] [9]

L. C. Auton, M. Aguareles, A. Valverde, T. G. Myers, M. Calvo-Schwarzwalder, An an- alytical investigation into solute transport and sorption via intra-particle diffusion in the dual-porosity limit, Applied Mathematical Modelling 130 (2024) 827–851

work page 2024

[10] [10]

Myers, F

T. Myers, F. Font, M. Hennessy, Mathematical modelling of carbon capture in a packed column by adsorption, Applied Energy 278 (2020) 115565

work page 2020

[11] [11]

Myers, F

T. Myers, F. Font, Mass transfer from a fluid flowing through a porous media, International Journal of Heat and Mass Transfer 163 (2020) 120374

work page 2020

[12] [12]

Mondal, S

R. Mondal, S. Mondal, K. V. Kurada, S. Bhattacharjee, S. Sengupta, M. Mondal, S. Kar- makar, S. De, I. M. Griffiths, Modelling the transport and adsorption dynamics of arsenic in a soil bed filter, Chemical Engineering Science 210 (2019) 115205

work page 2019

[13] [13]

N. A. Sobolev, K. S. Larionov, D. S. Mryasova, A. N. Khreptugova, A. B. Volikov, A. I. Konstantinov, D. S. Volkov, I. V. Perminova, Yedoma permafrost releases organic matter with lesser affinity for cu2+ and ni2+ as compared to peat from the non-permafrost area: Risk of rising toxicity of potentially toxic elements in the arctic ocean, Toxics 11 (6) (2023)

work page 2023

[14] [14]

Baraket, H

F.Z.Chajri, B.Meryem, B.Hatimi, A.Sanad, M.Joudi, A.Aarfane, M.Siniti, M.Bakasse, A. Baraket, H. Nasrellah, Study on wastewater treatment in the textile industry by ad- sorption of reactive red 141 dye using a phosphogypsum/vanadium composite developed from phosphate industry waste, Ecological Engineering & Environmental Technology 25 (2024) 46–62

work page 2024

[15] [15]

Sadaiyan, R

B. Sadaiyan, R. Karunanithi, Y. Karunanithi, Adsorptive removal of orange g dye from aqueous solution by ultrasonic-activated peanut shell powder: isotherm, kinetic and ther- modynamic studies, Environmental Technology (United Kingdom) (2023) 1–15

work page 2023

[16] [16]

Valverde, A

A. Valverde, A. Cabrera-Codony, M. Calvo-Schwarzwalder, T. G. Myers, Investigating the impact of adsorbent particle size on column adsorption kinetics through a mathematical model, International Journal of Heat and Mass Transfer 218 (2024) 124724

work page 2024

[17] [17]

Arnaut, H

L. Arnaut, H. Burrows, Chemical kinetics: from molecular structure to chemical reactivity, Elsevier, 2006

work page 2006

[18] [18]

Sips, On the structure of a catalyst surface, The Journal of Chemical Physics 16 (5) (1948) 490–495

R. Sips, On the structure of a catalyst surface, The Journal of Chemical Physics 16 (5) (1948) 490–495

work page 1948

[19] [19]

Danckwerts, Continuous flow systems

P. Danckwerts, Continuous flow systems. distribution of residence times, Chemical Engi- neering Sci. 2 (1953) 1–13

work page 1953

[20] [20]

Danckwerts

J. Pearson, A note on the “Danckwerts”boundary conditions for continuous flow reactors, Chemical Engineering Sci. 10 (1959) 281–284

work page 1959

[21] [21]

Cabrera-Codony, E

A. Cabrera-Codony, E. Santos-Clotas, C. O. Ania, M. J. Martin, Competitive siloxane adsorption in multicomponent gas streams for biogas upgrading, Chemical Engineering Journal 344 (2018) 565–573. 21

work page 2018

[22] [22]

A. H. Sulaymon, S. A. Yousif, M. M. Al-Faize, Competitive biosorption of lead mercury chromium and arsenic ions onto activated sludge in fixed bed adsorber, Journal of the Taiwan Institute of Chemical Engineers 45 (2) (2014) 325–337

work page 2014

[23] [23]

Dumortier, R

F. Dumortier, R. Roussarie, Canard Cycles and Center Manifolds, Vol. 121 (577) of Mem- oirs of the American Mathematical Society, American Mathematical Society, 1996

work page 1996

[24] [24]

P. D. Maesschalck, J. Dumortier, R. Roussarie, Canard Cycles. From Birth to Transition., Vol.73ofErgebnissederMathematikundihrerGrenzgebiete.3.Folge/ASeriesofModern Surveys in Mathematics, Springer Cham, 2021

work page 2021

[25] [25]

Myers, M

T. Myers, M. Calvo-Schwarzwalder, F. Font, A. Valverde, Modelling large mass removal in adsorption columns, International Communications in Heat and Mass Transfer 163 (2025) 108652

work page 2025

[26] [26]

J. A. Delgado, M. A. Uguina, J. L. Sotelo, B. Ruíz, Fixed-bed adsorption of carbon diox- ide–helium, nitrogen–helium and carbon dioxide–nitrogen mixtures onto silicalite pellets, Separation and Purification Technology 49 (1) (2006) 91–100

work page 2006

[27] [27]

T. G. Myers, A. Cabrera-Codony, A. Valverde, On the development of a consistent math- ematical model for adsorption in a packed column (and why standard models fail), Inter- national Journal of Heat and Mass Transfer 202 (2023) 123660. 22

work page 2023