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Analytical solutions for reactive shear dispersion with boundary adsorption and desorption

Published online by Cambridge University Press:  30 August 2022

Weiquan Jiang Open the ORCID record for Weiquan Jiang [Opens in a new window] ,
Li Zeng Open the ORCID record for Li Zeng [Opens in a new window] ,
Xudong Fu Open the ORCID record for Xudong Fu [Opens in a new window]  and
Zi Wu Open the ORCID record for Zi Wu [Opens in a new window]
Weiquan Jiang
Affiliation:
Department of Hydraulic Engineering, Tsinghua University, Beijing 100084, PR China State Key Laboratory of Hydroscience and Engineering, Tsinghua University, Beijing 100084, PR China
Li Zeng
Affiliation:
State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin, China Institute of Water Resources and Hydropower Research, Beijing 100038, PR China
Xudong Fu*
Affiliation:
Department of Hydraulic Engineering, Tsinghua University, Beijing 100084, PR China State Key Laboratory of Hydroscience and Engineering, Tsinghua University, Beijing 100084, PR China
Zi Wu*
Affiliation:
Department of Hydraulic Engineering, Tsinghua University, Beijing 100084, PR China State Key Laboratory of Hydroscience and Engineering, Tsinghua University, Beijing 100084, PR China
*
†Email addresses for correspondence: xdfu@tsinghua.edu.cn, wuzi@tsinghua.edu.cn
†Email addresses for correspondence: xdfu@tsinghua.edu.cn, wuzi@tsinghua.edu.cn
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Abstract

Surface reactions such as the adsorption and desorption at boundaries are very common for solute dispersion in many applications of chemistry, biology, hydraulics, etc. To study how reversible adsorption affects the transient dispersion, Zhang, Hesse & Wang (J. Fluid Mech., vol. 828, 2017, pp. 733–752) have investigated the temporal evolution of moments using the Laplace transform method. Owing to difficulties introduced by the adsorption–desorption boundary condition, great challenges arise from the inverse Laplace transform: dealing with the singularities by the residue theorem can tremendously increase complexities. This work provides a much simpler analytical method to derive solutions in a more compact form that is valid for the entire range of the reactive transport process. Such a progress demonstrates that the classic framework of separation of variables can be extended and applied to this more general adsorption–desorption condition, based on which higher-order statistics including skewness and kurtosis can be explicitly explored in practice. Also extended is Gill's generalised dispersion model for solute concentration distributions, which can now address the entire transient dispersion characteristics, instead of just applied for the long-time asymptotic reactive process as done previously. Regarding the most classic Taylor dispersion problem, we investigate the influence of the reversible adsorption–desorption on the solute cloud in a tube flow. Not only the transient dispersion characteristics of transverse-average concentration distribution but also those of the bulk, surface and total-average distributions are discussed. We further investigate the influence of initial conditions on the non-uniformity of the transient dispersion over the cross-section.

JFM classification

Mass Transport: Dispersion Reacting Flows: Laminar reacting flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 947 , 25 September 2022 , A37
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© The Author(s), 2022. Published by Cambridge University Press

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References

REFERENCES

Abdollahzadeh, M., Saidi, M.S. & Sadeghi, A. 2017 Enhancement of surface adsorption–desorption rates in microarrays invoking surface charge heterogeneity. Sens. Actuators B Chem. 242, 956–964.CrossRefGoogle Scholar
Agmon, N. 1984 Diffusion with back reaction. J. Chem. Phys. 81 (6), 2811–2817.CrossRefGoogle Scholar
Alexandre, A., Guérin, T. & Dean, D.S. 2021 Generalized Taylor dispersion for translationally invariant microfluidic systems. Phys. Fluids 33 (8), 082004.CrossRefGoogle Scholar
Allaire, G., Mikelić, A. & Piatnitski, A. 2010 Homogenization approach to the dispersion theory for reactive transport through porous media. SIAM J. Math. Anal. 42 (1), 125–144.CrossRefGoogle Scholar
Aminian, M., Bernardi, F., Camassa, R., Harris, D.M. & McLaughlin, R.M. 2016 How boundaries shape chemical delivery in microfluidics. Science 354 (6317), 1252–1256.CrossRefGoogle ScholarPubMed
Andersson, B. & Berglin, T. 1981 Dispersion in laminar flow through a circular tube. Proc. R. Soc. Lond. A 377 (1770), 251–268.Google Scholar
Andrews, S.S. 2009 Accurate particle-based simulation of adsorption, desorption and partial transmission. Phys. Biol. 6 (4), 046015.CrossRefGoogle ScholarPubMed
Aris, R. 1956 On the dispersion of a solute in a fluid flowing through a tube. Proc. R. Soc. Lond. A 235 (1200), 67–77.Google Scholar
Aris, R. 1959 On the dispersion of a solute by diffusion, convection and exchange between phases. Proc. R. Soc. Lond. A 252 (1271), 538–550.Google Scholar
Balakotaiah, V. & Chang, H.-C. 1995 Dispersion of chemical solutes in chromatographs and reactors. Phil. Trans. R. Soc. Lond. A 351 (1695), 39–75.Google Scholar
Balakotaiah, V. & Chang, H.-C. 2003 Hyperbolic homogenized models for thermal and solutal dispersion. SIAM J. Appl. Maths 63 (4), 1231–1258.Google Scholar
Barik, S. & Dalal, D.C. 2017 On transport coefficients in an oscillatory Couette flow with nonlinear chemical decay reactions. Acta Mechanica 228 (7), 2391–2412.CrossRefGoogle Scholar
Barik, S. & Dalal, D.C. 2022 Analytical solution for concentration distribution in an open channel flow with phase exchange kinetics. Acta Mechanica Sin. 38 (3), 321506.CrossRefGoogle Scholar
Barton, N.G. 1983 On the method of moments for solute dispersion. J. Fluid Mech. 126, 205–218.CrossRefGoogle Scholar
Barton, N.G. 1984 An asymptotic theory for dispersion of reactive contaminants in parallel flow. J. Austral. Math. Soc. 25 (3), 287–310.CrossRefGoogle Scholar
Berezhkovskii, A.M. & Skvortsov, A.T. 2013 Aris–Taylor dispersion with drift and diffusion of particles on the tube wall. J. Chem. Phys. 139 (8), 084101.CrossRefGoogle ScholarPubMed
Bishop, L.D.C., Misiura, A., Moringo, N.A. & Landes, C.F. 2020 Unraveling peak asymmetry in chromatography through stochastic theory powered Monte Carlo simulations. J. Chromatogr. A 1625, 461323.CrossRefGoogle ScholarPubMed
Bleys, G. & Joos, P. 1985 Adsorption kinetics of bolaform surfactants at the air/water interface. J. Phys. Chem. 89 (6), 1027–1032.CrossRefGoogle Scholar
Boano, F., Packman, A.I., Cortis, A., Revelli, R. & Ridolfi, L. 2007 A continuous time random walk approach to the stream transport of solutes. Water Resour. Res. 43 (10), W10425.CrossRefGoogle Scholar
Boccardo, G., Sokolov, I.M. & Paster, A. 2018 An improved scheme for a Robin boundary condition in discrete-time random walk algorithms. J. Comput. Phys. 374, 1152–1165.CrossRefGoogle Scholar
Boddington, T. & Clifford, A.A. 1983 The dispersion of a reactive species (atomic hydrogen) in a flowing gas. Proc. R. Soc. Lond. A 389 (1796), 179–196.Google Scholar
Chatwin, P.C. 1970 The approach to normality of the concentration distribution of a solute in a solvent flowing along a straight pipe. J. Fluid Mech. 43 (2), 321–352.CrossRefGoogle Scholar
Chirikjian, G.S. 2009 Stochastic Models, Information Theory, and Lie Groups, Vol. 1: Classical Results and Geometric Methods. Birkhäuser.CrossRefGoogle Scholar
Chu, H.C.W., Garoff, S., Tilton, R.D. & Khair, A.S. 2021 Macrotransport theory for diffusiophoretic colloids and chemotactic microorganisms. J. Fluid Mech. 917, A52.CrossRefGoogle Scholar
Clifford, A.A. 1989 Theory of open-tube chromatography: an exact proof of Golay's equations. J. Chromatogr. A 471, 61–69.CrossRefGoogle Scholar
Clifford, A.A., Gray, P., Mason, R.S. & Waddicor, J.I. 1982 Measurement of the diffusion coefficients of reactive species in dilute gases. Proc. R. Soc. Lond. A 380 (1779), 241–258.Google Scholar
Dagan, G. 1988 Time-dependent macrodispersion for solute transport in anisotropic heterogeneous aquifers. Water Resour. Res. 24 (9), 1491–1500.CrossRefGoogle Scholar
Davidson, M.R. & Schroter, R.C. 1983 A theoretical model of absorption of gases by the bronchial wall. J. Fluid Mech. 129, 313–335.CrossRefGoogle Scholar
Debnath, S., Ghoshal, K. & Kumar, J. 2021 Unsteady two-dimensional suspended sediment transport in open channel flow subject to deposition and re-entrainment. J. Engng Maths 126 (1), 6.CrossRefGoogle Scholar
Debnath, S., Jiang, W., Guan, M. & Chen, G. 2022 Effect of ring-source release on dispersion process in Poiseuille flow with wall absorption. Phys. Fluids 34 (2), 027106.CrossRefGoogle Scholar
Debnath, S., Saha, A.K., Mazumder, B.S. & Roy, A.K. 2019 Transport of a reactive solute in a pulsatile non-Newtonian liquid flowing through an annular pipe. J. Engng Maths 116 (1), 1–22.CrossRefGoogle Scholar
Deng, Y., Noel, A., Elkashlan, M., Nallanathan, A. & Cheung, K.C. 2015 Modeling and simulation of molecular communication systems with a reversible adsorption receiver. IEEE Trans. Mol. Biol. Multi-Scale Commun. 1 (4), 347–362.Google Scholar
Dentz, M. & Carrera, J. 2007 Mixing and spreading in stratified flow. Phys. Fluids 19 (1), 017107.CrossRefGoogle Scholar
van Duijn, C.J., Mikelić, A., Pop, I.S. & Rosier, C. 2008 Effective dispersion equations for reactive flows with dominant Péclet and Damkohler numbers. In Advances in Chemical Engineering (ed. G.B. Marin, D. West & G.S. Yablonsky), vol. 34, pp. 1–45. Academic.CrossRefGoogle Scholar
Elder, J.W. 1959 The dispersion of marked fluid in turbulent shear flow. J. Fluid Mech. 5 (4), 544–560.CrossRefGoogle Scholar
Erban, R. & Chapman, S.J. 2007 Reactive boundary conditions for stochastic simulations of reaction–diffusion processes. Phys. Biol. 4 (1), 16–28.CrossRefGoogle ScholarPubMed
Fang, F., Satulovsky, J. & Szleifer, I. 2005 Kinetics of protein adsorption and desorption on surfaces with grafted polymers. Biophys. J. 89 (3), 1516–1533.CrossRefGoogle ScholarPubMed
Fornstedt, T., Zhong, G. & Guiochon, G. 1996 Peak tailing and mass transfer kinetics in linear chromatography. J. Chromatogr. A 741 (1), 1–12.CrossRefGoogle Scholar
Frankel, I. & Brenner, H. 1989 On the foundations of generalized Taylor dispersion theory. J. Fluid Mech. 204, 97–119.CrossRefGoogle Scholar
Fu, X., Wang, G. & Shao, X. 2005 Vertical dispersion of fine and coarse sediments in turbulent open-channel flows. J. Hydraul. Engng ASCE 131 (10), 877–888.CrossRefGoogle Scholar
Giddings, J.C. & Eyring, H. 1955 A molecular dynamic theory of chromatography. J. Phys. Chem. 59 (5), 416–421.CrossRefGoogle Scholar
Gill, W.N. 1967 A note on the solution of transient dispersion problems. Proc. R. Soc. Lond. A 298 (1454), 335–339.Google Scholar
Gill, W.N. & Sankarasubramanian, R. 1970 Exact analysis of unsteady convective diffusion. Proc. R. Soc. Lond. A 316 (1526), 341–350.Google Scholar
Golay, M.J. 1958 Theory of chromatography in open and coated tubular columns with round and rectangular cross-sections. In Gas Chromatography (ed. D.H. Desty), pp. 36–55. Butterworths.Google Scholar
Goodrich, F.C. 1954 Random walk with semiadsorbing barrier. J. Chem. Phys. 22 (4), 588–594.CrossRefGoogle Scholar
Grebenkov, D.S. 2019 Reversible reactions controlled by surface diffusion on a sphere. J. Chem. Phys. 151 (15), 154103.CrossRefGoogle Scholar
Guan, M.Y., Zeng, L., Li, C.F., Guo, X.L., Wu, Y.H. & Wang, P. 2021 Transport model of active particles in a tidal wetland flow. J. Hydrol. 593, 125812.CrossRefGoogle Scholar
Guo, J., Jiang, W., Chen, G., Li, Z., Alharbi, N.S. & Wakeel, M. 2022 Solute dispersion in an open channel turbulent flow: solution by a generalized model. J. Hydrol. 604, 127239.CrossRefGoogle Scholar
Guo, J., Jiang, W., Zhang, L., Li, Z. & Chen, G. 2019 Effect of bed absorption on contaminant transport in wetland channel with rectangular cross-section. J. Hydrol. 578, 124078.CrossRefGoogle Scholar
Gupta, P.S. & Gupta, A.S. 1972 Effect of homogeneous and heterogeneous reactions on the dispersion of a solute in the laminar flow between two plates. Proc. R. Soc. Lond. A 330 (1580), 59–63.Google Scholar
Hlushkou, D., Gritti, F., Guiochon, G., Seidel-Morgenstern, A. & Tallarek, U. 2014 Effect of adsorption on solute dispersion: a microscopic stochastic approach. Analyt. Chem. 86 (9), 4463–4470.CrossRefGoogle ScholarPubMed
Horn, F.J.M. 1971 Calculation of dispersion coefficients by means of moments. AIChE J. 17 (3), 613–620.CrossRefGoogle Scholar
Jiang, W. & Chen, G. 2019 Solute transport in two-zone packed tube flow: long-time asymptotic expansion. Phys. Fluids 31 (4), 043303.Google Scholar
Jiang, W.Q. & Chen, G.Q. 2018 Solution of Gill's generalized dispersion model: solute transport in Poiseuille flow with wall absorption. Intl J. Heat Mass Transfer 127, 34–43.CrossRefGoogle Scholar
Khan, M.A. 1962 Non-equilibrium theory of capillary columns and the effect of interfacial resistance on column efficiency. In Gas Chromatography (ed. M. van Swaay), pp. 3–17. Butterworths.Google Scholar
Kim, B., Seo, I.W., Kwon, S., Jung, S.H. & Choi, Y. 2021 Modelling one-dimensional reactive transport of toxic contaminants in natural rivers. Environ. Model. Softw. 137, 104971.CrossRefGoogle Scholar
Kim, H. & Shin, K.J. 1999 Exact solution of the reversible diffusion-influenced reaction for an isolated pair in three dimensions. Phys. Rev. Lett. 82 (7), 1578–1581.CrossRefGoogle Scholar
Langevin, D. 2014 Rheology of adsorbed surfactant monolayers at fluid surfaces. Annu. Rev. Fluid Mech. 46 (1), 47–65.CrossRefGoogle Scholar
Lau, M.W. & Ng, C.O. 2007 On the early development of dispersion in flow through a tube with wall reactions. In New Trends in Fluid Mechanics Research: Proceedings of the Fifth International Conference on Fluid Mechanics (Shanghai, 2007) (ed. F.G. Zhuang & J.C. Li), pp. 670–673. Springer.CrossRefGoogle Scholar
Levesque, M., Bénichou, O., Voituriez, R. & Rotenberg, B. 2012 Taylor dispersion with adsorption and desorption. Phys. Rev. E 86 (3), 036316.CrossRefGoogle ScholarPubMed
Li, G., Jiang, W., Wang, P., Guo, J., Li, Z. & Chen, G.Q. 2018 Concentration moments based analytical study on Taylor dispersion: open channel flow driven by gravity and wind. J. Hydrol. 562, 244–253.CrossRefGoogle Scholar
Li, W., Zhang, W., Qian, F., Huang, D., Wang, Q. & Zhao, C. 2021 Numerical investigation of the solute dispersion in finite-length microchannels with the interphase transport. Electrophoresis 42 (3), 257–268.CrossRefGoogle ScholarPubMed
Lotter, S., Ahmadzadeh, A. & Schober, R. 2020 Channel modeling for synaptic molecular communication with re-uptake and reversible receptor binding. In ICC 2020 – 2020 IEEE International Conference on Communications (ICC), pp. 1–7.Google Scholar
Lotter, S., Ahmadzadeh, A. & Schober, R. 2021 Synaptic channel modeling for DMC: neurotransmitter uptake and spillover in the tripartite synapse. IEEE Trans. Commun. 69 (3), 1462–1479.CrossRefGoogle Scholar
Lupa, A.J. & Dranoff, J.S. 1966 Chemical reaction on the wall of an annular reactor. Chem. Engng Sci. 21 (10), 861–866.CrossRefGoogle Scholar
Mauri, R. 1991 Dispersion, convection, and reaction in porous media. Phys. Fluids A: Fluid 3 (5), 743–756.CrossRefGoogle Scholar
Mazumder, B.S. & Paul, S. 2012 Dispersion of reactive species with reversible and irreversible wall reactions. Heat Mass Transfer 48 (6), 933–944.CrossRefGoogle Scholar
McCune, E.D. & Gray, H.L. 2006 Cornish–Fisher and Edgeworth expansions. In Encyclopedia of Statistical Sciences. Wiley.CrossRefGoogle Scholar
Mederos, G., Arcos, J., Bautista, O. & Méndez, F. 2020 Hydrodynamics rheological impact of an oscillatory electroosmotic flow on a mass transfer process in a microcapillary with a reversible wall reaction. Phys. Fluids 32 (12), 122003.CrossRefGoogle Scholar
Mehmani, Y. & Balhoff, M.T. 2014 Generalized semi-analytical solution of advection–diffusion–reaction in finite and semi-infinite cylindrical ducts. Intl J. Heat Mass Transfer 78, 1155–1165.CrossRefGoogle Scholar
Mehta, R.V., Merson, R.L. & McCoy, B.J. 1974 Hermite polynomial representation of chromatography elution curves. J. Chromatogr. A 88 (1), 1–6.CrossRefGoogle Scholar
Mercer, G.N. & Roberts, A.J. 1994 A complete model of shear dispersion in pipes. Jpn. J. Ind. Appl. Maths 11 (3), 499.CrossRefGoogle Scholar
Mikelić, A., Devigne, V. & van Duijn, C.J. 2006 Rigorous upscaling of the reactive flow through a pore, under dominant Péclet and Damkohler numbers. SIAM J. Math. Anal. 38 (4), 1262–1287.CrossRefGoogle Scholar
Ng, C.-O. 2006 Dispersion in steady and oscillatory flows through a tube with reversible and irreversible wall reactions. Proc. R. Soc. Lond. A 462 (2066), 481–515.Google Scholar
Ng, C.-O. & Rudraiah, N. 2008 Convective diffusion in steady flow through a tube with a retentive and absorptive wall. Phys. Fluids 20 (7), 073604.CrossRefGoogle Scholar
Ng, C.-O. & Yip, T.L. 2001 Effects of kinetic sorptive exchange on solute transport in open-channel flow. J. Fluid Mech. 446, 321–345.CrossRefGoogle Scholar
Nordin, C.F. & Troutman, B.M. 1980 Longitudinal dispersion in rivers: the persistence of skewness in observed data. Water Resour. Res. 16 (1), 123–128.CrossRefGoogle Scholar
Pancharatnam, S. & Homsy, G.M. 1972 An asymptotic solution for tubular flow reactor with catalytic wall at high Péclet numbers. Chem. Engng Sci. 27 (6), 1337–1340.CrossRefGoogle Scholar
Paul, S. & Mazumder, B.S. 2011 Effects of nonlinear chemical reactions on the transport coefficients associated with steady and oscillatory flows through a tube. Intl J. Heat Mass Transfer 54 (1), 75–85.CrossRefGoogle Scholar
Pawula, R.F. 1967 Approximation of the linear Boltzmann equation by the Fokker–Planck equation. Phys. Rev. 162 (1), 186–188.CrossRefGoogle Scholar
Purnama, A. 1988 a Boundary retention effects upon contaminant dispersion in parallel flows. J. Fluid Mech. 195, 393–412.CrossRefGoogle Scholar
Purnama, A. 1988 b The effect of dead zones on longitudinal dispersion in streams. J. Fluid Mech. 186, 351–377.CrossRefGoogle Scholar
Purnama, A. 1995 The dispersion of chemically active solutes in parallel flow. J. Fluid Mech. 290, 263–277.CrossRefGoogle Scholar
Roy, A.K., Saha, A.K. & Debnath, S. 2020 Effect of multiple reactions on the transport coefficients in pulsatile flow through an annulus. Intl Commun. Heat Mass Transfer 110, 104369.CrossRefGoogle Scholar
Sadeghi, M., Saidi, M.H., Moosavi, A. & Sadeghi, A. 2020 Unsteady solute dispersion by electrokinetic flow in a polyelectrolyte layer-grafted rectangular microchannel with wall absorption. J. Fluid Mech. 887, A13.CrossRefGoogle Scholar
Sandoval, J., Mignot, E., Mao, L., Pastén, P., Bolster, D. & Escauriaza, C. 2019 Field and numerical investigation of transport mechanisms in a surface storage zone. J. Geophys. Res.: Earth 124 (4), 938–959.CrossRefGoogle Scholar
Sankarasubramanian, R. & Gill, W.N. 1973 Unsteady convective diffusion with interphase mass transfer. Proc. R. Soc. Lond. A 333 (1592), 115–132.Google Scholar
Sayre, W.W. 1967 Dispersion of mass in open-channel flow. USGS Numbered Series 67-192.CrossRefGoogle Scholar
Shankar, A. & Lenhoff, A.M. 1991 Dispersion and partitioning in short coated tubes. Ind. Engng Chem. Res. 30 (5), 828–835.CrossRefGoogle Scholar
Shapiro, M. & Brenner, H. 1987 Chemically reactive generalized Taylor dispersion phenomena. AIChE J. 33 (7), 1155–1167.CrossRefGoogle Scholar
Sherman, T., Paster, A., Porta, G. & Bolster, D. 2019 A spatial Markov model for upscaling transport of adsorbing-desorbing solutes. J. Contam. Hydrol. 222, 31–40.CrossRefGoogle ScholarPubMed
Sivasankar, V.S., Etha, S.A., Sachar, H.S. & Das, S. 2021 Thermo-osmotic transport in nanochannels grafted with pH-responsive polyelectrolyte brushes modelled using augmented strong stretching theory. J. Fluid Mech. 917, A31.CrossRefGoogle Scholar
Smith, R. 1983 Effect of boundary absorption upon longitudinal dispersion in shear flows. J. Fluid Mech. 134, 161–177.CrossRefGoogle Scholar
Stuart, A. & Ord, J.K. 2010 Kendall's Advanced Theory of Statistics, Vol. 1: Distribution Theory, 6th edn. Wiley.Google Scholar
Taghizadeh, E., Valdés-Parada, F.J. & Wood, B.D. 2020 Preasymptotic Taylor dispersion: evolution from the initial condition. J. Fluid Mech. 889, A5.CrossRefGoogle Scholar
Taylor, G. 1953 Dispersion of soluble matter in solvent flowing slowly through a tube. Proc. R. Soc. Lond. A 219 (1137), 186–203.Google Scholar
Taylor, G. 1954 The dispersion of matter in turbulent flow through a pipe. Proc. R. Soc. Lond. A 223 (1155), 446–468.Google Scholar
Valentine, E.M. & Wood, I.R. 1977 Longitudinal dispersion with dead zones. J. Hydraul. Div. ASCE 103 (9), 975–990.CrossRefGoogle Scholar
Valocchi, A.J. 1989 Spatial moment analysis of the transport of kinetically adsorbing solutes through stratified aquifers. Water Resour. Res. 25 (2), 273–279.CrossRefGoogle Scholar
Vanson, J.-M., Coudert, F.-X., Rotenberg, B., Levesque, M., Tardivat, C., Klotz, M. & Boutin, A. 2015 Unexpected coupling between flow and adsorption in porous media. Soft Matt. 11 (30), 6125–6133.CrossRefGoogle ScholarPubMed
Wang, B., Jiang, W., Chen, G. & Tao, L. 2022 Transient dispersion in a channel with crossflow and wall adsorption. Phys. Rev. Fluids 7 (7), 074501.CrossRefGoogle Scholar
Wang, B., Jiang, W., Chen, G., Tao, L. & Li, Z. 2021 Vertical distribution and longitudinal dispersion of gyrotactic microorganisms in a horizontal plane Poiseuille flow. Phys. Rev. Fluids 6 (5), 054502.CrossRefGoogle Scholar
Wang, P. & Chen, G.Q. 2017 Basic characteristics of Taylor dispersion in a laminar tube flow with wall absorption: exchange rate, advection velocity, dispersivity, skewness and kurtosis in their full time dependance. Intl J. Heat Mass Transfer 109, 844–852.CrossRefGoogle Scholar
Wang, P. & Cirpka, O.A. 2021 Surface transient storage under low-flow conditions in streams with rough bathymetry. Water Resour. Res. 57 (12), e2021WR029899.CrossRefGoogle Scholar
Wu, Z. & Chen, G.Q. 2014 Approach to transverse uniformity of concentration distribution of a solute in a solvent flowing along a straight pipe. J. Fluid Mech. 740, 196–213.CrossRefGoogle Scholar
Wu, Z., Singh, A., Foufoula-Georgiou, E., Guala, M., Fu, X. & Wang, G. 2021 A velocity-variation-based formulation for bedload particle hops in rivers. J. Fluid Mech. 912, A33.CrossRefGoogle Scholar
Yang, Y., Jiang, W.Q., Wu, Y.H., Wang, P., Wu, Z., Zhang, B. & Zeng, L. 2021 Migration of buoyancy-controlled active particles in a laminar open-channel flow. Adv. Water Resour. 156, 104023.CrossRefGoogle Scholar
Yang, Y., Tan, S.W., Zeng, L., Wu, Y.H., Wang, P. & Jiang, W.Q. 2020 Migration of active particles in a surface flow constructed wetland. J. Hydrol. 582, 124523.CrossRefGoogle Scholar
Yasuda, H. 1984 Longitudinal dispersion of matter due to the shear effect of steady and oscillatory currents. J. Fluid Mech. 148, 383–403.CrossRefGoogle Scholar
Yu, J.S. & Chang, W.S. 1991 Dispersion of solute in wall-bounded parallel shear flows. J. Engng Maths 25 (1), 31–62.CrossRefGoogle Scholar
Zaafouri, Z., Batôt, G., Nieto-Draghi, C., Rotenberg, B., Bauer, D. & Coasne, B. 2021 Lattice Boltzmann method for adsorption under stationary and transient conditions: interplay between transport and adsorption kinetics in porous media. Phys. Rev. E 104 (1), 015314.CrossRefGoogle ScholarPubMed
Zhang, L., Hesse, M.A. & Wang, M. 2017 Transient solute transport with sorption in Poiseuille flow. J. Fluid Mech. 828, 733–752.CrossRefGoogle Scholar
Zhang, L., Hesse, M.A. & Wang, M. 2019 Dispersion of charged solute in charged micro- and nanochannel with reversible sorption. Electrophoresis 40 (6), 838–844.CrossRefGoogle ScholarPubMed