Abstract
A multiple-scale homogenization technique is employed in the current research to show the dispersion phenomena in a Couette flow where the solute may undergoes a reversible phase exchange between the immobile phase (stationary boundary bed phase) and mobile phase (fluid phase). Analytical solutions are obtained to view the influences of retardation factor and phase exchange kinetics on transport coefficient as well as in the two-dimensional longitudinal and transverse concentration distributions. Effects of several transversal position and dispersion time on longitudinal real concentration and the impact of different downstream stations on transverse concentration distributions are also determined. It is seen that with the increment of Damkohlar number the effective dispersivity reduces.
Supported by UGC India and CSIR India
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References
Taylor, G.I.: Dispersion of soluble matter in solvent flowing slowly through a tube. Proc. R. Soc. Lond. A 219(1137), 186–203 (1953). https://doi.org/10.1098/rspa.1953.0139
Aris, R.: On the dispersion of a solute in a fluid flowing through a tube. Proc. Royal Soc. Lond. A. 235(1200), 67–77 (1956). https://doi.org/10.1098/rspa.1956.0065
Chatwin, P.C.: The approach to normality of the concentration distribution of a solute in a solvent flowing along a straight pipe. J. Fluid Mech. 43(02), 321 (1970). https://doi.org/10.1017/s0022112070002409
Mei, C.C., Auriault, J.L., Ng, C.O.: Some applications of the homogenization theory. Adv. Appl. Mech. 32, 277–348 (1996). https://doi.org/10.1016/s0065-2156(08)70078-4
Bandyopadhyay, S., Mazumder, B.S.: On contaminant dispersion in unsteady generalised Couette flow. Int. J. Eng. Sci. 37(11), 1407–1423 (1999). https://doi.org/10.1016/s0020-7225(98)00132-3
Ng, C.O., Yip, T.L.: Effects of kinetic sorptive exchange on solute transport in open-channel flow. J. Fluid Mech. 446, 321–345 (2001). https://doi.org/10.1017/S0022112001005791
Ng, C.O., Bai, Y.C.: Dispersion in oscillatory Couette flow with sorptive boundaries. Acta Mech. 178(1–2), 65–84 (2005). https://doi.org/10.1007/s00707-005-0230-6
Wu, Z., Chen, G.Q.: Approach to transverse uniformity of concentration distribution of a solute in a solvent flowing along a straight pipe. J. Fluid Mech. 740, 196–213 (2014). https://doi.org/10.1017/jfm.2013.648
Barik, S., Dalal, D.C.: Multi-scale analysis for concentration distribution in an oscillatory Couette flow. Proc. R. Soc. Lond. A 475(2221), 20180483 (2018). https://doi.org/10.1098/rspa.2018.0483
Poddar, N., Dhar, S., Mazumder, B.S., Mondal, K.K.: An exact analysis of scalar transport in hydromagnetic flow between two parallel plates: a multi-scale approach. Proc. R. Soc. Lond. A 477(2248), 20200830 (2021). https://doi.org/10.1098/rspa.2020.0830
Dhar, S., Poddar, N., Mondal, K.K., Mazumder, B.S.: On dispersion of solute in a hydromagnetic flow between two parallel plates with boundary absorption. Phys. Fluids 33, 083609 (2021). https://doi.org/10.1063/5.0060404
Das, D., Poddar, N.,Dhar S., Kairi, R.R., Mondal, K. K.: Multi-scale approach to analyze the dispersion of solute under the influence of homogeneous and inhomogeneous reactions through a channel. Int. Commun. Heat Mass Transf. 129, 105709 (2021). https://doi.org/10.1016/j.icheatmasstransfer.2021.105709
Mazumder, B.S., Paul, S.: Dispersion of reactive species with reversible and irreversible wall reactions. Heat Mass Transf. 48(6), 933–944 (2011). https://doi.org/10.1007/s00231-011-0920-7
Barik, S., Dalal, D. C.: Analytical solution for concentration distribution in an open channel flow with phase exchange kinetics. Acta Mech. Sin. 1 (2021). http://ams.cstam.org.cn/EN/abstract/abstract157644.shtml
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Poddar, N., Dhar, S., Mondal, K.K. (2022). Effect of Reversible Reaction on Concentration Distribution of Solute in a Couette Flow. In: Banerjee, S., Saha, A. (eds) Nonlinear Dynamics and Applications. Springer Proceedings in Complexity. Springer, Cham. https://doi.org/10.1007/978-3-030-99792-2_33
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DOI: https://doi.org/10.1007/978-3-030-99792-2_33
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