On mathematical modelling of the solid-liquid mixtures transport in porous axial-symmetrical container with Henry and Langmuir sorption kinetics
In this paper we study diffusion and convection filtration problem of one substance through the pores of a porous material which may absorb and immobilize some of the diffusing substances. As an example we consider round cylinder with filtration process in the axial direction. The cylinder is filled with sorbent i.e. absorbent material that passed through dirty water or liquid solutions. We can derive the system of two partial differential equations (PDEs), one expressing the rate of change of concentration of water in the pores of the sorbent and the other - the rate of change of concentration in the sorbent or kinetical equation for absorption. The approximation of corresponding initial boundary value problem of the system of PDEs is based on the conservative averaging method (CAM). This procedure allows reducing the 2-D axisymmetrical mass transfer problem decribed by a system of PDEs to initial value problem for a system of ordinary differential equations (ODEs) of the first order. We consider also model 1-D problem for investigation the depending the concentration of water and sorbent on the time.
This work is licensed under a Creative Commons Attribution 4.0 International License.
A.R. Appadu. Comparative study of three numerical schemes for contami-nant transport with kinetic Langmuir sorption. InInternational Conferenceof Numerical Analysis and Applied Mathematics 2015 (ICNAAM 2015), AIPConf. Proc. 1738, volume 1738, pp. 030021–1–030021–5. AIP Publishing, 2016. https://doi.org/10.1063/1.4951777.
A. Buikis, H. Kalis and I. Kangro. Special hyperbolic type spline for masstransfer problems in multi-layer 3-D domains. In Mathematical and Computation Methods in Applied Sciences, Proc. of 3-rd Int. Conf. on Applied, Numerical and Computational Mathematics (ICANCM’15), Sliema, Malta Aug. 17-19, 2015, volume 51, pp. 25–34. WSEAS Press, 2015.
A. Buikis, H. Kalis and I. Kangro.Special splines of exponen-tial type for the solutions of mass transfer problems in multilayerdomains.Mathematical Modelling and Analysis, 21(4):450–465, 2016. https://doi.org/10.3846/13926292.2016.1182594
A. A. Buikis and E. J. Titushkina. Application of the Macomark method forcalculating the filtration of liquid solutions in the soil. Mathematical Modelling,applied problems in mathematical physics, 2:71–80, 1991.
R. Čiegis and V. Starikovičius.Mathematical modelling of wood dray-ing process. Mathematical Modelling and Analysis, 7(2):177–190, 2002. https://doi.org/10.1080/13926292.2002.9637190
J. Crank.The mathematics of diffusion. Clarendon Press, Oxford, 1956.
W. Henry. III. experiments on the quantity of gases absorbed by water, atdifferent temperatures, and under different pressures. Philosophical Transactionsof the Royal Society, 93:29–274, 1803. https://doi.org/10.1098/rstl.1803.0004
H. Kalis and I. Kangro. Calculation of heat and moisture distribution in theporous media layer. Mathematical Modelling and Analysis, 12(1):91–100, 2007. https://doi.org/10.3846/1392-6292.2007.12.91-100
M. Kellow.Energy and Environment, Experiment instructions, CE 583, Adsorption. G.U.N.T., Geratebau, Barsbuttel, Germany, 2011.
I. Langmuir. The adsorption of gases on plane surfaces of glass, mica andplatinum. Journal of the American Chemical Society, 40(9):1361–1403, 1918. https://doi.org/10.1021/ja02242a004
G. Limousin, J. P. Gaudet, L. Charlet, S. Szenknect, V. Barthes andM. Krinissa. Sorption isotherms: A review on physical bases, mod-eling and measurement.Applied Geochemistry, 22(2):249–275, 2007. https://doi.org/10.1016/j.apgeochem.2006.09.010
M. Buike and A. Buikis. Modelling 3-d transport processes in anisotropic layeredstratum by conservative averaging method. WSEAS Transactions on Heat andMass Transfer, 1(4):430–437, 2006.
R. Čiegis and O. Iliev. On numerical simulation of liquid polymermoulding.Mathematical Modelling and Analysis, 8(3):181–202, 2003. https://doi.org/10.1080/13926292.2003.9637223
S. Ripperger, W. Gosele, Ch. Alt and Th. Loewe.Filtration, 1. Funda-mentals, pp. 1–38. American Cancer Society, 2013. ISBN 9783527306732. https://doi.org/10.1002/14356007.b0210.pub3 Available from Internet: https://onlinelibrary.wiley.com/doi/abs/10.1002/14356007.b02_10.pub3
V. Russo, R. Tesser, M. Trifuoggi, M. Giugni and M. Di Serio. A dynamic intra-particle model for fluidsolid adsorption kinetics.Computers & Chemical Engi-neering,74:66–74, 2015. https://doi.org/10.1016/j.compchemeng.2015.01.001
A.N. Tikhonov and A.A. Samarskii. Equations of Mathematical Physics. Nauka, Moskow, 1966. (in Russian)