Dynamic linear adsorption with solid adsorbent material


  • V.L. Poliakov Institute of Hydromechanics of the NAS of Ukraine, Kyiv




physical adsorption, filtration, adsorbent, suspension, filter, approximate solution


A mathematical problem of linear physical adsorption of a dissolved impurity is formulated, by consider-ing its diffusion transfer during the filtration of an aqueous suspension through a uniform adsorbent bed at a constant rate. By averaging the impurity concentrations in the free and bound states over an arbi-trary time period, an approximate solution of the problem is obtained, which is only expressed in terms of the elementary functions. On its basis, it is proposed to calculate the rational duration of the filter run. The solution is discussed and illustrated with a number of examples with typical input data.


Koganovsky, A. M., Klimenko, N. A. & Levchenko, T. M. (1990). Adsorption of organic substances from water. Leningrad : Himiya (in Russian).

Zapolsky, A. K., Mishkova-Klimenko, N. A., Astrelin, I. M., Brik, M. G., Gvozdyak, P. I. & Knyazkova, T. V. (2000). Physico-chemical foundations of water treatment technology. Kyiv: Libra (in Ukrainian).

Poliakov, V. L. (2012). Modeling of water treatment in adsorber medium. Dopov. Nac. akad. nauk Ukr., No. 5, pp. 63-71 (in Russian).

Chaudhary, D. S., Vigneswaran, S., Jegatheesan, V., Ngo, H. H., Moon, H., Shim, V. G. & Kim, S. H. (2002). Granular activated carbon (GAC) adsorption in tertiary wastewater treatment: experiments and models. Water Sci. Tech., 47, No. 1, pp. 113-120.

Crittenden, J. C., Hutzler, N. J., Geyer, D. G., Oravitz, J. L. & Friedman, G. (1986).Transport of organic compounds with saturated groundwater flow: model development and parameter sensitivity. Water Resour. Res., 22, pp.271-284.

Sorial, G. A., Suidan, M. T., Vidic, R. D. & Maloney, S. W. (1993). Competitive adsorption of phenols on

GAC. I. Adsorption equilibrium. J. Environ. Eng., 119, pp. 1026-1043.

Khan, A. R., Al-Bahri, T. A. & Al-Haddad, A. (1997).Adsorption of phenol based organic pollutants on activated carbon from multi-component dilute aqueous solutions. Water Res., 31, No. 8, pp. 2102-2112.

Ko, D. C. K., Porter, J. F. & McKay, G. (2001). Film-pore diffusion model for the fixed-bed sorption of

copper and cadmium ions onto bone char. Water Res., 35, pp. 3876-3886.

Meshko, V., Markovska, L., Mincheva, M. & Rodrigues, A. E. (2001). Adsorption of basic dyes on granular activated carbon and natural zeolite. Water Res., 14, pp. 3357-3366.

Mollah, A. H. & Robinson, C. W. (1996). Pentachlorophenol adsorption and desorption characteristics of granular activated carbon. Water Res., 30(12), I. Isotherms, pp. 2901-2906, II. Kinetics, pp. 2907-2913.

Sotelo, J. L., Ovejero, G., Delgado, J. A. & Martinez, I. (2002). Comparison of adsorption equilibrium and kinetics of four chlorinated organics from water onto GAC. Water Res., 36, pp. 599-608.

Poliakov, V. L. (2011). Engineering calculation of suspension filtration through two-layer filter medium at linear kinetics of mass-exchange. J. Water Chemistry and Technology, 33, No. 4, pp. 367-380 (in Russian).

Lindstrom, F. T. & Boersma, L. (1973). A theory of the mass transport of previously distributed chemicals in a water-saturated sorbing porous medium: III. Exact solution for first-order kinetic sorption. Soil Science., 115, No. 1, pp. 5-10.

Imboden, D. M. (1993). Environmental organic chemistry. New-York: Wiley Interscience.

Walker, G. M. & Weatherley, L. R. (1997). Adsorption of acid dyes on to granular activated carbon in fixed beds. Water Res., 31, No. 8, pp. 2093-2101.




How to Cite

Poliakov, V. (2021). Dynamic linear adsorption with solid adsorbent material. Reports of the National Academy of Sciences of Ukraine, (4), 46–52. https://doi.org/10.15407/dopovidi2021.04.046