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ISSN 2617-4162 e-ISSN 2617-4170

Social and Legal Studios

Current

Social and Legal Studios

Vol. 9, No. 1, 2026

Social and Legal Studios

ISSN 2617-4162

e-ISSN 2617-4170

Publisher: Lviv State University of Internal Affairs

Article

Mathematical Model of Migration of Pollution in the Environment with Consideration of Adsorption Processes


Abstract

Simulation of the processes of migration of toxic substances in soils is of great importance for the environmental safety of the environment. The literature presents many models of description of migration processes, but they are predominantly theoretical and can not be implemented in practice. Another class of models is based on the assumption that the process of accumulation of soil contamination can be described by equations for the description of chemical processes of the first, second, pseudo second and higher orders. In such models, the process of interaction of the pollutant with the soil environment is taken into account from the point of view of chemical interaction, but does not take into account the diffusion processes taking place during the migration processes at all. The problem of environmental pollution with heavy metals, mineral fertilizers as sources of heavy metals, the degree of contamination by heavy metals and anthropogenic contamination of soil cover, the mechanisms of accumulation of heavy metals by plants, and the valuation of toxic substances in the soil are described. A mathematical model was developed for predicting the migration of heavy metals in the soil environment, taking into account adsorption. The proposed model allows to predict the distribution of the component at the interface between the solids and the liquid in the dimensionless height of the sorbent layer, taking into account the adsorption process. The developed model is adequate for the external diffusion region. Taking into account that the establishment of the equilibrium of the adsorption system is accompanied by adsorption and desorption processes of the component in the sorbent layer, under dynamic conditions the adsorption process will be complicated by the hydrodynamics of the moving material flow in the sorbent layer. Experimental studies of the process of adsorption of heavy metal cations in a column type device showed that the process takes place in the exterior diffusion region. Bio criterion in the experimental conditions was Bi = 900, diffusion coefficient D = 2.3∙10-10 m2/s, coefficient of mass tansfer β = 3∙10-5 m/s. The comparison of experimental and theoretical data showed good convergence of results and the adequacy of the mathematical model for its application for the basic algorithm in environmental modeling programs


Keywords: heavy metals, migration, adsorption, soil, mathematical model


Suggested citation

Gumnitsky, Ja.M., Sabadash, V.V., & Halyna Leskiv (2018). Mathematical Model of Migration of Pollution in the Environment with Consideration of Adsorption Processes. Social and Legal Studios, 1(1), 172-179. https://doi.org/10.32518/2617-4162-2018-1-172-179
References
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