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An new methody for physical and chemical adsorption modeling in column apparatuses is presented. A convection‐diffusion model is obtained in the approximations of the continua mechanics, where the mathematical point is equivalent to the medium elementary volume which is sufficiently small with respect to the column volume and at the same time sufficiently large with respect to the intermolecular volumes of the medium. The created convection‐diffusion type model allows performing qualitative analysis of the process and obtaining the effect of the velocity radial nonuniformity in the column. An average concentration model is applied for quantitative description of physical and chemical adsorption in the column apparatus. The methods for model equation solutions and model parameter identifications are described.

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This study proposes a mathematical modeling approach for evaluating the effect of applying a permanent electric field on the biodegradation of 1,2-dibromoethane by bacterial cells of Bradyrhizobium japonicum 273. Two models for inhibited microbial growth including product inhibition were composed—one using the Monod–Yerusalimsky approach and another one—the Levenspiel kinetic equation. The models were used to process own experimental data obtained without an electric field and ones obtained at the application of an electric field. The experiments were carried out at an optimum anode potential of 0.8 V vs. the standard hydrogen electrode (SHE). Three initial concentrations of substrate were tested: 0.05, 0.1, and 0.15 g dm−3. The modeling takes into account the product inhibition on microbial growth assuming 2-bromoethanol as the first biodegradation product. It was found that the positive effect of the electric field is the enhancement of microbial growth, expressed by the increase in the maximum specific growth rate and the increase in the inhibition constant when the model of Monod–Yerusalimsky is applied. The main effect of the electric field is in the increase in the rate constant of 2-bromoethanol removal by electrochemical oxidation, enabling the enhancement the microbial growth and substrate conversion to the product. The obtained results show that the application of a permanent electric field leads to a higher electrochemical oxidation rate (with a rate constant up to 60% higher than for the control experiments) and complete substrate and 2-bromoethanol biodegradation. The model of Levenspiel is not so sensitive to the effects of the electric field on product inhibition.