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Mathematical Modelling of a Nanoparticle Motion in a Membrane Pore under Action of Molecular Forces

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Abstract

A mathematical model is developed to describe microfiltration on membrane filters with plane-parallel and cylindrical pores. Consideration is given to two cases of motion of Brownian particles having a radius R comparable to the radius of the filter channel a. Relations are presented for the dependence of the efficiency of particle deposition on the channel walls on the parameter \({{æ }} = R{{a}^{{ - 1}}}\) with different values of the molecular interaction constant and with allowance for the hydrodynamic factor. The results of modeling microfiltration on membrane filters with plane-parallel and cylindrical pores are compared. It is shown that there is a qualitative agreement between the main characteristics of the microfiltration process for these two types of membrane channel cross-section. It is established that the efficiency of purification on membrane filters with cylindrical pores is considerably more significant than the efficiency attained with plane-parallel pores.

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Funding

This work was supported by the Ministry of Science and Higher Education of the Russian Federation in the Framework of the Basic Part of the State Task (project no. FSWE-2020-0008).

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Authors and Affiliations

  1. Nanotechnology and Biotechnology Department, Nizhny Novgorod State Technical University, Nizhny Novgorod, Russia

    V. M. Vorotyntsev, A. N. Petukhov, D. M. Zarubin, A. D. Kulikov, E. A. Stepanova, A. V. Vorotyntsev & V. M. Malyshev

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  1. V. M. Vorotyntsev
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  2. A. N. Petukhov
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  3. D. M. Zarubin
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  4. A. D. Kulikov
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  6. A. V. Vorotyntsev
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  7. V. M. Malyshev
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Correspondence to V. M. Vorotyntsev.

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Vorotyntsev, V.M., Petukhov, A.N., Zarubin, D.M. et al. Mathematical Modelling of a Nanoparticle Motion in a Membrane Pore under Action of Molecular Forces. Membr. Membr. Technol. 3, 245–253 (2021). https://doi.org/10.1134/S2517751621040077

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  • DOI: https://doi.org/10.1134/S2517751621040077

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