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2018/3
Influence of external electric field on permeability of charged porous layer
Technical sciences

Authors: Anatoly N. FILIPPOV graduated from the M.V. Lomonosov Moscow State University in 1982. He is Doctor of Physical and Mathematical Sciences, Professor at the Department of Higher Mathematics of Gubkin Russian State University of Oil and Gas (National Research University). He is author of over 340 scientific papers in the field of physical-chemical mechanics, colloid chemistry and mathematics. E-mail: filippov.a@gubkin.ru
Tamara S. FILIPPOVA graduated from the M.V. Lomonosov Moscow State University in 1982. She is Lecturer at the Department of Higher Mathematics of Gubkin Russian State University of Oil and Gas (National Research University). She is author of around 25 publications in the field of mechanics and mathematics. E-mail: filippova.tam@yandex.ru
Vasily V. KALININ graduated from the M.V. Lomonosov Moscow State University in 1974. He is Doctor of Physico-Mathematical Sciences, Head of the Department of Higher Mathematics of Gubkin Russian State University of Oil and Gas (National Research University). He is author of more than 70 publications in the fields of physicochemical hydrodynamics, colloid chemistry and mathematics. E-mail: vm@gubkin.ru

Abstract: On the basis of the cellular model of porous medium and thermodynamics of irreversible processes (Onsager approach), a new method for calculating the flow of solvent (water) and electric current flowing through a charged porous layer (membrane) under simultaneous action of an external pressure gradient and electric potential is proposed. It is shown that the total permeability of the porous structure both due to filtration and due to the electroosmotic transfer of the solvent increases with the electrolyte concentration

Index UDK: 517.958:536.71; 532:541.135.1; 539.219.3; 544.6

Keywords: charged porous layer, ion exchange membrane, exchange capacity, cell model, Onsager approach, kinetic coefficients, stokes, Brinkman, Poisson and Nernst-Planck equations

Bibliography:
1. Happel J., Brenner H. Low Reynolds Number Hydrodynamics. Moscow, Mir, 1976, 630 p.
2. Filippov A.N. Cell model of ion-exchange membrane. Hydrodynamic permeability. Colloid Journal, 2018, vol. 80, no. 6.
3. Filippov A.N. Cell model of ion-exchange membrane. Electroconductivity and electroosmotic permeability. Colloid Journal, 2018, vol. 80, no. 6.
4. Brinkman H.C. A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles. Appl. Sci., 1947, p. 27–34.
5. Sidorova M.P., Ermakova L.E., Savina I.A., Fridrikhsberg D.A. Electrochemistry of weakly charged membranes. Journal of Membrane Science, 1993, vol. 79, p. 159–179.
6. Sobolev V.D., Filippov A.N., Vorob’eva T.A., Sergeeva I.P. Determination of the Surface Potential for Hollow-Fiber Membranes by the Streaming—Potential Method. Colloid Journal, 2017, vol. 79, no. 5, p. 677–684.
7. Tong K., Zhang Y., Chu P.K. Evaluation of calcium chloride for synergistic demulsification of super heavy oil wastewater. Colloids Surf. A., 2013, vol. 419, p. 46–52.
8. Dorokhov V.M., Martynov G.A., Starov V.M., Churayev N.V. Theory of the reverse osmotic separation of electrolyte solutions. Influence of the charge of the surface of membrane pores. [Colloid Journal], 1984, vol. 46, no. 6, p. 1088–1093.
9. Filippov A.N., Shkirskaya S. Cell model of ion-exchange membrane and its experimental verification. Processing of Institute Conference “Ion Transport in Organic and Inorganic Membranes”, (Sochi-Krasnodar, May 21–26), 2018, p. 89–91.

2018/1
Possibility of determinating membrane exchange capacity by dynamic method
Technical sciences

Authors: Tamara S. PHILIPPOVA graduated from the M.V. Lomonosov Moscow State University in 1982. She is Lecturer at the Department of Higher Mathematics at Gubkin Russian State University of Oil and Gas (National Research University). She is author of more than 20 publications in the field of mechanics and mathematics. E-mail: filippova.tam@yandex.ru
Vasily V. KALININ (b. 1952) graduated from the M.V. Lomonosov Moscow State University in 1974. He is Doctor of Physical-Mathematical Sciences, Head of the Department of Higher Mathematics at Gubkin Russian State University of Oil and Gas (National Research University). He is author of more than 70 publications in the fields of physicochemical hydrodynamics, colloid chemistry and mathematics. E-mail: vm@gubkin.ru
Anatoly N. FILIPPOV was born in 1960, graduated from the M.V. Lomonosov Moscow State University in 1982. He is Doctor of Physical and Mathematical Sciences, Professor at the Department of Higher Mathematics Gubkin Russian State University of Oil and Gas (National Research University). He is author of over 300 scientific papers in the field of physical-chemical mechanics, colloid chemistry and mathematics. E-mail: filippov.a@gubkin.ru

Abstract: A new dynamic method for the experimental determination of the exchange capacity of an ion-exchange membrane is proposed. The method is based on solving the non-stationary system of Nernst-Planck equations by the method of integral relations (moments)

Index UDK: 517.958:536.71;532:541.135.1;539.219.3;544.6

Keywords: on exchange membrane, exchange capacity, method of integral moments, Nernst-Plank equation

Bibliography:
1. Zharkikh N.I. Theory of non-equilibrium electro-surface phenomena in concentrated weakly charged dispersions and membranes. Diss. kand. khim. nauk. Kiev, 1982, 129 p. (in Russian).
2. Martynov G.A., Starov V.M., Churayev N.V. Theory of membrane separation of solutions. Formulation of the problem and a solution to transfer equations. Kolloidnyi Zhurnal [Colloid Journal], 1980, vol. 42, no. 3, p. 489-499.
3. Theory of the reverse osmotic separation of electrolyte solutions. Influence of the charge of the surface of membrane pores/Dorokhov V.M., Martynov G.A., Starov V.M., Churayev N.V. Kolloidnyi Zhurnal [Colloid Journal], 1984, vol. 46, no. 6, p. 1088–1093.
4. Filippov А., Afonin D., Kononenko N., L’vov Yu., Vinokurov V. New approach to characterization of hybrid nanocomposites. Colloids and Surfaces A — Physicochemical and Engineering Aspects, 2017, vol. 521, p. 251-259.
5. Sidorova M.P., Ermakova L.E., Savina I.A., Fridrikhsberg D.A. Colloidal-chemical parameters of weakly charged membranes. Khimiya i Tekhnologiya Vody [ Water Chemistry and Technology ], 1991, vol. 13, no. 4, p. 291-301.
6. Sidorova M.P., Ermakova L.E., Savina I.A. Fridrikhsberg D.A. Electrochemistry of weakly charged membranes. Journal of Membrane Science, 1993, vol. 79, issue 2-3, p. 159-179.
7. GOST 17552-72. Membrany ionoobmennye. Metody opredeleniya polnoi i ravnovesnoi obmennoi emkosti (s Izmeneniem № 1). http://docs.cntd.ru/document/1200018368
8. Filippov A.N., Safronova E.Yu., Yaroslavtsev A.B. Theoretical and experimental investigation of diffusion permeability of hybrid MF—4SC membranes with silica nanoparticles. Journal of Membrane Science, 2014, vol. 471, p. 110-117.
9. Filippov A.N., Safronova E.Yu., Yaroslavtsev A.B. Theoretical and experimental investigation of diffusion permeability of hybrid MF—4SC membranes with silica nanoparticles. Journal of Membrane Science, 2014, vol. 471, p. 110-117.
10. Filippov A., Kononenko N., Afonin D., Vinokurov V. Synthesis and Prediction of Transport Properties of Hybrid Bi-layer Ion-Exchange Membranes. Surface Innovations, 2017, vol. 5, no. 3, p. 130-137.