Models and problems in electrohydrodynamics

V. A. Polyansky   ; I. L. Pankratieva

Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 157 (2015) no. 3, pp. 21-33

Résumé

A survey of mathematical models employed in modern electrohydrodynamics of weakly conducting fluids is given. The models are described in the order of increasing complexity. Some results obtained in the framework of each model are presented. The models considered include: the model of a unipolarly charged medium consisting of a continuous carrier fluid and an admixture of charged particles of the same sign; a more sophisticated two-ion model containing two charged admixtures of opposite signs; and the model with three different kinds of ions. In the framework of the aforementioned models, it is possible to adequately interpret almost all experimental data related to electrohydrodynamic flows that can be found in the literature. Further elaboration of the model may be needed to simulate particular electrochemical processes without introducing averaged (“effective”) macroscopic parameters. Four basic phenomena of fluid electrization (generation of an uncompensated electric space charge in the fluid) are described and analyzed.

Détail

Keywords: electrohydrodynamics, electric field, weakly conducting fluid, mathematical model, electric space charge, electrochemical reactions, electrization.

Bibliographie

[1] Gogosov V. V., Polyanskii V. A., “Elektrogidrodinamika: zadachi i prilozheniya, osnovnye uravneniya, razryvnye resheniya”, Itogi nauki i tekhniki. Mekhanika zhidkosti i gaza, 10, VINITI, M., 1976, 5–85

[2] Pankratieva I. L., Polyansky V. A., “On discharge phenomena in nonpolar liquids”, J. Electrostatics, 51–52 (2001), 476–480 | DOI

[3] Perez A. T., Castellanos A., “Role of charge diffusion in finite-amplitude electroconvection”, Phys. Rev. A, 40:10 (1989), 5844–5855 | DOI

[4] Fernandes D. V., Lee H.-D., Park S., Yong Kweon Suh, “Electrohydrodynamic instability of dielectric liquid between concentric circular cylinders subjected to unipolar charge injection”, J. Mech. Sci. Technol., 27:2 (2013), 461–467 | DOI

[5] Polyanskii V. A., Pankrateva I. L., “O nekotorykh osobennostyakh nelineinoi poteri ustoichivosti v elektrogidrodinamicheskikh techeniyakh”, Tez. dokl. XVII shkoly-seminara “Sovremennye problemy aerogidrodinamiki”, Izd-vo Mosk. un-ta, M., 2014, 102–103

[6] Gogosov V. V., Polyanskii V. A., Semenova I. P., Yakubenko A. E., “Uravneniya elektrogidrodinamiki i koeffitsienty perenosa v silnom elektricheskom pole”, Izv. RAN. Mekhanika zhidkosti i gaza, 1969, no. 2, 31–45

[7] Vázquez P. A., Castellanos A., “Numerical simulation of EHD flows using Discontinuous Galerkin Finite Element methods”, Computers Fluids, 84 (2013), 270–278 | DOI | MR | Zbl

[8] Traoré P., Wu J., “On the limitation of imposed velocity field strategy for Coulomb-driven electroconvection flow simulations”, J. Fluid Mech., 727 (2013), R3-1–R3-12 | DOI

[9] Wu J., Traore P., Vazquez P. A., Perez A. T., “Onset of convection in a finite two-dimensional container due to unipolar injection of ions”, Phys. Rev. E, 88 (2013), Art. 053018, 9 pp.

[10] Faizullin R. T., Pankratieva I. L., Polyansky V. A., Sakharov V. I., “On some electrohydrodynamic phenomena due to charge injection into a flow of a low-conductivity liquid”, Conf. Record of 12 Int. Conf. on Conduction and Breakdown in Dielectric Liquids, Roma, Italy, 1996, 547–549

[11] Gogosov V. V., Polyansky V. A., “Shock waves in electrohydrodynamics”, Progr. Aerosp. Sci., 20:2–3 (1983), 125–216 | DOI

[12] Gogosov V. V., Polyanskii V. A., “Razryvy v elektrogidrodinamike”, Prikl. matem. i mekhanika, 35:5 (1971), 761–772 | Zbl

[13] Pankrateva I. L., Polyanskii V. A., “Modelirovanie elektrogidrodinamicheskikh techenii v slaboprovodyaschikh zhidkostyakh”, Prikl. matem. i tekhn. fizika, 36:4 (1995), 36–44 | Zbl

[14] Pankrateva I. L., Polyanskii V. A., “Ob ionizatsii elektronno-vozbuzhdennykh molekul silnym elektricheskim polem”, Dokl. RAN, 437:5 (2011), 617–620 | Zbl

[15] Vartanyan A. A., Gogosov V. V., Polyanskii V. A., Polyanskii K. V., Shaposhnikova G. A., “Modelirovanie nestatsionarnykh protsessov v kanalakh EGD-nasosov”, Izv. RAN. Mekhanika zhidkosti i gaza, 1994, no. 3, 30–41 | Zbl

[16] Pankrateva I. L., Polyanskii V. A., “Volny plotnosti ob'emnogo zaryada v slaboprovodyaschikh zhidkostyakh”, Dokl. RAN, 365:4 (1999), 471–474

[17] Polyansky V. A., Pankratieva I. L., “Electric current oscillations in low-conducting liquids”, J. Electrostatics, 48:1 (1999), 27–41 | DOI

[18] Touchard G., “Flow electrification of liquids”, J. Electrostatics, 51–52 (2001), 440–447 | DOI

[19] Bograchev D., Martemianov S., Paillat T., “Modelling of electrification in steady state and transient regimes”, J. Electrostatics, 70:6 (2012), 517–523 | DOI

[20] Pankrateva I. L., Polyanskii V. A., “Elektrizatsiya slaboprovodyaschikh zhidkostei vblizi stenki”, Izv. RAN. Mekhanika zhidkosti i gaza, 2006, no. 2, 3–16 | Zbl

[21] Pribylov V. N., “Eksperimentalnoe issledovanie toka elektrizatsii dielektricheskikh zhidkostei v tsilindricheskoi trubke”, Kolloidnyi zhurn., 58:4 (1996), 524–527

[22] Pankrateva I. L., “Osobennosti elektrizatsii slaboprovodyaschikh sred pri ikh techenii v ploskom kanale, stenki kotorogo imeyut raznye elektrokhimicheskie svoistva”, Vestn. Mosk. un-ta. Ser. 1 Matem., Mekhanika, 2008, 60–63

[23] Ban H., Lin B., Song Z., “Effect of electrical double layer on electric conductivity and pressure drop in a pressure-driven microchannel flow”, Biomicrofluidics, 4:1 (2010), 014104-1–014104-13 | DOI

[24] Polyanskii V. A., Pankrateva I. L., “Ob elektrovyazkom effekte pri elektrizatsii zhidkostei v mikrokanalakh”, Vestn. Nizhegor. un-ta im. N. I. Lobachevskogo, 2011, no. 4(5), 2430–2432

[25] Daiguji H., Yang P., Szeri A., Majumdar A., “Electrochemomechanical Energy Conversion in Nanofluidic Channels”, Nano Lett., 4:12 (2004), 2315–1331 | DOI

[26] Karnik R., Fan R., Yue M., Li D., Yang P., Majumdar A., “Electrostatic Control of Ions and Molecules in Nanofluidic Transistors”, Nano Lett., 5:5 (2005), 943–948 | DOI

[27] Postler T., Slouka Z., Svoboda M., Pribyl M., Snita D., “Parametrical studies of electroosmotic transport characteristics in submicrometer channels”, J. Colloid Interface Sci., 320:1 (2008), 321–332 | DOI

[28] Polyanskii V. A., Pankrateva I. L., “Osobennosti techenii vyazkikh elektrizuyuschikhsya zhidkostei v nanorazmernykh kanalakh”, Sovremennye problemy elektrofiziki i elektrogidrodinamiki zhidkostei, Sb. dokl. X Mezhdunar. nauch. konf., SOLO, SPb., 2012, 76–78

[29] Vatazhin A. B., Ulybyshev K. E., “Model formirovaniya elektricheskogo toka vynosa v kanalakh aviatsionnykh reaktivnykh dvigatelei”, Izv. RAN. Mekhanika zhidkosti i gaza, 2000, no. 5, 139–148 | Zbl

[30] Polyansky V. A., Pankratieva I. L., “Space charge generation in flows of weakly conductive media with large difference charged particles mobilities”, J. Electrostatics, 66:7–8 (2008), 432–437 | DOI

[31] Apfelbaum M. S., Polyanskii V. A., “Ob obrazovanii ob'emnogo zaryada v slaboprovodyaschikh sredakh”, Magnitnaya gidrodinamika, 1982, no. 1, 71–76 | Zbl

[32] Pankrateva I. L., Polyanskii V. A., “K raschetu sil, deistvuyuschikh na slaboprovodyaschuyu zhidkost v elektricheskom pole”, Prikl. matem. i mekhanika, 49:5 (1985), 766–773

[33] Ryu J., Park H., Park J., Kang K., “New electrohydrodynamic flow caused by the onsager effect”, Phys. Rev. Lett., 104:10 (2010), Art. 104502, 4 pp. | DOI

[34] Kim W., Ryu J., Suh Y., Hyoung K., “Pumping of dielectric liquids using non-uniform-field induced electrohydrodynamic flow”, Appl. Phys. Lett., 99 (2011), Art. 224102, 3 pp.

[35] Aravin G. S., Vlasov P. A., Karasevich Yu. K., Makolkin E. V., Pankrateva I. L., Polyanskii V. A., “Zondovyi metod diagnostiki v plotnoi nestatsionarnoi pokoyascheisya plazme pri nalichii neravnovesnykh khimicheskikh protsessov”, Khimicheskie reaktsii v neravnovesnoi plazme, Nauka, M., 1983, 55–57

[36] Vlasov P. A., Karasevich Yu. K., Pankrateva I. L., Polyanskii V. A., “Metody issledovaniya kinetiki ionizatsii v udarnykh volnakh”, Fiziko-khimicheskaya kinetika v gazovoi dinamike. Elektron. zhurn., 6 (2008), 1–32, svobodnyi URL: http://chemphys.edu.ru/issues/2008-6/articles/286/

[37] Polyansky V. A., Pankratieva I. L., “Ionization of electronically excited molecules in hydrocarbon combustion under the action of a strong electric field”, J. Electrostatics, 70:2 (2012), 201–206 | DOI

[38] Kuprijanov S., “Ionization of Highly Excited Atoms and Ions of Noble Gases in an Electric Field and Near a Metallic Surface”, JETP Lett., 5:8 (1967), 197–200

[39] Pankrateva I. L., Polyanskii V. A., “Issledovanie mekhanizma protekaniya toka v slaboprovodyaschikh zhidkostyakh pri nalichii ob'emnykh i poverkhnostnykh elektrokhimicheskikh protsessov”, Trudy MIAN, 223, 1998, 248–254 | Zbl

[40] Polyansky V. A., Pankratieva I. L., “Multilayer charged structure in nonpolar dielectric liquids”, J. Colloid Interface Sci., 230:2 (2000), 306–311 | DOI

[41] Pankrateva I. L., Polyanskii V. A., “Obrazovanie silnykh elektricheskikh polei pri techenii zhidkosti v uzkikh kanalakh”, Dokl. RAN, 403:5 (2005), 619–622 | Zbl

[42] Monakhov A. A., Polyanskii V. A., Pankrateva I. L., “Elektrizatsiya i svechenie slabo-provodyaschei zhidkosti v dielektricheskom kanale”, Sovremennye problemy elektrofiziki i elektrogidrodinamiki zhidkostei, Sb. dokl. X Mezhdunar. nauch. konf., SOLO, SPb., 2012, 24–26

[43] Pankrateva I. L., Polyanskii V. A., “Elektrizatsiya slaboprovodyaschikh mnogokomponentnykh zhidkostei pri laminarnom techenii v ploskom kanale”, Fiziko-khimicheskaya kinetika v gazovoi dinamike. Elektron. zhurn., 4 (2006), 1–22, svobodnyi URL: http://chemphys.edu.ru/issues/2006-4/articles/92/