Определение предпробивного электрического поля вблизи катодного стримера в воде
Ключевые слова:
электростатическое поле, катодный стример, эффект Керра, математическое моделирование, дипольное насыщение, вода
Аннотация
Электрическая прочность жидкостей при воздействии импульсного напряжения определяется инициированием стримера и его распространением. Чтобы стример рос и развивался, вблизи его головки необходимо наличие сильного электрического поля. Проводится оценка напряженности поля вблизи развивающегося катодного стримера в воде. Статья посвящена компьютерному моделированию уже проведённых электрооптических исследований предпробивной стадии в воде в субмикросекундном диапазоне и анализу этих процессов. При моделировании полностью воспроизводились все геометрические, оптические и электрофизические условия эксперимента. Рассматривается катодный стример, развивающийся в системе сферических электродов в воде. Математическое моделирование проводилось методом конечных элементов в пределах объёма измерительной ячейки. В рамках применяемой модели расчётным путём было воспроизведено поле распределения интенсивностей экспериментальной керрограммы. Полученная двумерная матрица была визуализирована и проведено сравнение расчетной керрограммы с экспериментальной. Шаг расчётов в пределах 2,5–5 мкм позволял детально анализировать интересующие фрагменты. Рассмотрено два варианта модели стримера – упрощённая и модифицированная, более приближённая к реальному виду стримера. Компьютерное моделирование поля вблизи стримера показало, что если считать диэлектрическую проницаемость не зависящей от напряженности поля, то ее значение у головки катодного стримера не превышало 1,9 МВ/см. Учёт же нелинейности диэлектрической проницаемости на обоих вариантах модели стримера позволил оценить напряжённость поля как 2,4–3,1 МВ/см. Показано, что несмотря на некоторое превышение напряжённости поля над пороговым значением 3 МВ/см, при котором возможно состояние дипольного насыщения, это не приводит к заметному изменению результата. Тем самым подтверждено существенно меньшее значение напряжённости поля вблизи катодного стримера по сравнению с анодным стримером.
Литература
1. Sunka P., et al. Generation of Chemically Active Species by Electrical Discharges in Water. – Plasma Sources Science and Technology, 1999, vol. 8(2), pp. 258–265, DOI:10.1088/0963-0252/8/2/006.
2. Dang T.H., et al. Degradation of Organic Molecules by Streamer Discharges in Water: Coupled Electrical and Chemical Measurements. – Plasma Sources Science Technology, 2008, vol. 17(2), pp.4–13, DOI:10.1088/0963-0252/17/2/024013.
3. Akiyama H. Streamer Discharges in Liquids and Their Applications. – IEEE Transactions on Dielectrics and Electrical Insulation, 2000, vol. 7(5), pp. 646–653, DOI:10.1109/94.879360.
4. Fuhr J., Schmidt W.F, Sato S. Spark Breakdown of Liquid Hydrocarbons. I. Fast Current and Voltage Meas-urements of the Spark Breakdown in liquid n-hexane. – Journal of Applied Physics, 1986, vol.59, iss. 11. pp. 3694–3701, DOI: 10.1063/1.336751.
5. Lewis T.J. Basic Electrical Processes in Dielectric Liquids. – IEEE Transactions on Dielectrics and Electrical Insulation, 1994, vol. 1(4). pp. 630–643, DOI: 10.1109/94.311706.
6. Lehtinen N.G., Marskar R. What Determines the Parameters of a Propagating Streamer: A Comparison of Outputs of the Streamer Parameter Model and of Hydrodynamic Simulations. – Atmosphere, 2021, vol. 12, pp. 1664–1675.
7. Kolb J.F., et al. Streamers in Water and Other Dielectric Li-quids. – Journal of Physics D: Applied Physics, 2008, vol. 41(23), 234007, DOI:10.1088/0022-3727/41/23/234007.
8. Bruggeman P., Leys C. Non-Thermal Plasmas in and in Con-tact with Liquids. – Journal of Physics D: Applied Physics, 2009, vol. 42(5), 053001, DOI:10.1088/0022-3727/42/5/053001.
9. Sun A., Huo C., Zhuang J. Formation Mechanism of Streamer Discharges in Liquids: a review. – High Voltage, 2016, 1(2), pp. 74–80, DOI:10.1049/HVE.2016.0016.
10. Duy C., et al. Streamer Propagation and Breakdown in Natural Ester at High Voltage. – IEEE Transactions on Dielectrics and Electrical Insulation, 2009, 16(6), pp. 1582–1594, DOI: 10.1109/TDEI.2009.536157.
11. Schoenbach K., et al. Electrical Breakdown of Water in Microgaps. – Plasma Sources Science and Technology, 2008, 17(2), 024010, DOI:10.1088/0963-0252/17/2/024010.
12. Ruma, et al. Effects of Pulse Frequency of Input Power on the Physical and Chemical Properties of Pulsed Streamer Discharge Plasmas in Water. – Journal of Physics D: Applied Physics, 2013, vol. 46(12), 125202; DOI:10.1088/0022-3727/46/12/125202.
13. Sarkisov G.S., Woodworth J.R. Observation of Electric Field Enhancement in a Water Streamer Using Kerr Effect. – Journal of Applied Physics, 2006, vol. 99, DOI:10.1063/1.2189215.
14. Dobrynin D., et al. Non-Equilibrium Nanosecond-Pulsed Plasma Generation in the Liquid Phase (Water, PDMS) without Bubbles: Fast Imaging, Spectroscopy and Leader-Type Model. – Journal of Physics D: Applied Physics, 2013, vol. 46(10), DOI:10.1088/0022-3727/46/10/105201.
15. Starikovskiy A., et al. Non-Equilibrium Plasma in Liquid Water: Dynamics of Generation and Quenching. – Plasma Sources Science and Technology, 2011, vol. 20(2), 024003, DOI:10.1088/0963-0252/20/2/024003.
16. Yassinskiy V., et al. Simulation of Electrooptical Measurements of Prebreakdown Electric Fields in Water. Part 1. Electric Field Near Anode Streamer. – IEEE Transactions on Plasma Science, 2022, vol. 50, iss. 5, pp. 1262–1268, DOI: 10.1109/TPS.2022.3166595.
17. Wagenaars E., Bowden M.D., Kroesen G.M.W. Mea-surements of Electric-Field Strengths in Ionization Fronts During Breakdown. – Physical Review Letters, 2007, vol. 98(7), DOI:10.1103/physrevlett.98.075002.
18. Korobeynikov S.M., et al. Optical Study of Prebreak down Cathode Processes in Deionized Water. – IEEE Transactions on Dielectrics and Electrical Insulation, 2009, vol. 16(2), pp. 504–508, DOI:10.1109/tdei.2009.4815185.
19. Korobeynikov S.M., Kuznetsova Yu.A., Yassinskiy V.B. Simulation of Electrooptical Experiments in Liq-uids. – Journal of Electrostatics, 2020,vol. 106, DOI: 10.1016/j.elstat.2020.103452.
20. Коробейников С.М., Мелехов А.В. Оценки напряжённости поля безэлектродных стримеров в воде. – Теплофизика высоких температур, 2014, т. 52, вып. 1, c. 139–141.
21. Соловейчик Ю.Г., Рояк М.Э., Персова М.Г. Метод конечных элементов для решения скалярных и векторных задач. Новосибирск: Изд-во НГТУ, 2007, 896 с.
22. Ушаков В.Я. и др. Пробой жидкостей при импульсном напряжении. Томск: Изд-во НТЛ, 2005, 488 с.
23. Bockris J., Conway B., Ashok K. Modern Aspects of Electrochemistry. – Plenum Press. New York: A Di-vision of Plenum Publishing Corporation, 1985, 521 p.
24. Booth F. The Dielectric Constant of Water and the Saturation Effect. –Journal Chem. Phys., 1951, vol.19, iss. 4, pp. 391–394, DOI:10.1063/1.1748233.
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Работа выполнена при финансовой поддержке Минобрнауки России (НИЛ «Моделирование и обработка данных высоких технологий», код проекта ФСАН-2020-0012)
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1. Sunka P., et al. Generation of Chemically Active Species by Electrical Discharges in Water. – Plasma Sources Science and Technology, 1999, vol. 8(2), pp. 258–265, DOI:10.1088/0963-0252/8/2/006.
2. Dang T.H., et al. Degradation of Organic Molecules by Streamer Discharges in Water: Coupled Electrical and Chemical Measurements. – Plasma Sources Science Technology, 2008, vol. 17(2), pp.4–13, DOI:10.1088/0963-0252/17/2/024013.
3. Akiyama H. Streamer Discharges in Liquids and Their Applications. – IEEE Transactions on Dielectrics and Electrical Insulation, 2000, vol. 7(5), pp. 646–653, DOI:10.1109/94.879360.
4. Fuhr J, Schmidt W.F., Sato S. Spark Breakdown of Liquid Hydrocarbons. I. Fast Current and Voltage Measurements of the Spark Breakdown in liquid n-hexane. – Journal of Applied Physics, 1986, vol.59, iss. 11. pp. 3694–3701, DOI: 10.1063/1.336751.
5. Lewis T.J. Basic Electrical Processes in Dielectric Liquids. – IEEE Transactions on Dielectrics and Electrical Insulation, 1994, vol. 1(4). pp. 630–643, DOI: 10.1109/94.311706.
6. Lehtinen N.G., Marskar R. What Determines the Parameters of a Propagating Streamer: A Comparison of Outputs of the Streamer Parameter Model and of Hydrodynamic Simulations. – Atmosphere, 2021, vol. 12, pp. 1664–1675.
7. Kolb J.F., et al. Streamers in Water and Other Dielectric Liquids. – Journal of Physics D: Applied Physics, 2008, vol. 41(23), 234007, DOI:10.1088/0022-3727/41/23/234007.
8. Bruggeman P., Leys C. Non-Thermal Plasmas in and in Contact with Liquids. – Journal of Physics D: Applied Physics, 2009, vol. 42(5), 053001, DOI:10.1088/0022-3727/42/5/053001.
9. Sun A., Huo C., Zhuang J. Formation Mechanism of Streamer Discharges in Liquids: a review. – High Voltage, 2016, 1(2), pp. 74–80, DOI:10.1049/HVE.2016.0016.
10. Duy C., et al. Streamer Propagation and Breakdown in Natural Ester at High Voltage. – IEEE Transactions on Dielectrics and Electrical Insulation, 2009, 16(6), pp. 1582–1594, DOI: 10.1109/TDEI.2009.536157.
11. Schoenbach K., et al. Electrical Breakdown of Water in Microgaps. – Plasma Sources Science and Technology, 2008, 17(2), 024010, DOI:10.1088/0963-0252/17/2/024010.
12. Ruma, et al. Effects of Pulse Frequency of Input Power on the Physical and Chemical Properties of Pulsed Streamer Discharge Plasmas in Water. – Journal of Physics D: Applied Physics, 2013, vol. 46(12), 125202; DOI:10.1088/0022-3727/46/12/125202.
13. Sarkisov G.S., Woodworth J.R. Observation of Electric Field Enhancement in a Water Streamer Using Kerr Effect. – Journal of Applied Physics, 2006, vol. 99, DOI:10.1063/1.2189215.
14. Dobrynin D., et al. Non-Equilibrium Nanosecond-Pulsed Plasma Generation in the Liquid Phase (Water, PDMS) without Bubbles: Fast Imaging, Spectroscopy and Leader-Type Model. – Journal of Physics D: Applied Physics, 2013, vol. 46(10), DOI:10.1088/0022-3727/46/10/105201.
15. Starikovskiy A., et al. Non-Equilibrium Plasma in Liquid Water: Dynamics of Generation and Quenching. – Plasma Sources Science and Technology, 2011, vol. 20(2), 024003, DOI:10.1088/0963-0252/20/2/024003.
16. Yassinskiy V., et al. Simulation of Electrooptical Measurements of Prebreakdown Electric Fields in Water. Part 1. Electric Field Near Anode Streamer. – IEEE Transactions on Plasma Science, 2022, vol. 50, iss. 5, pp. 1262–1268, DOI: 10.1109/TPS.2022.3166595.
17. Wagenaars E., Bowden M.D., Kroesen G.M.W. Measu-rements of Electric-Field Strengths in Ionization Fronts During Bre-akdown. – Physical Review Letters, 2007, vol. 98(7), DOI:10.1103/physrevlett.98.075002.
18. Korobeynikov S.M., et al. Optical Study of Prebreak down Cathode Processes in Deionized Water. – IEEE Transactions on Dielectrics and Electrical Insulation, 2009, vol. 16(2), pp. 504–508, DOI:10.1109/tdei.2009.4815185.
19. Korobeynikov S.M., Kuznetsova Yu.A., Yassinskiy V.B. Simulation of Electrooptical Experiments in Liquids. – Journal of Electrostatics, 2020, vol. 106, DOI: 10.1016/j.elstat.2020.103452.
20. Korobeynikov S.М., Melekhov A.V. Teplofizika vysokih temperatur – in Russ. (Thermophysics of High Temperatures), 2014, vol. 52, iss. 1, pp. 139–141.
21. Soloveychik Yu.G., Royak M.E., Persova M.G. Metod konechnyh elementov dlya resheniya skalyarnyh i vektornyh zadach (Finite Element Method for Solving Scalar and Vector Problems). Novosibirsk: Izd-vo NGTU, 2007, 896 p.
22. Ushakov V.Ya., et al. Proboy zhidkostey pri impul'snom napryazhenii (Breakdown of Liquids at Pulsed Voltage). Tomsk: Izd-vo NTL, 2005, 488 p.
23. Bockris J., Conway B., Ashok K. Modern Aspects of Electrochemistry. – Plenum Press. New York: A Di-vision of Plenum Publishing Corporation, 1985, 521 p.
24. Booth F. The Dielectric Constant of Water and the Saturation Effect. – Journal Chem. Phys., 1951, vol.19, iss. 4, pp. 391–394, DOI:10.1063/1.1748233.
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The work was financially supported by the Ministry of Science and Higher Education of the Russian Federation (Research Laboratory "Modeling and data processing of high technologies", the project code is FSUN-2020-0012)
2. Dang T.H., et al. Degradation of Organic Molecules by Streamer Discharges in Water: Coupled Electrical and Chemical Measurements. – Plasma Sources Science Technology, 2008, vol. 17(2), pp.4–13, DOI:10.1088/0963-0252/17/2/024013.
3. Akiyama H. Streamer Discharges in Liquids and Their Applications. – IEEE Transactions on Dielectrics and Electrical Insulation, 2000, vol. 7(5), pp. 646–653, DOI:10.1109/94.879360.
4. Fuhr J., Schmidt W.F, Sato S. Spark Breakdown of Liquid Hydrocarbons. I. Fast Current and Voltage Meas-urements of the Spark Breakdown in liquid n-hexane. – Journal of Applied Physics, 1986, vol.59, iss. 11. pp. 3694–3701, DOI: 10.1063/1.336751.
5. Lewis T.J. Basic Electrical Processes in Dielectric Liquids. – IEEE Transactions on Dielectrics and Electrical Insulation, 1994, vol. 1(4). pp. 630–643, DOI: 10.1109/94.311706.
6. Lehtinen N.G., Marskar R. What Determines the Parameters of a Propagating Streamer: A Comparison of Outputs of the Streamer Parameter Model and of Hydrodynamic Simulations. – Atmosphere, 2021, vol. 12, pp. 1664–1675.
7. Kolb J.F., et al. Streamers in Water and Other Dielectric Li-quids. – Journal of Physics D: Applied Physics, 2008, vol. 41(23), 234007, DOI:10.1088/0022-3727/41/23/234007.
8. Bruggeman P., Leys C. Non-Thermal Plasmas in and in Con-tact with Liquids. – Journal of Physics D: Applied Physics, 2009, vol. 42(5), 053001, DOI:10.1088/0022-3727/42/5/053001.
9. Sun A., Huo C., Zhuang J. Formation Mechanism of Streamer Discharges in Liquids: a review. – High Voltage, 2016, 1(2), pp. 74–80, DOI:10.1049/HVE.2016.0016.
10. Duy C., et al. Streamer Propagation and Breakdown in Natural Ester at High Voltage. – IEEE Transactions on Dielectrics and Electrical Insulation, 2009, 16(6), pp. 1582–1594, DOI: 10.1109/TDEI.2009.536157.
11. Schoenbach K., et al. Electrical Breakdown of Water in Microgaps. – Plasma Sources Science and Technology, 2008, 17(2), 024010, DOI:10.1088/0963-0252/17/2/024010.
12. Ruma, et al. Effects of Pulse Frequency of Input Power on the Physical and Chemical Properties of Pulsed Streamer Discharge Plasmas in Water. – Journal of Physics D: Applied Physics, 2013, vol. 46(12), 125202; DOI:10.1088/0022-3727/46/12/125202.
13. Sarkisov G.S., Woodworth J.R. Observation of Electric Field Enhancement in a Water Streamer Using Kerr Effect. – Journal of Applied Physics, 2006, vol. 99, DOI:10.1063/1.2189215.
14. Dobrynin D., et al. Non-Equilibrium Nanosecond-Pulsed Plasma Generation in the Liquid Phase (Water, PDMS) without Bubbles: Fast Imaging, Spectroscopy and Leader-Type Model. – Journal of Physics D: Applied Physics, 2013, vol. 46(10), DOI:10.1088/0022-3727/46/10/105201.
15. Starikovskiy A., et al. Non-Equilibrium Plasma in Liquid Water: Dynamics of Generation and Quenching. – Plasma Sources Science and Technology, 2011, vol. 20(2), 024003, DOI:10.1088/0963-0252/20/2/024003.
16. Yassinskiy V., et al. Simulation of Electrooptical Measurements of Prebreakdown Electric Fields in Water. Part 1. Electric Field Near Anode Streamer. – IEEE Transactions on Plasma Science, 2022, vol. 50, iss. 5, pp. 1262–1268, DOI: 10.1109/TPS.2022.3166595.
17. Wagenaars E., Bowden M.D., Kroesen G.M.W. Mea-surements of Electric-Field Strengths in Ionization Fronts During Breakdown. – Physical Review Letters, 2007, vol. 98(7), DOI:10.1103/physrevlett.98.075002.
18. Korobeynikov S.M., et al. Optical Study of Prebreak down Cathode Processes in Deionized Water. – IEEE Transactions on Dielectrics and Electrical Insulation, 2009, vol. 16(2), pp. 504–508, DOI:10.1109/tdei.2009.4815185.
19. Korobeynikov S.M., Kuznetsova Yu.A., Yassinskiy V.B. Simulation of Electrooptical Experiments in Liq-uids. – Journal of Electrostatics, 2020,vol. 106, DOI: 10.1016/j.elstat.2020.103452.
20. Коробейников С.М., Мелехов А.В. Оценки напряжённости поля безэлектродных стримеров в воде. – Теплофизика высоких температур, 2014, т. 52, вып. 1, c. 139–141.
21. Соловейчик Ю.Г., Рояк М.Э., Персова М.Г. Метод конечных элементов для решения скалярных и векторных задач. Новосибирск: Изд-во НГТУ, 2007, 896 с.
22. Ушаков В.Я. и др. Пробой жидкостей при импульсном напряжении. Томск: Изд-во НТЛ, 2005, 488 с.
23. Bockris J., Conway B., Ashok K. Modern Aspects of Electrochemistry. – Plenum Press. New York: A Di-vision of Plenum Publishing Corporation, 1985, 521 p.
24. Booth F. The Dielectric Constant of Water and the Saturation Effect. –Journal Chem. Phys., 1951, vol.19, iss. 4, pp. 391–394, DOI:10.1063/1.1748233.
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Работа выполнена при финансовой поддержке Минобрнауки России (НИЛ «Моделирование и обработка данных высоких технологий», код проекта ФСАН-2020-0012)
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1. Sunka P., et al. Generation of Chemically Active Species by Electrical Discharges in Water. – Plasma Sources Science and Technology, 1999, vol. 8(2), pp. 258–265, DOI:10.1088/0963-0252/8/2/006.
2. Dang T.H., et al. Degradation of Organic Molecules by Streamer Discharges in Water: Coupled Electrical and Chemical Measurements. – Plasma Sources Science Technology, 2008, vol. 17(2), pp.4–13, DOI:10.1088/0963-0252/17/2/024013.
3. Akiyama H. Streamer Discharges in Liquids and Their Applications. – IEEE Transactions on Dielectrics and Electrical Insulation, 2000, vol. 7(5), pp. 646–653, DOI:10.1109/94.879360.
4. Fuhr J, Schmidt W.F., Sato S. Spark Breakdown of Liquid Hydrocarbons. I. Fast Current and Voltage Measurements of the Spark Breakdown in liquid n-hexane. – Journal of Applied Physics, 1986, vol.59, iss. 11. pp. 3694–3701, DOI: 10.1063/1.336751.
5. Lewis T.J. Basic Electrical Processes in Dielectric Liquids. – IEEE Transactions on Dielectrics and Electrical Insulation, 1994, vol. 1(4). pp. 630–643, DOI: 10.1109/94.311706.
6. Lehtinen N.G., Marskar R. What Determines the Parameters of a Propagating Streamer: A Comparison of Outputs of the Streamer Parameter Model and of Hydrodynamic Simulations. – Atmosphere, 2021, vol. 12, pp. 1664–1675.
7. Kolb J.F., et al. Streamers in Water and Other Dielectric Liquids. – Journal of Physics D: Applied Physics, 2008, vol. 41(23), 234007, DOI:10.1088/0022-3727/41/23/234007.
8. Bruggeman P., Leys C. Non-Thermal Plasmas in and in Contact with Liquids. – Journal of Physics D: Applied Physics, 2009, vol. 42(5), 053001, DOI:10.1088/0022-3727/42/5/053001.
9. Sun A., Huo C., Zhuang J. Formation Mechanism of Streamer Discharges in Liquids: a review. – High Voltage, 2016, 1(2), pp. 74–80, DOI:10.1049/HVE.2016.0016.
10. Duy C., et al. Streamer Propagation and Breakdown in Natural Ester at High Voltage. – IEEE Transactions on Dielectrics and Electrical Insulation, 2009, 16(6), pp. 1582–1594, DOI: 10.1109/TDEI.2009.536157.
11. Schoenbach K., et al. Electrical Breakdown of Water in Microgaps. – Plasma Sources Science and Technology, 2008, 17(2), 024010, DOI:10.1088/0963-0252/17/2/024010.
12. Ruma, et al. Effects of Pulse Frequency of Input Power on the Physical and Chemical Properties of Pulsed Streamer Discharge Plasmas in Water. – Journal of Physics D: Applied Physics, 2013, vol. 46(12), 125202; DOI:10.1088/0022-3727/46/12/125202.
13. Sarkisov G.S., Woodworth J.R. Observation of Electric Field Enhancement in a Water Streamer Using Kerr Effect. – Journal of Applied Physics, 2006, vol. 99, DOI:10.1063/1.2189215.
14. Dobrynin D., et al. Non-Equilibrium Nanosecond-Pulsed Plasma Generation in the Liquid Phase (Water, PDMS) without Bubbles: Fast Imaging, Spectroscopy and Leader-Type Model. – Journal of Physics D: Applied Physics, 2013, vol. 46(10), DOI:10.1088/0022-3727/46/10/105201.
15. Starikovskiy A., et al. Non-Equilibrium Plasma in Liquid Water: Dynamics of Generation and Quenching. – Plasma Sources Science and Technology, 2011, vol. 20(2), 024003, DOI:10.1088/0963-0252/20/2/024003.
16. Yassinskiy V., et al. Simulation of Electrooptical Measurements of Prebreakdown Electric Fields in Water. Part 1. Electric Field Near Anode Streamer. – IEEE Transactions on Plasma Science, 2022, vol. 50, iss. 5, pp. 1262–1268, DOI: 10.1109/TPS.2022.3166595.
17. Wagenaars E., Bowden M.D., Kroesen G.M.W. Measu-rements of Electric-Field Strengths in Ionization Fronts During Bre-akdown. – Physical Review Letters, 2007, vol. 98(7), DOI:10.1103/physrevlett.98.075002.
18. Korobeynikov S.M., et al. Optical Study of Prebreak down Cathode Processes in Deionized Water. – IEEE Transactions on Dielectrics and Electrical Insulation, 2009, vol. 16(2), pp. 504–508, DOI:10.1109/tdei.2009.4815185.
19. Korobeynikov S.M., Kuznetsova Yu.A., Yassinskiy V.B. Simulation of Electrooptical Experiments in Liquids. – Journal of Electrostatics, 2020, vol. 106, DOI: 10.1016/j.elstat.2020.103452.
20. Korobeynikov S.М., Melekhov A.V. Teplofizika vysokih temperatur – in Russ. (Thermophysics of High Temperatures), 2014, vol. 52, iss. 1, pp. 139–141.
21. Soloveychik Yu.G., Royak M.E., Persova M.G. Metod konechnyh elementov dlya resheniya skalyarnyh i vektornyh zadach (Finite Element Method for Solving Scalar and Vector Problems). Novosibirsk: Izd-vo NGTU, 2007, 896 p.
22. Ushakov V.Ya., et al. Proboy zhidkostey pri impul'snom napryazhenii (Breakdown of Liquids at Pulsed Voltage). Tomsk: Izd-vo NTL, 2005, 488 p.
23. Bockris J., Conway B., Ashok K. Modern Aspects of Electrochemistry. – Plenum Press. New York: A Di-vision of Plenum Publishing Corporation, 1985, 521 p.
24. Booth F. The Dielectric Constant of Water and the Saturation Effect. – Journal Chem. Phys., 1951, vol.19, iss. 4, pp. 391–394, DOI:10.1063/1.1748233.
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The work was financially supported by the Ministry of Science and Higher Education of the Russian Federation (Research Laboratory "Modeling and data processing of high technologies", the project code is FSUN-2020-0012)
