mireabulletinRussian Technological JournalRussian Technological Journal2782-32102500-316XRTU MIREA10.32362/2500-316X-2021-9-5-57-66mireabulletin-368Research ArticleМАТЕМАТИЧЕСКОЕ МОДЕЛИРОВАНИЕMATHEMATICAL MODELINGИспарение жидкой лежащей капли в условиях вынужденной конвекцииEvaporation of a liquid sessile droplet subjected to forced convectionhttps://orcid.org/0000-0002-3413-8855КоренченкоА. Е.KorenchenkoA. Е.

Коренченко Анна Евгеньевна, д.ф.-м.н., профессор, кафедра высшей математики Института комплексной безопасности и специального приборостроения

119454, Москва, пр-т Вернадского, д. 78

Scopus Author ID 10043443100

Anna E. Korenchenko, Dr. Sci. (Phys.-Math.), Professor, Department of High Mathematics, Institute of Integrated Safety and Special Instrument Engineering

78, Vernadskogo pr.,  Moscow,  119454  

Scopus Author ID 10043443100

korenchenko@mirea.ruhttps://orcid.org/0000-0003-4511-1882ЖуковаА. А.ZhukovaA. A.

Жукова Анна Александровна, к.х.н., доцент, кафедра аналитической, физической и коллоидной химии

105043, Москва, 5-ая Парковая ул., 21

Scopus Author ID 12757009400

Anna A. Zhukova, Cand. Sci. (Chem.), Associate Professor

21, 5 Parkovaya ul., Moscow, 105043

Scopus Author ID 12757009400

anyazhu@gmail.com«МИРЭА – Российский технологический университет»РоссияMIREA – Russian Technological UniversityRussian FederationПервый Московский государственный медицинский университет им. И.М. Сеченова РоссияSechenov First Moscow State Medical UniversityRussian Federation202125102021955766Copyright © Коренченко А.Е., Жукова А.А., 20212021Коренченко А.Е., Жукова А.А.Korenchenko A.Е., Zhukova A.A.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://www.rtj-mirea.ru/jour/article/view/368

Результаты экспериментов по измерению скорости испарения с поверхности жидкой лежащей капли в воздух указывают, что конвективные потоки над поверхностью увеличивают скорость испарения. Однако данные относительно того, в какой мере конвекция влияет на процесс испарения, сильно разнятся, часто противоречивы и требуют уточнения. В работе проведен численный анализ испарения с поверхности капли воды в нейтральный газ – воздух в присутствии конвективных течений в газовой фазе. Капля располагается на горизонтальной, гладкой, изотермической подложке, рассмотрена мода с постоянным углом смачивания. Задача решена в осесимметричном приближении, течения вынужденной конвекции, совместимые с условиями симметрии, представлены потоками, направленными вниз вдоль оси системы и расходящимися по сторонам вблизи капли и подложки. Математическая модель учитывает влияние сил поверхностного натяжения, тяготения и вязкости в обеих средах, возможную свободную гравитационную конвекцию в газовой и жидкой средах, конвекцию Марангони в капле и построена для испарения, контролируемого диффузией в газовой фазе. Получены результаты, свидетельствующие о взаимном влиянии жидкой и газовой сред: капля колеблется под влиянием движений в атмосфере, что порождает волну плотности в газе: колеблющаяся капля «звучит». Величина скорости в жидкой среде в 50 раз меньше характерной скорости в воздухе. Обнаружено, что скорость испарения не изменяется в присутствии течений вынужденной конвекции, что противоречит большинству экспериментальных работ. Предположительная причина расхождений заключается в возникновении неравновесных условий на границе конденсированной фазы, при которых режим испарения перестает быть диффузионным.

Experiments on measuring the rate of evaporation of liquid sessile droplets into air show that the rate of evaporation increases in the presence of forced convection flows. However, data on the effect of convection on evaporation are often contradictory and should be clarified. The paper presents a numerical analysis of evaporation from the surface of a water droplet subjected to forced convection in the gas phase. The drop is located on a smooth horizontal isothermal substrate; the mode with constant contact angle is considered. The shape of the drop has axial symmetry, the same for the velocities and pressure. Forced convection compatible with the symmetry conditions are represented by flows directed downward along the axis of the system and diverging along the sides near the drop and the substrate. The mathematical model is constructed for evaporation controlled by diffusion in the gas phase and takes into account surface tension, gravity, and viscosity in both media, buoyancy and Marangoni convection. The results indicate the existence of the mutual influence of liquid and gaseous media. Thus, a drop vibrates under the influence of movements in the atmosphere, which generates a density wave in the gas: the drop «sounds». The magnitude of the velocity in a liquid is 50 times less than the characteristic velocity in air. It is found that the evaporation rate does not change in the presence of forced convection flows, which contradicts most of the experimental works. The reason for the discrepancies is supposed to be the appearance of nonequilibrium conditions at the boundary of the condensed phase: under these conditions, the evaporation regime ceases to be diffusional.

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The authors declare that there are no conflicts of interest present.