Fine Structure of the Substance Distribution Pat-tern of a Free – Falling Drop on the Surface and in the Thickness of the Target Fluid in the Impact Mode of Merging




High-speed video recording was used have been used to trace the evolution of the matter trans-fer pattern of a free-falling drop in a target fluid at rest in the impact mode of coalescence, when the kinetic energy (KE) of the drop exceeds its available potential surface energy (APSE). The combined use of transparent and colored fluids enables simultaneously traces the deformation of the free surface and the evolution of the matter transfer pattern in the thickness and on the surface of the target fluid. In the impact mode, a drop merging with a fluid at rest breaks up into individual fibers that form linear and mesh structures on the surface of the cav-ity and crown. Selected frames in lateral and frontal projections illustrate the main forms of a rapidly evolving pattern of matter distribution, composed of individual fibers. Given schemes of flow in intrusive and impact modes present the domains of rapid internal energy transforma-tion where the free surface of coalescing fluids is eliminated. The influence of energy trans-formation processes on the formation of the fine structure of flows, the main components of which, ligaments, are described by singular solutions of the system of fundamental equations, is discussed.

drop, cavity, crown, matter transfer, fibers, energy.


Volume 24, issue 2, 2023 year


Тонкая структура картины распределения вещества свободно падающей капли на поверхности и в толще принимающей жидкости в импактном режиме слияния

Эволюция картины переноса вещества свободно падающей капли в покоящейся принимающей жид-кости в импактном режиме слияния, когда кинетическая энергия (КИ) капли превышает ее доступ-ную потенциальную поверхностную энергию (ДППЭ) изучена методами высокоскоростной видео-регистрации. Совместное применение прозрачных и окрашенных жидкостей позволяет одновременно прослеживать деформацию свободной поверхности и эволюцию картины переноса вещества в толще и на поверхности принимающей жидкости. В импактном режиме сливающаяся с покоящейся жидкостью капля распадается на отдельные волокна, образующие линейчатые и сетча-тые структуры на поверхности каверны и венца. Выборки из видеограмм в боковой и фронтальной проекциях иллюстрируют основные формы быстро эволюционирующей картины распределения вещества, составленной из отдельных волокон. Приводятся схемы течения в интрузивном и импакт-ном режимах, построенные с учетом локализации областей быстрой трансформации внутренней энергии при уничтожении свободной поверхности сливающихся жидкостей. Обсуждается влияние процессов трансформации энергии на формирование тонкой структуры течений, основные компо-ненты которой – лигаменты – описываются сингулярными решениями системы фундаментальных уравнений.

капля, каверна, венец, перенос вещества, волокна, энергия


Volume 24, issue 2, 2023 year



1. Worthington A.M., Cole R.S. Impact with a liquid surface, studied by the aid of instantaneous photog-raphy. Phil. Trans. R. Soc. Lond. A. 1897, 189, 137–148 https://doi.org/10.1098/rspl.1899.0014
2. Edgerton H.E., Killian Jr. J.R. Flash!: Seeing the unseen by ultra high-speed photography. Hale, Cush-man and Flint: Boston, USA. 1939. 203 p.
3. Peck B., Sigurdson L., Faulkner B., Buttar I. An apparatus to study drop-formed vortex rings. Measure-ment Science and Technology. 1995. V.6(10). P. 1538–1545. DOI 10.1088/0957-0233/6/10/014
4. Taylor G. I. Dispersion of soluble matter in solvent flowing slowly through a tube // Proceedings of the Royal Society of London. Series A. 1953. V. 219. P. 186–203.
5. Taylor G. I. The dispersion of matter in turbulent flow through a pipe // Proceedings of the Royal Soci-ety of London. Series A. 1954. V. 223. P. 446–468.
6. Taylor G. I. Conditions under which dispersion of a solute in a stream of solvent can be used to measure molecular diffusion // Proc. Roy. Soc. London A. 1954. V. 225. P. 473–477
7. Nadolin K. A. Simplified three-dimensional mathematical models of hydrodynamics and passive mass transfer in calm channel flows // Itogi nauki i tekhniki. Sovremennaya matematika i yeye prilozheniya. Tematicheskiye obzory. 2021. T. 196. C. 66-89. DOI: 10.36535/0233-6723-2021-196-66-89. (In Russ.) Results of science and technology. Modern mathematics and its applications. Subject reviews.
8. Оkabe J., Inoue S. The Generation of Vortex Ring // Kyushu Univ., Rep. Res. Inst. Appl. Mech. 1960, 8(32), 91–101.
9. Okabe J., Inoue S. The generation of vortex rings, II. // Rep. Res. Inst. Appl. Mech., Kyushu University, 1961, 9, 147–161.
10. Batchelor, G. K. An Introduction to Fluid Dynamics. Cambridge. CUP. UK. 1967. 615 p.
11. Feistel R. Thermodynamic properties of seawater, ice and humid air: TEOS-10, before and beyond. Ocean. Sci. 2018. V. 14. P. 471–502 https://doi.org/10.5194/os-14-471-2018
12. Mendeleyev D.I. Ob uprugosti gazov. Tipo. A. M. Kotomina. SPb.: Rossiya. 1875. 262 s. (In Russ.) Mendeleev D.I. On the elasticity of gases.
13. Popov N.I., Fedorov K.N., Orlov V.M. Morskaya voda. Spravochnoye rukovodstvo. Nauka: Moskva, Rossiya, 1979; 327 p. (In Russ.). Popov N.I., Fedorov K.N., Orlov V.M. Sea water. Reference guide.
14. Landau L. D., Lifshitz E. M. Course of Theoretical Physics, Vol. 6: Fluid Mechanics (Nauka, Moscow, 1986; Pergamon, New York, 1987)
15. Chashechkin Y.D. Foundations of engineering mathematics applied for fluid flows // Axioms. 2021. Vol. 10. iss. 4, p. 286. https://doi.org/10.3390/axioms10040286.
16. Chashechkin Yu.D. Singularly perturbed components of flows – linear precursors of shock waves // Mathematical Modelling of Natural Phenomena. 2018. Vol. 13. No. 2. P. 1-29. https://doi.org/10.1051/mmnp/2018020
17. Dubrovin K., Zarvin A., Gorbachev Y., Yaskin A., Kalyada V. V. Features of the energy exchange process in a clustered argon stream at the initiation of radiation by an electron beam // Physical-Chemical Kinetics in Gas Dynamics. 2022. V.23, iss. 4 [In Russian]. DOI: 10.33257/PhChGD.23.4.1007
18. Emelyanov V., Teterina I., Volkov K. Drag and heat transfer of metal and oxide agglomerates in flow of combustion products of solid propellant // Physical-Chemical Kinetics in Gas Dynamics. 2020. V.21, iss. 1 [In Russian]. DOI: 10.33257/PhChGD.21.1.893
19. Chashechkin Yu.D. Packets of capillary and acoustic waves of drop impact // Herald of the Bauman Moscow State Technical University, Series Natural Sciences. 2021. No. 1 (94). P. 73–92 (in Russ.). DOI: 10.18698/1812-3368-2021-1-73-91
20. Chashechkin Yu.D., Kistovich A.V. Calculation of the structure of periodic flows in a continuously stratified fluid with allowance for diffusion // Doklady Physics. 2003. V.48. No. 12. P. 710–714 DOI:10.1134/1.1639443
21. Chashechkin Yu.D.1, Ilinykh A.Yu. Distribution of the Drop Substance in the Target Fluid at the Coa-lescence Intrusive Mode // Physical-Chemical Kinetics in Gas Dynamics 2022 V 23(6). P. 1-18. http://chemphys.edu.ru/issues/2022-23-6/articles/1023.
22. Chashechkin Y. D., Prokhorov V. E. Visualization of the flow pattern of the impact of a freely falling drop during the generation of sound packets // Physical-Chemical Kinetics in Gas Dynamics. 2022. V.23, iss. 5 [In Russ.]. DOI:10.33257/PhChGD.23.5.1011
23. Chashechkin Y. D., Ilinykh A. Y. The delay in cavity formation in the intrusive mode of coalescence of a freely falling drop with a target liquid // Doklady Physics. 2021. Vol. 66, no. 1. P. 20–25. DOI: 10.1134/s102833582101002x
24. Chashechkin Y. D., Ilinykh A. Y. Drop decay into individual fibers at the boundary of the contact area with the target fluid // Doklady Physics. 2021. Vol. 66, no. 4. P. 101–105 DOI: 10.1134/S1028335821040078
25. Chashechkin Y. D., Ilinykh A. Y. Banded structures in the distribution pattern of a drop over the surface of the target fluid // Doklady Physics. 2018. Vol. 63, no. 7. P. 282–287. DOI: 10.1134/S1028335818070066
26. Li E. Q., Thoraval M.-J., Marston J. O., Thoroddsen S. T. Early azimuthal instability during drop im-pact // J. Fluid Mech. 2018. Vol. 848, p. 821–835. https://doi.org/10.1017/jfm.2018.383
27. Chashechkin Y. D. Evolution of the fine structure of the matter distribution of a free-falling droplet in mixing liquids // Izvestiya - Atmospheric and Oceanic Physics. 2019. Vol. 55, no. 3. P. 285–294. DOI: 10.1134/S0001433819020026
28. Ersoy N. E., Eslamian M. Capillary surface wave formation and mixing of miscible liquids during drop-let impact onto a liquid film // Physics of Fluids. 2019. Vol. 31. Iss. 1, p. 012107. https://doi.org/10.1063/1.5064640
29. Kistovich A.V., Chashechkin Y.D. Dynamics of gravity-capillary waves on the surface of a nonuni-formly heated fluid // Izvestiya - Atmospheric and Oceanic Physics. 2007. V. 43. P.95–102 DOI:10.1134/S0001433807010112
30. Chashechkin Yu. D., Ochirov A.A. Periodic waves and ligaments on the surface of a viscous exponen-tially stratified fluid in a uniform gravity field // Axioms. 2022. V. 11(8). p. 402. doi: 10.3390/axioms11080402
31. Chashechkin Y.D. Conventional partial and new complete solutions of the fundamental equations of fluid mechanics in the problem of periodic internal waves with accompanying ligaments generation // Mathematics. 2021. V. 9(6). P. 586 DOI:10.3390/math9060586.
32. Eisenberg D., Kauzmann W. The structure and properties of water (Oxford Classic texts in the physical sciences). Oxford University Press: Oxford, UK. 2005. 308 p.
33. Malenkov G.G., Naberukhin Yu.I., Voloshin V. Collective effects in diffusional motion of water mole-cules: Computer simulation // Structural Chemistry. 2011. V. 22(2). P. 459–463. DOI:10.1007/s11224-011-9766-3
34. GFK IPMech RAS: Hydrophysical Complex for Modeling Hydrodynamic Processes in the Environ-ment and their Impact on Underwater Technical Objects, as well as the Spread of Impurities in the Ocean and Atmosphere. http://www.ipmnet.ru/uniqequip/gfk/#equip
35. Chashechkin Yu. D., Ilinykh A. Yu. Multiple emissions of splashes upon drop impact // Doklady Phys-ics 2020. V. 65(10). P 384–388. DOI: 10.1134/S1028335820100067.
36. Chashechkin Yu.D., Ilinykh A.Yu. Formation of a system of inclined loops in the flows of a drop im-pact // Doklady Physics. 2021. V. 66(8). P. 234–242 DOI: 10.1134/S1028335821080036.
37. Bunkin N.F., Suyazov N.V., Shkirin A.V., Ignat’ev P.S., Indukaev K.V. Study of Nanostructure of highly purified water by measuring scattering matrix elements of laser radiation // Physics of Wave Phenomena. 2008. V. 16. P. 243–260 DOI:10.3103/S1541308X08040018
38. Teschke O., de Souza E. Water molecule clusters measured at water/air interfaces using atomic force microscopy. Physical Chemistry – Chemical Physics Journal. 2005. V. 7. P. 3856–3865. DOI: 10.1039/b511257e.
39. Chashechkin Yu. D., Ilinykh A. Yu. Visualization of media contact areas in drop impact flows with chemical reactions // Doklady Physics. 2021. V. 66(10). P. 285–292 DOI: 10.1134/S1028335821100013.
40. Chashechkin Yu. D. Transfer of the substance of a colored drop in a liquid layer with travelling plane gravity–capillary waves // Izvestiya, Atmospheric and Oceanic Physics. 2022. V. 58 (2). P. 188–197 DOI: 10.1134/S0001433822020037
41. Stepanova E. V., Trofimova M. V., Chaplina T. O., Chashechkin Yu. D. mailto:chakin@ipmnet.ruStructural stability of substance transport in a compound vortex // Izvestiya, Atmospheric and Oceanic Physics. 2012. V. 48 (5). P. 516-527 DOI 10.1134/S000143381205009X