{"id":4639,"date":"2021-03-12T13:56:40","date_gmt":"2021-03-12T11:56:40","guid":{"rendered":"http:\/\/journals.khnu.km.ua\/vestnik\/?p=4639"},"modified":"2021-03-17T12:26:30","modified_gmt":"2021-03-17T10:26:30","slug":"%d0%bc%d0%b0%d1%82%d0%b5%d0%bc%d0%b0%d1%82%d0%b8%d1%87%d0%bd%d0%b5-%d0%bc%d0%be%d0%b4%d0%b5%d0%bb%d1%8e%d0%b2%d0%b0%d0%bd%d0%bd%d1%8f-%d0%b4%d0%b8%d1%84%d1%83%d0%b7%d1%96%d1%97-%d0%bf%d0%b0%d1%81","status":"publish","type":"post","link":"https:\/\/journals.khnu.km.ua\/vestnik\/?p=4639","title":{"rendered":"\u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u043d\u0435 \u043c\u043e\u0434\u0435\u043b\u044e\u0432\u0430\u043d\u043d\u044f \u0434\u0438\u0444\u0443\u0437\u0456\u0457 \u043f\u0430\u0441\u0438\u0432\u043d\u043e\u0457 \u0434\u043e\u043c\u0456\u0448\u043a\u0438 \u0432 \u0440\u0456\u0434\u043a\u043e\u043c\u0443 \u0441\u0435\u0440\u0435\u0434\u043e\u0432\u0438\u0449\u0456 \u043f\u0456\u0434 \u0432\u043f\u043b\u0438\u0432\u043e\u043c \u0443\u043b\u044c\u0442\u0440\u0430\u0437\u0432\u0443\u043a\u0443"},"content":{"rendered":"

<\/p>\n

\u041c\u0410\u0422\u0415\u041c\u0410\u0422\u0418\u0427\u041d\u0415 \u041c\u041e\u0414\u0415\u041b\u042e\u0412\u0410\u041d\u041d\u042f \u0414\u0418\u0424\u0423\u0417\u0406\u0407 \u041f\u0410\u0421\u0418\u0412\u041d\u041e\u0407 \u0414\u041e\u041c\u0406\u0428\u041a\u0418 \u0412 \u0420\u0406\u0414\u041a\u041e\u041c\u0423 \u0421\u0415\u0420\u0415\u0414\u041e\u0412\u0418\u0429\u0406 \u041f\u0406\u0414 \u0412\u041f\u041b\u0418\u0412\u041e\u041c \u0423\u041b\u042c\u0422\u0420\u0410\u0417\u0412\u0423\u041a\u0423<\/p>\n

MATHEMATICAL MODELLING OF PASSIVE IMPURITY DIFFUSION IN A LIQUID MEDIUM UNDER THE INFLUENCE OF ULTRASOUND<\/p>\n

\"\"<\/a> \u0421\u0442\u043e\u0440\u0456\u043d\u043a\u0438: 296-301. \u041d\u043e\u043c\u0435\u0440: \u21165, 2020 (289)<\/strong>
\n\u0410\u0432\u0442\u043e\u0440\u0438:<\/strong>
\n\u0412.\u041f. \u0425\u041e\u0420\u041e\u041b\u042c\u0421\u042c\u041a\u0418\u0419, \u0412.\u041c. \u0421\u0415\u0420\u0415\u0411\u0420\u0415\u041d\u0418\u041a\u041e\u0412, \u042e.\u041c. \u041a\u041e\u0420\u0415\u041d\u0415\u0426\u042c
\n\u0414\u043e\u043d\u0435\u0446\u044c\u043a\u0438\u0439 \u043d\u0430\u0446\u0456\u043e\u043d\u0430\u043b\u044c\u043d\u0438\u0439 \u0443\u043d\u0456\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442 \u0435\u043a\u043e\u043d\u043e\u043c\u0456\u043a\u0438 \u0456 \u0442\u043e\u0440\u0433\u0456\u0432\u043b\u0456 \u0456\u043c\u0435\u043d\u0456 \u041c\u0438\u0445\u0430\u0439\u043b\u0430 \u0422\u0443\u0433\u0430\u043d-\u0411\u0430\u0440\u0430\u043d\u043e\u0432\u0441\u044c\u043a\u043e\u0433\u043e, \u043c. \u041a\u0440\u0438\u0432\u0438\u0439 \u0420\u0456\u0433
\nV. KHOROLSKY, V. SEREBRENIKOV, Yu. KORENETS
\nDonetsk National University of Economy and Trade named after Mikhailo Tugan-Baranovsky, Kryvyi Rih
\nDOI:<\/strong> https:\/\/www.doi.org\/10.31891\/2307-5732-2020-289-5-296-301<\/a>
\n\u0420\u0435\u0446\u0435\u043d\u0437\u0456\u044f\/Peer review :<\/strong> 05.10.2020 \u0440.
\n\u041d\u0430\u0434\u0440\u0443\u043a\u043e\u0432\u0430\u043d\u0430\/Printed :<\/strong> 27.11.2020 \u0440.<\/p>\n

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\n\u041a\u043b\u044e\u0447\u043e\u0432\u0456 \u0441\u043b\u043e\u0432\u0430:<\/strong> \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u043d\u0435 \u043c\u043e\u0434\u0435\u043b\u044e\u0432\u0430\u043d\u043d\u044f, \u0434\u0438\u0444\u0443\u0437\u0456\u044f, \u043f\u0430\u0441\u0438\u0432\u043d\u0430 \u0434\u043e\u043c\u0456\u0448\u043a\u0430, \u0440\u0456\u0434\u043a\u0435 \u0441\u0435\u0440\u0435\u0434\u043e\u0432\u0438\u0449\u0435, \u0443\u043b\u044c\u0442\u0440\u0430\u0437\u0432\u0443\u043a.<\/p>\n

\u0420\u043e\u0437\u0448\u0438\u0440\u0435\u043d\u0430 \u0430\u043d\u043e\u0442\u0430\u0446\u0456\u044f \u0430\u043d\u0433\u043b\u0456\u0439\u0441\u044c\u043a\u043e\u044e \u043c\u043e\u0432\u043e\u044e<\/strong><\/p>\n

The article considers the question of developing a mathematical model of the process of diffusion of passive impurities in a liquid medium under the influence of ultrasound. When an ultrasonic wave passes through a liquid medium, the phenomenon of acoustic cavitation occurs. Unlike hydrodynamic cavitation, it does not occur locally, but throughout the volume of the liquid, because it is caused by rarefaction regions in the field of ultrasonic vibrations, the pressure of which is lower than the saturated vapour pressure of the liquid medium. The presence of acoustic cavitation causes difficulties in mathematical modelling of this process. As is known, the passive impurity in a liquid medium does not affect the hydrodynamics of the flow and this allows us to consider the hydrodynamic problem separately from the problem of mass transfer. The physics of the process of diffusion of impurities in a liquid medium under the influence of ultrasound is quite complex, but qualitatively it can be represented as follows: during acoustic cavitation throughout the volume there are oscillations and collapse of bubbles, due to this microscopic cumulative jets and shock waves are formed. intensification of impurity stirring in a liquid medium. It should be noted that such mixing occurs locally, without the presence of macroscopic flow. This is analogous to turbulence, where pulsations and small vortices are decisive. Thus, one of the approaches to modelling such local mixing in turbulence theory is the Boussinesq hypothesis. However, Boussinesq’s hypothesis on the theory of turbulence makes it possible to describe the local mixing that occurs during acoustic cavitation using the cavitation diffusion coefficient. This made it possible to use the methods of mathematical physics to model the process of diffusion of passive impurities in a liquid medium under the influence of ultrasound. In the course of the research, the expediency of constructing a mathematical model in the form of a differential equation in partial derivatives of the second order of the parabolic type with boundary conditions of the second type was substantiated.
\nKey words:<\/strong> mathematical modelling, diffusion, passive impurity, liquid medium, ultrasound.<\/p>\n

References<\/strong><\/p>\n

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