D. A. Gubaidullin, D. D. Gubaidullina, Yu. V. Fedorov
{"title":"Acoustics of a Viscoelastic Liquid with Perfluorocarbon Droplets in the Presence of Phase Transitions","authors":"D. A. Gubaidullin, D. D. Gubaidullina, Yu. V. Fedorov","doi":"10.1134/s1995080224602169","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In this work, a modified Rayleigh–Lamb equation which takes into account the radial oscillations of a perfluorocarbon droplet with a vapor bubble in the center in a viscoelastic liquid has been derived. The viscoelasticity of the carrier medium has been taken into account based on the Zener rheological model. For small inclusion oscillations, the problem of heat and mass transfer between vapor, liquid phase and carrier liquid has been solved. The energy equation has been found. Based on the obtained equations of radial oscillations of the inclusion, energy and the well-known wave equation for a bubbly liquid, the dispersion relation has been determined. For a mixture of polydimethylsiloxane with droplets of octafluoropropane C<span>\\({}_{3}\\)</span>F<span>\\({}_{8}\\)</span> and vapor bubbles in the center, the dependencies of the phase velocity and attenuation coefficient on the perturbation frequency have been plotted. The influence of the shear modulus and relaxation time of the elastic carrier liquid on the dynamics of acoustic waves has been illustrated.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Lobachevskii Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1134/s1995080224602169","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this work, a modified Rayleigh–Lamb equation which takes into account the radial oscillations of a perfluorocarbon droplet with a vapor bubble in the center in a viscoelastic liquid has been derived. The viscoelasticity of the carrier medium has been taken into account based on the Zener rheological model. For small inclusion oscillations, the problem of heat and mass transfer between vapor, liquid phase and carrier liquid has been solved. The energy equation has been found. Based on the obtained equations of radial oscillations of the inclusion, energy and the well-known wave equation for a bubbly liquid, the dispersion relation has been determined. For a mixture of polydimethylsiloxane with droplets of octafluoropropane C\({}_{3}\)F\({}_{8}\) and vapor bubbles in the center, the dependencies of the phase velocity and attenuation coefficient on the perturbation frequency have been plotted. The influence of the shear modulus and relaxation time of the elastic carrier liquid on the dynamics of acoustic waves has been illustrated.
期刊介绍：
Lobachevskii Journal of Mathematics is an international peer reviewed journal published in collaboration with the Russian Academy of Sciences and Kazan Federal University. The journal covers mathematical topics associated with the name of famous Russian mathematician Nikolai Lobachevsky (Lobachevskii). The journal publishes research articles on geometry and topology, algebra, complex analysis, functional analysis, differential equations and mathematical physics, probability theory and stochastic processes, computational mathematics, mathematical modeling, numerical methods and program complexes, computer science, optimal control, and theory of algorithms as well as applied mathematics. The journal welcomes manuscripts from all countries in the English language.
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