Mathematical Modeling of the Wave Dynamics of an Encapsulated Perfluorocarbon Droplet in a Viscoelastic Liquid

Damir A. Gubaidullin, Dilya D. Gubaidullina and Yuri V. Fedorov ()
Additional contact information
Damir A. Gubaidullin: Department of Continuum Mechanics, Institute of Mechanics and Engineering, FRC Kazan Scientific Center, Russian Academy of Sciences, Kazan 420111, Russia
Dilya D. Gubaidullina: Department of Continuum Mechanics, Institute of Mechanics and Engineering, FRC Kazan Scientific Center, Russian Academy of Sciences, Kazan 420111, Russia
Yuri V. Fedorov: Department of Continuum Mechanics, Institute of Mechanics and Engineering, FRC Kazan Scientific Center, Russian Academy of Sciences, Kazan 420111, Russia

Mathematics, 2023, vol. 11, issue 5, 1-10

Abstract: A mathematical model has been developed and a numerical study of vapor bubble growth as a result of acoustic evaporation of an encapsulated perfluorocarbon droplet in a viscoelastic liquid is presented. The viscoelasticity of the droplet shell and the carrier liquid is taken into account according to the Kelvin–Voigt rheological model. The problem is reduced to solving a system of ordinary differential equations for the radius and temperature of the bubble, the radius of the droplet and the shell together with the thermal conductivity equation for the internal liquid. Spatial discretization of the thermal conductivity equation is carried out using an implicit finite difference scheme. ODEs are solved by the fifth order Runge–Kutta method with an adaptive computational step. To check the correctness of the numerical calculation in a particular case, the theory has been compared with known experimental data. The influence of the shear modulus of the shell and the carrier liquid, and the shell thickness on the radial dynamics of a vapor bubble inside an encapsulated droplet in an external viscoelastic liquid is demonstrated.

Keywords: mathematical model; acoustic field; perfluorocarbon drop; vapor bubble; viscoelastic shell and liquid; phase transition (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/5/1083/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/5/1083/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:11:y:2023:i:5:p:1083-:d:1076158

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().