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Matem. Mod., 2017, Volume 29, Number 9, Pages 77–89 (Mi mm3888)  

Boundary element modeling of dynamics of a bubble contacting with a solid surface at low Reynolds numbers

Yu. A. Pityuka, N. A. Gumerovab, O. A. Abramovaa, I. Sh. Akhatovc

a Center for Micro and Nanoscale Dynamics of Dispersed Systems, Bashkir State University, Ufa, Russia
b University of Maryland, Institute of Advanced Computer Study, College Park, MD, USA
c Center for Design, Manufacturing & Materials, Skolkovo Institute of Science & Engineering (Skoltech), Moscow, Russia

Abstract: In the present study the dynamics of surface attached acoustic driven bubble at low Reynolds numbers is considered. The approach is based on the boundary element method (BEM) for Stokes flows, which is especially effective for the numerical solution of problems in threedimensional case. However computation of compressible bubbles dynamics caused some difficulties in formulation due to the degeneration of conventional BEM for Stokes equations. In the present approach an additional relation based on the Lorenz reciprocity principle is used to resolve the problem. To describe the contact line dynamics a semi-empirical law of motion is used. Such approach allows one to bypass a known issue of nonintegrability stresses in the moving triple point. The behavior of a surface attached bubble in the cases of a pinned or moving contact line is studied. The developed method can be used for detailed study of the bubble dynamics in the contact with a solid wall in order to determine the optimal conditions and parameters of surface cleaning processes.

Keywords: bubble dynamics, solid surface, contact angle, boundary element method, Stokes flow.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-31-00029_мол_а
Ministry of Education and Science of the Russian Federation MK-3503.2017.8


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English version:
Mathematical Models and Computer Simulations, 2018, 10:2, 209–217

Received: 30.05.2016

Citation: Yu. A. Pityuk, N. A. Gumerov, O. A. Abramova, I. Sh. Akhatov, “Boundary element modeling of dynamics of a bubble contacting with a solid surface at low Reynolds numbers”, Matem. Mod., 29:9 (2017), 77–89; Math. Models Comput. Simul., 10:2 (2018), 209–217

Citation in format AMSBIB
\Bibitem{PitGumAbr17}
\by Yu.~A.~Pityuk, N.~A.~Gumerov, O.~A.~Abramova, I.~Sh.~Akhatov
\paper Boundary element modeling of dynamics of a bubble contacting with a solid surface at low Reynolds numbers
\jour Matem. Mod.
\yr 2017
\vol 29
\issue 9
\pages 77--89
\mathnet{http://mi.mathnet.ru/mm3888}
\elib{http://elibrary.ru/item.asp?id=29972281}
\transl
\jour Math. Models Comput. Simul.
\yr 2018
\vol 10
\issue 2
\pages 209--217
\crossref{https://doi.org/10.1134/S2070048218020102}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85044958795}


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