Geodesic
Boundary element modeling of dynamics of a bubble contacting with a solid surface at low Reynolds numbers
Matematičeskoe modelirovanie, Tome 29 (2017) no. 9, pp. 77-89

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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, contact angle, boundary element method, Stokes flow.
Mots-clés : solid surface 
@article{MM_2017_29_9_a5,
     author = {Yu. A. Pityuk and N. A. Gumerov and O. A. Abramova and I. Sh. Akhatov},
     title = {Boundary element modeling of dynamics of a bubble contacting with a solid surface at low {Reynolds} numbers},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {77--89},
     publisher = {mathdoc},
     volume = {29},
     number = {9},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2017_29_9_a5/}
}
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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. Matematičeskoe modelirovanie, Tome 29 (2017) no. 9, pp. 77-89. http://geodesic.mathdoc.fr/item/MM_2017_29_9_a5/