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,
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
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.
bubble dynamics, solid surface, contact angle, boundary element method, Stokes flow.
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Mathematical Models and Computer Simulations, 2018, 10:2, 209–217
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
\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.
\jour Math. Models Comput. Simul.
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