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JOURNALS // Matematicheskoe modelirovanie

Mat. Model., 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. Pityuk, N. A. Gumerov, O. A. Abramova, I. Sh. Akhatov

References

1. E.P. Prokopev, S.P. Timoshenkov, V.V. Kalugin, “Tekhnologiia KNI struktur”, Peterburgskii zhurnal elektroniki, 1 (2000), 8–25
2. M. Kornfeld, L. Suvorov, “On the destructive action of cavitation”, J. Appl. Phys., 15 (1944), 495  crossref
3. L. Crum, “Surface oscillations and jet development in pulsating bubbles”, J. Phys., 41 (1979), 285–288
4. E.B.V. Dussan, “The moving contact line: the slip boundary condition”, Journal of Fluid Mechanics, 77:4 (1976), 665–684  crossref  zmath
5. E.B.V. Dussan, “On the spreading of liquids on solid surfaces: static and dynamic contact lines”, Ann. Rev. Fluid Mech., 11 (1979), 371–400  crossref
6. L.M. Hocking, “The damping of capillary-gravity waves at a rigid boundary”, J. Fluid Mech., 179 (1987), 253–263  crossref  mathscinet
7. L.M. Hocking, “Waves produced by a vertically oscillating plate”, J. Fluid Mech., 179 (1987), 267–281  crossref  zmath
8. L.M. Hocking, “The spreading of drops with intermolecular forces”, Physics of Fluids, 6:10 (1994), 3224–3228  crossref  zmath
9. P.G.D. Gennes, “Wetting: statics and dynamics”, Rev. Mod. Phys., 57 (1985), 827–863  crossref
10. Y.D. Shikhmurzaev, “Moving contact lines in liquid/liquid/solid systems”, Journal of Fluid Mechanics, 334 (1997), 211–249  crossref  mathscinet  zmath
11. L.M. Hocking, “A moving fluid interface. The removal of the force singularity by a slip flow”, J. Fluid Mech., 79 (1977), 209–229  crossref  zmath
12. C. Huh, S.G. Mason, “The steady movement of a liquid meniscus in a capillary tube”, J. Fluid Mech., 81 (1977), 401–419  crossref
13. H.P. Greenspan, “On the motion of a small viscous droplet that wets a surface”, Journal of Fluid Mechanics, 84:1 (1978), 125–143  crossref  zmath
14. T. Young, “An essay on the cohesion of fluids”, Philos. Trans. R. Soc. London, 95 (1805), 65–87  crossref
15. R. Mettin, P.E. Frommhold, X. Xi, F. Cegla, H. Okorn-Schmidt, A. Lippert, F. Holsteyns, “Acoustic Bubbles: Control and Interaction with Particles Adhered to a Solid Substrate”, Ultra Clean Processing of Semiconductor Surfaces XI, Solid State Phenomena, 195, Switzerland, 2013, 161–164  crossref  elib
16. F. Prabowo, C.-D. Ohl, “Surface oscillation and jetting from surface attached acoustic driven bubbles”, Ultrasonics Sonochemistry, 18 (2011), 431–435  crossref  elib
17. S. Shklyaev, A.V. Straube, “Linear oscillations of a compressible hemispherical bubble on a solid substrate”, Phys. Fluids, 20 (2008), 052102  crossref  zmath
18. C. Pozrikidis, Boundary Integral and Singularity Methods for Linearized Viscous Flow, Cambridge University Press, New York, 1992, 271 pp.  mathscinet  zmath
19. C. Pozrikidis, “Computation of the pressure inside bubbles and pores in Stokes flow”, J. Fluid Mech., 474 (2003), 319–337  crossref  mathscinet  zmath
20. Y.J. Liu, “A new fast multipole boundary element method for solving 2-D Stokes flow problems based on a dual BIE formulation”, Eng. Anal. Bound. Elem., 32 (2008), 139–151  crossref  mathscinet  zmath
21. H. Power, “The interaction of a deformable bubble with a rigid wall at small Reynolds number: a general approach via integral equations”, Eng. Anal. Bound. Elem., 19 (1997), 291–297  crossref
22. Yu.A. Itkulova, O.A. Abramova, N.A. Gumerov, “Boundary element simulations of compressible bubble dynamics in Stokes flow”, ASME 2013 International Mechanical Engineering Congress and Exposition, American Society of Mechanical Engineers, 2013, IMECE2013-63200, V07BT08A010  crossref
23. O.A. Abramova, I.S. Akhatov, N.A. Gumerov, Yu.A. Itkulova (Pityuk), “BEM-based numerical study of three-dimensional compressible bubble dynamics in a Stokes flow”, Computational Mathematics and Mathematical Physics, 54:9 (2014), 1481–1488  mathnet  crossref  crossref  mathscinet  zmath  elib
24. R.I. Nigmatulin, Dinamika mnogofaznykh sistem, Nauka, M., 1987
25. V.P. Zhitnikov, N.M. Sherykhalina, Modelirovanie techenii vesomoi zhidkosti s primeneniem metodov mnogokomponentnogo analiza, Nauchnoe izdanie, Ufa, 2009, 336 pp.


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