Abstract.
In this short review, we visualize the fluid velocity generated by a point force close to a plane free surface or a plane rigid wall. We present separately contributions from all the multipoles which form the corresponding classical systems of images. Such graphical images might be useful in the theoretical and numerical modeling of the dynamics of micro-objects moving close to an interface.
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References
M.D. Graham, Annu. Rev. Fluid Mech. 43, 273 (2011)
H. Ma, M.D. Graham, Phys. Fluids 17, 083103 (2005)
K. Ishimoto, E.A. Gaffney, Phys. Rev. E 88, 062702 (2013)
I. Llopis, I. Pagonabarraga, J. Non-Newton. Fluid 165, 946 (2010)
W.H. Mitchell, S.E. Spagnolie, J. Fluid Mech. 772, 600 (2015)
W.E. Uspal, H.B. Eral, P.S. Doyle, Nat. Commun. 4, 2666 (2013)
B. Felderhof, Phys. Fluids 22, 113604 (2010)
B. Felderhof, Eur. Phys. J. E 37, 110 (2014)
D. Crowdy, S. Lee, O. Samson, E. Lauga, A. Hosoi, J. Fluid Mech. 681, 24 (2011)
D. Pimponi, M. Chinappi, P. Gualtieri, C.M. Casciola, Microfluid. Nanofluid. 16, 571 (2014)
D. Pimponi, M. Chinappi, P. Gualtieri, C.M. Casciola, J. Fluid Mech. 789, 514 (2016)
D. Pimponi, M. Chinappi, P. Gualtieri, Eur. Phys. J. E 41, 28 (2018)
J. Elgeti, R.G. Winkler, G. Gompper, Rep. Prog. Phys. 78, 056601 (2015)
J. Elgeti, G. Gompper, Eur. Phys. J. ST 225, 2333 (2016)
E. Lauga, T.R. Powers, Rep. Prog. Phys. 72, 096601 (2009)
E. Lauga, Annu. Rev. Fluid Mech. 48, 105 (2016)
S.E. Spagnolie, E. Lauga, J. Fluid Mech. 700, 105 (2012)
K. Schaar, A. Zöttl, H. Stark, Phys. Rev. Lett. 115, 038101 (2015)
A.P. Berke, L. Turner, H.C. Berg, E. Lauga, Phys. Rev. Lett. 101, 038102 (2008)
R. Di Leonardo, D. Dell’Arciprete, L. Angelani, V. Iebba, Phys. Rev. Lett. 106, 038101 (2011)
W.R. DiLuzio, L. Turner, M. Mayer, P. Garstecki, D.B. Weibel, H.C. Berg, G.M. Whitesides, Nature 435, 1271 (2005)
E. Lauga, W.R. DiLuzio, G.M. Whitesides, H.A. Stone, Biophys. J. 90, 400 (2006)
K. Martens, L. Angelani, R. Di Leonardo, L. Bocquet, Eur. Phys. J. E 35, 84 (2012)
J.S. Guasto, R. Rusconi, R. Stocker, Annu. Rev. Fluid Mech. 44, 373 (2012)
M. Garcia, S. Berti, P. Peyla, S. Rafaï, Phys. Rev. E 83, 035301 (2011)
H. Kurtuldu, D. Tam, A. Hosoi, K.A. Johnson, J. Gollub, Phys. Rev. E 88, 013015 (2013)
D. Smith, E. Gaffney, J. Blake, J. Kirkman-Brown, J. Fluid Mech. 621, 289 (2009)
A. Kumar, M.D. Graham, Soft Matter 8, 10536 (2012)
P.M. Vlahovska, D. Barthes-Biesel, C. Misbah, C. R. Phys. 14, 451 (2013)
W. Uspal, M.N. Popescu, S. Dietrich, M. Tasinkevych, Soft Matter 11, 434 (2015)
R. Dreyfus, J. Baudry, M.L. Roper, M. Fermigier, H.A. Stone, J. Bibette, Nature 437, 862 (2005)
S. Martínez-Aranda, F.J. Galindo-Rosales, L. Campo-Deaño, Soft Matter 12, 2334 (2016)
K. Drescher, R.E. Goldstein, N. Michel, M. Polin, I. Tuval, Phys. Rev. Lett. 105, 168101 (2010)
K. Drescher, J. Dunkel, L.H. Cisneros, S. Ganguly, R.E. Goldstein, Proc. Natl. Acad. Sci. U.S.A. 108, 10940 (2011)
L. Jibuti, W. Zimmermann, S. Rafaï, P. Peyla, Phys. Rev. E 96, 052610 (2017)
S. Kim, S.J. Karrila, Microhydrodynamics: Principles and Selected Applications (Courier Corporation, 2013)
J.R. Blake, Math. Proc. Cambridge 70, 303 (1971)
J. Blake, A. Chwang, J. Eng. Math. 8, 23 (1974)
R. Jones, B. Felderhof, J. Deutch, Macromolecules 8, 680 (1975)
G. Perkins, R. Jones, Physica A 171, 575 (1991)
H. Lorenz, Zittingsversl. Akad. Wet. 5, 168 (1896)
H. Lorenz, Abh. Theor. Phys. 1, 23 (1907)
A. Venkatalaxmi, B. Padmavathi, T. Amaranath, Mech. Res. Commun. 31, 465 (2004)
Z. Gimbutas, L. Greengard, S. Veerapaneni, J. Fluid Mech. 776, R1 (2015)
W. Yan, M. Shelley, arXiv preprint, arXiv:1803.02424 (2018)
M. Lisicki, B. Cichocki, E. Wajnryb, J. Chem. Phys. 145, 034904 (2016)
T.M. Squires, M.P. Brenner, Phys. Rev. Lett. 85, 4976 (2000)
M. Bukowicki, M. Gruca, M.L. Ekiel-Jeżewska, J. Fluid Mech. 767, 95 (2015)
J. Bławzdziewicz, M. Ekiel-Jezewska, E. Wajnryb, J. Chem. Phys. 133, 114703 (2010)
M.L. Ekiel-Jeżewska, in Human Factors of a Global Society: A System of Systems Perspective, edited by J. Kantola, T. Marek, W. Karwowski, M. Frankowicz, P. Zgaga (CRC Press, 2014) Chapt. 79: Experimenting with teaching contexts, pp. 895--905
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Ekiel-Jeżewska, M., Boniecki, R., Bukowicki, M. et al. Stokes velocity generated by a point force in various geometries. Eur. Phys. J. E 41, 120 (2018). https://doi.org/10.1140/epje/i2018-11727-3
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DOI: https://doi.org/10.1140/epje/i2018-11727-3