Abstract.
We study experimentally the flow of a foam confined as a bubble monolayer between two plates through a convergent channel. We quantify the velocity, the distribution and orientation of plastic events, and the elastic stress, using image analysis. We use two different soap solutions: a sodium dodecyl sulfate (SDS) solution, with a negligible wall friction between the bubbles and the confining plates, and a mixture containing a fatty acid, giving a large wall friction. We show that for SDS solutions, the velocity profile obeys a self-similar form which results from the superposition of plastic events, and the elastic deformation is uniform. For the other solution, the velocity field differs and the elastic deformation increases towards the exit of the channel. We discuss and quantify the role of wall friction on the velocity profile, the elastic deformation, and the rate of plastic events.
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I. Cantat, S. Cohen-Addad, F. Elias, F. Graner, R. Höhler, O. Pitois, F. Rouyer, A. Saint-Jalmes, Foams, Structure and Dynamics, edited by S.J. Cox (Oxford University Press, 2013)
G.K. Batchelor, J. Fluid Mech. 41, 545 (1970)
C. Raufaste, B. Dollet, K. Mader, S. Santucci, R. Mokso, EPL 111, 38004 (2015)
Y. Wang, K. Krishan, M. Dennin, Phys. Rev. E 73, 031401 (2006)
G. Katgert, M.E. Möbius, M. van Hecke, Phys. Rev. Lett. 101, 058301 (2008)
B. Dollet, A. Scagliarini, M. Sbragaglia, J. Fluid Mech. 766, 556 (2015)
B. Dollet, M. Aubouy, F. Graner, Phys. Rev. Lett. 95, 168303 (2005)
B. Dollet, M. Durth, F. Graner, Phys. Rev. E 73, 061404 (2006)
B. Dollet, F. Graner, J. Fluid Mech. 585, 181 (2007)
Y. Bertho, C. Becco, N. Vandewalle, Phys. Rev. E 73, 056309 (2006)
B. Dollet, J. Rheol. 54, 741 (2010)
T. Okuzono, K. Kawasaki, Phys. Rev. E 51, 1246 (1995)
D.J. Durian, Phys. Rev. Lett. 75, 4780 (1995)
I. Cantat, Soft Matter 7, 448 (2011)
C. Raufaste, B. Dollet, S. Cox, Y. Jiang, F. Graner, Eur. Phys. J. E 23, 217 (2007)
I.T. Davies, S.J. Cox, Colloids Surf. A 344, 8 (2009)
I. Cheddadi, P. Saramito, B. Dollet, C. Raufaste, F. Graner, Eur. Phys. J. E 34, 1 (2011)
F. Boulogne, S.J. Cox, Phys. Rev. E 83, 041404 (2011)
S.A. Jones, B. Dollet, N. Slosse, Y. Jiang, S.J. Cox, F. Graner, Colloids Surf. A 382, 18 (2011)
V.J. Langlois, J. Rheol. 58, 799 (2014)
D.A. Reinelt, A.M. Kraynik, J. Fluid Mech. 311, 327 (1996)
D.A. Reinelt, A.M. Kraynik, J. Rheol. 44, 453 (2000)
N.D. Denkov, S. Tcholakova, K. Golemanov, K.P. Ananthapadmanabhan, A. Lips, Soft Matter 5, 3389 (2009)
S. Arif, J.C. Tsai, S. Hilgenfeldt, EPL 92, 38001 (2010)
S. Arif, J.C. Tsai, S. Hilgenfeldt, J. Rheol. 56, 485 (2012)
I. Ben Salem, I. Cantat, B. Dollet, J. Fluid Mech. 714, 258 (2013)
J.C. Earnshaw, A.H. Jaafar, Phys. Rev. E 49, 5408 (1994)
D. Chen, K.W. Desmond, E.R. Weeks, Soft Matter 8, 10486 (2012)
D. Chen, K.W. Desmond, E.R. Weeks, Phys. Rev. E 91, 062306 (2015)
G.B. Jeffery, Philos. Mag. 29, 455 (1915)
G. Hamel, Jahresber. Deutsch. Math.-Verein. 25, 34 (1916)
K. Pohlhausen, Z. Angew. Math. Mech. 1, 252 (1921)
L. Landau, E. Lifshitz, Mécanique des fluides, 3ème édition (Mir, 1994)
K. Golemanov, N.D. Denkov, S. Tcholakova, M. Vethamuthu, A. Lips, Langmuir 24, 9956 (2008)
L. Bocquet, A. Colin, A. Ajdari, Phys. Rev. Lett. 103, 036001 (2009)
D.J. Durian, D.A. Weitz, D.J. Pine, Science 252, 686 (1991)
S.J. Cox, F. Graner, M.F. Vaz, Soft Matter 4, 1871 (2008)
K.W. Desmond, E.R. Weeks, Phys. Rev. Lett. 115, 098302 (2015)
B. Embley, P. Grassia, Colloids Surf. A 382, 8 (2011)
P. Marmottant, F. Graner, Soft Matter 9, 9602 (2013)
M. Durand, H.A. Stone, Phys. Rev. Lett. 97, 226101 (2006)
A.L. Biance, S. Cohen-Addad, R. Höhler, Soft Matter 5, 4672 (2009)
V. Mansard, A. Colin, P. Chaudhuri, L. Bocquet, Soft Matter 9, 7489 (2013)
J.D. Barry, D. Weaire, S. Hutzler, Philos. Mag. Lett. 91, 432 (2011)
A. Scagliarini, B. Dollet, M. Sbragaglia, Colloids Surf. A 473, 133 (2015)
P. Saramito, J. Non-Newtonian Fluid Mech. 145, 1 (2007)
J. Goyon, A. Colin, G. Ovarlez, A. Ajdari, L. Bocquet, Nature 454, 84 (2008)
E. Janiaud, D. Weaire, S. Hutzler, Phys. Rev. Lett. 97, 038302 (2006)
D. Weaire, S. Hutzler, V.J. Langlois, R.J. Clancy, Philos. Mag. Lett. 88, 387 (2008)
A. Prosperetti, Advanced Mathematics for Applications (Cambridge University Press, 2011)
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Dollet, B., Bocher, C. Flow of foam through a convergent channel. Eur. Phys. J. E 38, 123 (2015). https://doi.org/10.1140/epje/i2015-15123-3
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DOI: https://doi.org/10.1140/epje/i2015-15123-3