Abstract.
The aim of this article is to discuss the concepts of non-local rheology and fluidity, recently introduced to describe dense granular flows. We review and compare various approaches based on different constitutive relations and choices for the fluidity parameter, focusing on the kinetic elasto-plastic model introduced by Bocquet et al. (Phys. Rev. Lett 103, 036001 (2009)) for soft matter, and adapted for granular matter by Kamrin et al. (Phys. Rev. Lett. 108, 178301 (2012)), and the gradient expansion of the local rheology \(\mu\)(I) that we have proposed (Phys. Rev. Lett. 111, 238301 (2013)). We emphasise that, to discriminate between these approaches, one has to go beyond the predictions derived from linearisation around a uniform stress profile, such as that obtained in a simple shear cell. We argue that future tests can be based on the nature of the chosen fluidity parameter, and the related boundary conditions, as well as the hypothesis made to derive the models and the dynamical mechanisms underlying their dynamics.
Graphical abstract
Similar content being viewed by others
References
B. Andreotti, S. Douady, Phys. Rev. E 63, 031305 (2001)
J. Rajchenbach, Phys. Rev. Lett. 90, 144302 (2003)
J.T. Jenkins, Phys. Fluids 18, 103307 (2006)
B. Andreotti, EPL 79, 34001 (2007)
J. Goyon, A. Colin, G. Ovarlez, A. Ajdari, L. Bocquet, Nature 454, 84 (2008)
L. Bocquet, A. Colin, A. Ajdari, Phys. Rev. Lett. 103, 036001 (2009)
J. Goyon, A. Colin, L. Bocquet, Soft Matter 6, 2668 (2010)
P. Chaudhuri, V. Mansard, A. Colin, L. Bocquet, Phys. Rev. Lett. 109, 036001 (2012)
V. Mansard, A. Colin, Soft Matter 8, 4025 (2012)
I.S. Aranson, L.S. Tsimring, Phys. Rev. E 64, 020301(R) (2001)
I.S. Aranson, L.S. Tsimring, Phys. Rev. E 65, 061303 (2002)
D. Volfson, L.S. Tsimring, I.S. Aranson, Phys. Rev. E 68, 021301 (2003)
I.S. Aranson, L.S. Tsimring, F. Malloggi, E. Clément, Phys. Rev. E 78, 031303 (2008)
P.D. Olmsted, Rheol. Acta 47, 283 (2008)
M. Trulson, M. Bouzid, J. Kurchan, E. Clément, P. Claudin, B. Andreotti, EPL 111, 18001 (2015)
M.D. Ediger, C.A. Angell, S.R. Nagel, J. Phys. Chem. 100, 13200 (1996)
P. Debenedetti, F. Stillinger, Nature 410, 259 (2001)
R. Mari, F. Krzakala, J. Kurchan, Phys. Rev. Lett. 103, 025701 (2009)
P. Olsson, S. Teitel, Phys. Rev. Lett. 99, 178001 (2007)
P.N. Pusey, W. van Megen, Nature 320, 340 (1985)
T.G. Mason, D.A. Weitz, Phys. Rev. Lett. 75, 2770 (1995)
G.L. Hunter, E.R. Weeks, Rep. Prog. Phys. 75, 066501 (2012)
J. Mewis, N. Wagner, Colloidal Suspension Rheology (Cambridge University Press, New York, 2012). 0.9pt
M. Cloitre, R. Borrega, F. Monit, L. Leibler, Phys. Rev. Lett. 90, 068303 (2003)
D.S. Fisher, Phys. Rep. 301, 113 (1998)
A. Tanguy, F. Leonforte, J.-L. Barrat, Eur. Phys. J. E 20, 355 (2006)
H.G.E. Hentschel, S. Karmakar, E. Lerner, I. Procaccia, Phys. Rev. Lett. 104, 025501 (2010)
B. Andreotti, Y. Forterre, O. Pouliquen, Granular Media: Between Fluid and Solid (Cambridge University Press, 2013). 0.9pt
A.J. Liu, S.R. Nagel, Nature 396, 21 (1998)
GDR MiDi, Eur. Phys. J. E 14, 341 (2004)
F. da Cruz, S. Emam, M. Prochnow, J.N. Roux, F. Chevoir, Phys. Rev. E 72, 021309 (2005)
M. Trulsson, M. Bouzid, P. Claudin, B. Andreotti, EPL 103, 38002 (2013)
O. Pouliquen, Phys. Fluids. 11, 542 (1999)
P. Jop, Y. Forterre, O. Pouliquen, Nature. 441, 727 (2006)
F. Boyer, E. Guazzelli, O. Pouliquen, Phys. Rev. Lett. 107, 188301 (2011)
M. Trulsson, B. Andreotti, P. Claudin, Phys. Rev. Lett. 109, 118305 (2012)
M. Bouzid, M. Trulsson, P. Claudin, E. Clément, B. Andreotti, Phys. Rev. Lett. 111, 238301 (2013)
G. Katgert, B.P. Tighe, M.E. Möbius, M. van Hecke, EPL 90, 54002 (2010)
J.T. Jenkins, S.B. Savage, J. Fluid Mech. 130, 187 (1983)
T.S. Komatsu, S. Inagaki, N. Nakagawa, S. Nasuno, Phys. Rev. Lett. 86, 1757 (2001)
N. Taberlet, P. Richard, A. Valance, W. Losert, J.M. Pasini, J.T. Jenkins, R. Delannay, Phys. Rev. Lett. 91, 264301 (2003)
N. Taberlet, P. Richard, R. Delannay, Comput. Math. Appl. 55, 230 (2008)
V.B. Nguyen, T. Darnige, A. Bruand, E. Clément, Phys. Rev. Lett. 107, 138303 (2011)
F. Malloggi, B. Andreotti, E. Clément, Phys. Rev. E 91, 052202 (2015)
S. Deboeuf, E. Lajeunesse, O. Dauchot, B. Andreotti, Phys. Rev. Lett. 97, 158303 (2006)
K. Nichol, A. Zanin, R. Bastien, E. Wandersman, M. van Hecke, Phys. Rev. Lett. 104, 078302 (2010)
K.A. Reddy, Y. Forterre, O. Pouliquen, Phys. Rev. Lett. 106, 108301 (2011)
E. Wandersman, M. Van Hecke, EPL 105, 24002 (2014)
R. Harich, T. Darnige, E. Kolb, E. Clément, EPL 96, 54003 (2011)
H.B. Mühlhaus, I. Vardoulakis, Géotechnique 37, 271 (1987)
C. Derec, A. Ajdari, F. Lequeux, Eur. Phys. J. E 4, 355 (2001)
F. Malloggi, J. Lanuza, B. Andreotti, E. Clément, Europhys. Lett. 75, 825 (2006)
I.S. Aranson, F. Malloggi, E. Clément, Phys. Rev. E 73, 050302(R) (2006)
E. Clément, F. Malloggi, B. Andreotti, I.S. Aranson, Granular Matter 10, 3 (2007)
K. Kamrin, G. Koval, Phys. Rev. Lett. 108, 178301 (2012)
O. Pouliquen, Y. Forterre, Philos. Trans. R. Soc. A 367, 5091 (2009)
M. Bouzid, PhD Thesis, Comportement rhéologiques et effets non-locaux dans les écoulements granulaires denses, Université Paris Diderot (2014). 0.9pt
M. Johnson, D. Segalman, J. Non-Newton. Fluid Mech. 2, 255 (1977)
P.D. Olmsted, O. Radulescu, C.-Y.D. Lu, Jou. Rheol. 44, 257 (2000)
P. Marmottant, F. Graner, Eur. Phys. J. E 23, 337 (2007)
A. Amon, V.B. Nguyen, A. Bruand, J. Crassous, E. Clément, Phys. Rev. Lett. 108, 135502 (2012)
D. Chen, K.W. Desmond, E.R. Weeks, Phys. Rev. E 91, 062306 (2015)
K.W. Desmond, E.R. Weeks, Phys. Rev. Lett. 115, 098302 (2015)
M.L. Falk, J.S. Langer, Phys. Rev. E 57, 7192 (1998)
P. Hébraud, F. Lequeux, Phys. Rev. Lett. 81, 2934 (1998)
V. Mansard, L. Bocquet, A. Colin, Soft Matter 10, 6984 (2014)
A. Lemaitre, C. Caroli, Phys. Rev. Lett. 103, 065501 (2009)
D.L. Henann, K. Kamrin, Proc. Natl. Acad. Sci. U.S.A. 110, 6730 (2013)
B.J. Glasser, I. Goldhirsch, Phys. Fluids 13, 407 (2001)
C. Goldenberg, I. Goldhirsch, Phys. Rev. Lett. 89, 084302 (2002)
D.L. Henann, K. Kamrin, Phys. Rev. Lett. 113, 178001 (2014)
R. Benzi, M. Sbragaglia, A. Scagliarini, P. Perlekar, M. Bernaschi, S. Succi, F. Toschi, Soft Matter 11, 1271 (2015)
K.A. Dahmen, Y. Ben-Zion, J.T. Uhl, Nat. Phys. 7, 554 (2011)
M. Bouzid, M. Trulsson, P. Claudin, E. Clément, B. Andreotti, EPL 109, 24002 (2015)
E. Rojas, M. Trulsson, B. Andreotti, E. Clément, R. Soto, EPL 109, 64002 (2015)
A. Le Bouil, A. Amon, S. McNamara, J. Crassous, Phys. Rev. Lett. 112, 246001 (2014)
M. Wyart, EPL 85, 24003 (2009)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Bouzid, M., Izzet, A., Trulsson, M. et al. Non-local rheology in dense granular flows. Eur. Phys. J. E 38, 125 (2015). https://doi.org/10.1140/epje/i2015-15125-1
Received:
Accepted:
Published:
DOI: https://doi.org/10.1140/epje/i2015-15125-1