A small-gap effective-temperature model of transient shear band formation during flow

Journal of Rheology

Volumn 60, Issue 5, 2016, Pages 873-882

  Hinkle, Adam R ^a   Falk, Michael L ^a,b  

^a Johns Hopkins University   (United States)

^b JOHNS HOPKINS UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

FLUIDIZATION; SHEAR BANDS; TEMPERATURE;

EFFECTIVE TEMPERATURE; MECHANICAL RESPONSE; PHYSICAL PARAMETERS; QUANTITATIVE COMPARISON; SOLID-FLUID TRANSITIONS; SPATIALLY HOMOGENEOUS; STRUCTURAL EVOLUTION; TRANSIENT BEHAVIOR;

SHEAR FLOW;

EID: 84987668145     PISSN: 01486055     EISSN: 15208516     Source Type: Journal    
DOI: 10.1122/1.4960514     Document Type: Article

References (61)

1. Bonn, A., and M. Denn, "Yield stress fluids slowly yield to analysis," Science 324, 1401-1402 (2009). 10.1126/science.1174217
2. Ragouilliaux, A., G. Ovarlez, N. Shahidzadeh-Bonn, B. Herzhaft, T. Palermo, and P. Coussot, "Transition from a simple yield-stress fluid to a thixotropic material," Phys. Rev. E 76, 051408 (2007). 10.1103/PhysRevE.76.051408
3. Møller, P. C., A. Fall, V. Chikkadi, D. Derks, and D. Bonn, "An attempt to categorize yield stress fluid behaviour," Philos. Trans. R. Soc. A 367, 5139-5155 (2009). 10.1098/rsta.2009.0194
4. Møller, P. C., J. Mewis, and D. Bonn, "Yield stress and thixotropy: On the difficulty of measuring yield stress in practice," Soft Matter 2, 274-283 (2006). 10.1039/b517840a
5. Coussot, P., "Rheophysics of pastes: A review of microscopic modelling approaches," Soft Matter 3, 528-540 (2007). 10.1039/b611021p
6. Barnes, H. A., "Thixotropy a review," J. Non-Newtonian Fluid Mech. 70, 1-33 (1997). 10.1016/S0377-0257(97)00004-9
7. Ovarlez, G., S. Rodts, X. Chateau, and P. Coussot, "Phenomenology and physical origin of shear localization and shear banding in complex fluids," Rheol. Acta 48, 831-844 (2009). 10.1007/s00397-008-0344-6
8. Schall, P., and M. van Hecke, "Shear bands in matter with granularity," Annu. Rev. Fluid Mech. 42, 67-88 (2010). 10.1146/annurev-fluid-121108-145544
9. Bird, R. B., G. C. Dai, and B. J. Yarusso, "The rheology and flow of viscoplastic materials," Rev. Chem. Eng. 1, 1-70 (1982).
10. Coussot, P., Rheometry of Pastes, Suspensions, and Granular Materials (Wiley, New York, 2005).
11. Varnik, F., L. Bocquet, J. L. Barrat, and L. Berthier, "Shear localization in a model glass," Phys. Rev. Lett. 90, 095702 (2003). 10.1103/PhysRevLett.90.095702
12. Fielding, S. M., "Shear banding in soft glassy materials," Rep. Prog. Phys. 77, 102601 (2014). 10.1088/0034-4885/77/10/102601
13. Boukany, P. E., and S. Q. Wang, "Exploring the transition from wall slip to bulk shear banding in well-entangled DNA solutions," Soft Matter 5, 780-789 (2009). 10.1039/B804791J
14. Boukany, P. E., and S. Q. Wang, "Shear banding or not in entangled DNA solutions," Macromolecules 43, 6950-6952 (2010). 10.1021/ma101267b
15. Ravindranath, S., S. Q. Wang, M. Ofechnowicz, and R. Quirk, "Banding in simple steady shear of entangled polymer solutions," Macromolecules 41, 2663-2670 (2008). 10.1021/ma7027352
16. Tapadia, P., and S. Q. Wang, "Direct visualization of continuous simple shear in non-newtonian polymeric fluids," Phys. Rev. Lett. 96, 016001 (2006). 10.1103/PhysRevLett.96.016001
17. Helgeson, M. E., P. A. Vasquez, E. W. Kaler, and N. J. Wagner, "Rheology and spatially-resolved structure of cetyltrimethylammonium bromide micelles through the shear banding transition," J. Rheol. 53, 727-756 (2009). 10.1122/1.3089579
18. Hu, Y. T., C. Palla, and A. Lips, "Comparison between shear banding and shear thinning in entangled micellar solutions," J. Rheol. 52, 379-400 (2008). 10.1122/1.2836937
19. Decruppe, J. P., S. Lerouge, and J. F. Berret, "Insight in shear banding under transient flow," Phys. Rev. E 63, 022501 (2001). 10.1103/PhysRevE.63.022501
20. Britton, M. M., and P. T. Callaghan, "Two-phase shear band structures at uniform stress," Phys. Rev. Lett. 78, 4930-4933 (1997). 10.1103/PhysRevLett.78.4930
21. Gilbreth, C., S. Sullivan, and M. Dennin, "Flow transitions in two-dimensional foams," Phys. Rev. E 74, 051406 (2006). 10.1103/PhysRevE.74.051406
22. Ovarlez, G., K. Krishan, and S. Cohen-Addad, "Investigation of shear banding in three-dimensional foams," Europhys. Lett. 91, 68005-68010 (2010). 10.1209/0295-5075/91/68005
23. Rodts, S., J. C. Baudez, and P. Coussot, "From "discrete" to "continuum" flow in foams," Europhys. Lett. 69, 636-642 (2005). 10.1209/epl/i2004-10374-3
24. Ovarlez, G., S. Rodts, A. Ragouilliaux, P. Coussot, J. Goyon, and A. Colin, "Couette flows of dense emulsions: Local concentration measurements, and comparison between macroscopic and local constitutive law measurements through magnetic resonance imaging," Phys. Rev. E 78, 036307 (2008). 10.1103/PhysRevE.78.036307
25. Ovarlez, G., S. Cohen-Addad, K. Krishan, J. Goyon, and P. Coussot, "On the existence of a simple yield stress fluid behavior," J. Non-Newtonian Fluid Mech. 193, 68-79 (2013). 10.1016/j.jnnfm.2012.06.009
26. Divoux, T., D. Tamarii, C. Barentin, and S. Manneville, "Transient shear banding in a simple yield stress fluid," Phys. Rev. Lett. 104, 208301 (2010). 10.1103/PhysRevLett.104.208301
27. Divoux, T., V. Grenard, and S. Manneville, "Rheological hysteresis in soft glassy materials," Phys. Rev. Lett. 110, 018304 (2013). 10.1103/PhysRevLett.110.018304
28. Divoux, T., C. Barentin, and S. Manneville, "From stress-induced fluidization processes to Herschel-Bulkley behaviour in simple yield stress fluids," Soft Matter 7, 8409-8418 (2011). 10.1039/c1sm05607g
29. Divoux, T., D. Tamarii, C. Barentin, S. Teitel, and S. Manneville, "Yielding dynamics of a Herschel-Bulkley fluid: A critical-like fluidization behaviour," Soft Matter 8, 4151-4164 (2012). 10.1039/c2sm06918k
30. Fielding, S. M., M. E. Cates, and P. Sollich, "Shear banding, aging and noise dynamics in soft glassy materials," Soft Matter 5, 2378-2382 (2009). 10.1039/B812394M
31. Moorcroft, R. L., and S. M. Fielding, "Criteria for shear banding in time-dependent flows of complex fluids," Phys. Rev. Lett. 110, 086001 (2013). 10.1103/PhysRevLett.110.086001
32. Illa, X., A. Puisto, A. Lehtinen, M. Mohtaschemi, and M. J. Alava, "Transient shear banding in time-dependent fluids," Phys. Rev. E 87, 022307 (2013). 10.1103/PhysRevE.87.022307
33. Besseling, R., L. Isa, P. Ballesta, G. Petekidis, M. E. Cates, and W. C. K. Poon, "Shear banding and flow-concentration coupling in colloidal glasses," Phys. Rev. Lett. 105, 268301 (2010). 10.1103/PhysRevLett.105.268301
34. Bouchbinder, E., and J. S. Langer, "Nonequilibrium thermodynamics of driven amorphous materials. iii. shear-transformation-zone plasticity," Phys. Rev. E 80, 031133 (2009). 10.1103/PhysRevE.80.031133
35. Falk, M. L., and J. S. Langer, "Dynamics of viscoplastic deformation in amorphous solids," Phys. Rev. E 57, 7192-7205 (1998). 10.1103/PhysRevE.57.7192
36. Pechenik, L., "Dynamics of shear-transformation zones in amorphous plasticity: Nonlinear theory at low temperatures," Phys. Rev. E 72, 021507 (2005). 10.1103/PhysRevE.72.021507
37. Pechenik, L., and J. S. Langer, "Dynamics of shear-transformation zones in amorphous plasticity: Energetic constraints in a minimal theory," Phys. Rev. E 68, 061507 (2003). 10.1103/PhysRevE.68.061507
38. Bouchbinder, E., and J. S. Langer, "Nonequilibrium thermodynamics of driven amorphous materials. i. internal degrees of freedom and volume deformation," Phys. Rev. E 80, 031131 (2009). 10.1103/PhysRevE.80.031131
39. Bouchbinder, E., and J. S. Langer, "Nonequilibrium thermodynamics of driven amorphous materials. ii. effective-temperature theory," Phys. Rev. E 80, 031132 (2009). 10.1103/PhysRevE.80.031132
40. Bouchbinder, E., "Effective temperature dynamics in an athermal amorphous plasticity theory," Phys. Rev. E 77, 051505 (2008). 10.1103/PhysRevE.77.051505
41. Bouchbinder, E., and J. S. Langer, "Shear-transformation-zone theory of linear glassy dynamics," Phys. Rev. E 83, 061503 (2011). 10.1103/PhysRevE.83.061503
42. Langer, J. S., "Dynamics of shear-transformation zones in amorphous plasticity: Formulation in terms of an effective disorder temperature," Phys. Rev. E 70, 041502 (2004). 10.1103/PhysRevE.70.041502
43. Falk, M. L., and J. S. Langer, "Deformation and failure of amorphous, solidlike materials," Annu. Rev. Condens. Matter Phys. 2, 353-373 (2011). 10.1146/annurev-conmatphys-062910-140452
44. Manning, M. L., J. S. Langer, and J. M. Carlson, "Strain localization in a shear transformation zone model for amorphous solids," Phys. Rev. E 76, 056106 (2007). 10.1103/PhysRevE.76.056106
45. Manning, M. L., E. Daub, J. S. Langer, and J. M. Carlson, "Rate-dependent shear bands in a shear-transformation-zone model of amorphous solids," Phys. Rev. E 79, 016110 (2009). 10.1103/PhysRevE.79.016110
46. Langer, J. S., and M. L. Manning, "Steady-state, effective-temperature dynamics in a glassy material," Phys. Rev. E 76, 056107 (2007). 10.1103/PhysRevE.76.056107
47. Lundberg, M., K. Krishna, N. Xu, C. S. O'Hern, and M. Dennin, "Reversible plastic events in amorphous materials," Phys. Rev. E 77, 041505 (2008). 10.1103/PhysRevE.77.041505
48. Daub, E., D. Klaumünzer, and J. Löffler, "Effective temperature dynamics of shear bands in metallic glasses," Phys. Rev. E 90, 062405 (2014). 10.1103/PhysRevE.90.062405
49. Argon, A., and H. Kuo, "Plastic flow in a disordered bubble raft (an analog of a metallic glass)," Mater. Sci. Eng. 39, 101-109 (1979). 10.1016/0025-5416(79)90174-5
50. Argon, A., "Plastic deformation in metallic glasses," Acta Metall. 27, 47-58 (1979). 10.1016/0001-6160(79)90055-5
51. Turnbull, D., and M. H. Cohen, "On the free volume model of the liquid glass transition," J. Chem. Phys. 52, 3038-3041 (1970). 10.1063/1.1673434
52. Spaepen, F., "A microscopic mechanism for steady state inhomogeneous flow in metallic glasses," Acta Metall. 25, 407-415 (1977). 10.1016/0001-6160(77)90232-2
53. Dieterich, E., J. Camunas-Soler, M. Ribezzi-Crivellari, U. Seifert, and F. Ritort, "Single-molecule measurement of the effective temperature in non-equilibrium steady states," Nat. Phys. 11, 971-977 (2015). 10.1038/nphys3435
54. Shi, Y., M. B. Katz, H. Li, and M. L. Falk, "Evaluation of the disorder temperature and free-volume formalisms via simulations of shear banding in amorphous solids," Phys. Rev. Lett. 98, 185505 (2007). 10.1103/PhysRevLett.98.185505
55. Lemaître, A., Jamming, Yielding and Irreversible Deformation in Condensed Matter, edited by M. C. Miguel and J. M. Rubi (Springer, New York, 2004).
56. Edwards, S. F., and D. V. Grinev, "Granular materials: Towards the statistical mechanics of jammed configurations," Adv. Phys. 51, 1669-1684 (2002). 10.1080/0001873021000030780
57. Ono, I., C. O'Hern, D. Durian, S. A. Langer, A. J. Liu, and S. R. Nagel, "Effective temperatures of a driven system near jamming," Phys. Rev. Lett. 89, 095703 (2002). 10.1103/PhysRevLett.89.095703
58. Haxton, T. K., and A. J. Liu, "Activated dynamics and effective temperature in a steady state sheared glass," Phys. Rev. Lett. 99, 195701 (2007). 10.1103/PhysRevLett.99.195701
59. Fisher, R. A., "The wave of advance of advantageous genes," Ann. Eugenics 7, 355-369 (1937). 10.1111/j.1469-1809.1937.tb02153.x
60. Kolmogorov, A., I. Petrovsky, and N. Piskunov, "Study of the diffusion equation with growth of the quantity of matter and its application to a biology problem (translated)," Bull. Univ. Moscow, Ser. Intern., Sec. A 1, 1-25 (1937).
61. van Saarloos, W., "Front propagation into unstable states," Phys. Rep. 386, 29-222 (2003). 10.1016/j.physrep.2003.08.001