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Effects of nonlocal stress on the determination of shear banding flow

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Lu, C.-Y. David, Olmsted, Peter D. and Ball, R. C.. (2000) Effects of nonlocal stress on the determination of shear banding flow. Physical Review Letters, Vol.84 (No.4). pp. 642-645. ISSN 0031-9007

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Official URL: http://dx.doi.org/10.1103/PhysRevLett.84.642

Abstract

We analyze the steady planar shear Row of the modified Johnson-Segalman model, which has an added nonlocal term. We find that the new term allows for unambiguous selection of the stress at which two "phases" coexist, in contrast to the original model. For general differential constitutive models we show the singular nature of stress selection in terms of a saddle connection between fixed points in the equivalent dynamical system. The result means that stress selection is unique under most conditions for space nonlocal models. Finally, illustrated by simple models, we show that stress selection generally depends on the form of the nonlocal terms (weak universality).

Item Type:	Journal Article
Subjects:	Q Science > QC Physics
Divisions:	Faculty of Science > Physics
Library of Congress Subject Headings (LCSH):	Shear flow, Rheology
Journal or Publication Title:	Physical Review Letters
Publisher:	American Physical Society
ISSN:	0031-9007
Date:	24 January 2000
Volume:	Vol.84
Number:	No.4
Number of Pages:	4
Page Range:	pp. 642-645
Identification Number:	10.1103/PhysRevLett.84.642
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Open Access
References:	[1] J. G. Oldroyd, J. Non-Newt. Fluid Mech. 14, 9 (1984). [2] P.-G. de Gennes, Physica 118A, 44 (1983). G. Ryskin, Phys. Rev. A 32, 1239 (1985). [3] H. Rehage and H. Hoffman, Mol. Phys. 74, 933 (1991). [4] J.-F. Berret, D. C. Roux, and G. Porte, J. Phys. (France) 4, 1261 (1994). [5] V. Schmitt, F. Lequeux, A. Pousse, and D. Roux, Langmuir 10, 955 (1994). [6] C. Grand, J. Arrault, and M. E. Cates, J. Phys. II (France) 7, 1071 (1997). [7] P. T. Callaghan, private communication. [8] M. M. Denn, Ann. Rev. Fluid Mech., 22, 13 (1990). [9] P. T. Callaghan, M. E. Cates, C. J. Rofe, and J. B. A. F. Smeulders, J. Phys. II (France) 6, 375 (1996). [10] M. Doi and S. F. Edwards, The Theory of Polymer Dynamics (Clarendon, Oxford, 1989). [11] M. E. Cates, J. Phys. Chem. 94, 371 (1990). [12] N. A. Spenley and M. E. Cates, Macromolecules 27, 3850 (1994). [13] F. Greco and R. C. Ball, J. Non-Newt. Fluid Mech. 69, 195 (1997). [14] D. S. Malkus, J. S. Nohel, and B. J. Plohr, J. Comp. Phys. 87 (1990) 464; SIAM J. Appl. Math. 51 (1991) 899. [15] Y. Y. Renardy, Th. Comp. Fl. Mech. 7, 463 (1995). [16] From our point of view, 2D flow solver results which show a selected stress for a local model [17] should be examined further to see whether the algorithm implicitly introduced non-locality (numerical diffusion). [17] N. A. Spenley, X. F. Yuan, and M. E. Cates, J. Phys. II (France) 6, 551 (1996). [18] P. D Olmsted, O. Radulescu, and C.-Y. D. Lu, in preparation (1999). [19] G. Porte, J. F. Berret and J. L. Harden, J. Phys. II (France) 7, 459 (1997). [20] M. E. Cates, T. McLeish, G. Marrucci, Europhys. Lett. 21, 451, (1993). [21] V. Schmitt, C. M. Marques, and F. Lequeux, Phys. Rev. E52, 4009 (1995). [22] J. R. A. Pearson, J. Rheol. 38, 309 (1994). [23] P. D. Olmsted and P. M. Goldbart, Phys. Rev. A41, 4578 (1990); ibid, A46, 4966 (1992). [24] P. D. Olmsted and C.-Y. D. Lu, Phys. Rev. E 56, R55 (1997). [25] R. G. Larson, Constitutive Equations for Polymer Melts and Solutions, (Butterworth, Boston,1988). [26] A. W. El-Kareh and L. G. Leal, J. Non-Newt. Fl. Mech. 33, 257 (1989). [27] Note that although the velocity is not a constant, it cannot enter the equation of motion alone, due to Galilean invariance. [28] R. H. Abraham and C. D. Shaw, Dynamics – The Geometry of Behavior, 2nd. ed., (Addison-Wesley, NY, 1992). [29] It is possible to have a functional whose bulk contribution is indifferent to the interface location, in which case the interface contribution plays the decisive role. [30] We assume A and B are the only singular points on the saddle connection, so that s(A,B) does not change along the connection. [31] X.-F. Yuan, Europhys. Lett. 46, 542, (1999).
URI:	http://wrap.warwick.ac.uk/id/eprint/13760