2013 Impact factor 2.183
EPJ E - Soft Matter and Biological Physics
Soft Matter and Biological Physics
Eur. Phys. J. E 11, 65-83 (2003)
DOI: 10.1140/epje/i2002-10128-7

Flow phase diagrams for concentration-coupled shear banding

S.M. Fielding and P.D. Olmsted

Polymer IRC and Department of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, UK

physf@irc.leeds.ac.uk
p.d.olmsted@leeds.ac.uk

(Received 20 December 2002 and Received in final form 15 April 2003 / Published online: 11 June 2003)

Abstract
After surveying the experimental evidence for concentration coupling in the shear banding of wormlike micellar surfactant systems, we present flow phase diagrams spanned by shear stress $\Sigma$ (or strain rate $\dot{\gamma}$) and concentration, calculated within the two-fluid, non-local Johnson-Segalman (d-JS- $\phi$) model. We also give results for the macroscopic flow curves $\Sigma(\bar{\dot{\gamma}},\bar{\phi})$ for a range of (average) concentrations $\bar{\phi}$. For any concentration that is high enough to give shear banding, the flow curve shows the usual non-analytic kink at the onset of banding, followed by a coexistence "plateau" that slopes upwards, $ \drm \Sigma/ \drm \bar{\dot{\gamma}}>0$. As the concentration is reduced, the width of the coexistence regime diminishes and eventually terminates at a non-equilibrium critical point $[\Sigma_{\rm c},\bar{\phi}_{\rm c},\bar{\dot{\gamma}}_{\rm c}]$. We outline the way in which the flow phase diagram can be reconstructed from a family of such flow curves, $\Sigma(\bar{\dot{\gamma}},\bar{\phi})$, measured for several different values of $\bar{\phi}$. This reconstruction could be used to check new measurements of concentration differences between the coexisting bands. Our d-JS- $\phi$ model contains two different spatial gradient terms that describe the interface between the shear bands. The first is in the viscoelastic constitutive equation, with a characteristic (mesh) length l. The second is in the (generalised) Cahn-Hilliard equation, with the characteristic length $\xi$ for equilibrium concentration-fluctuations. We show that the phase diagrams (and so also the flow curves) depend on the ratio $r\equiv l/\xi$, with loss of unique state selection at r=0. We also give results for the full shear-banded profiles, and study the divergence of the interfacial width (relative to l and $\xi$) at the critical point.

PACS
47.50.+d - Non-Newtonian fluid flows.
47.20.-k - Hydrodynamic stability.
83.10.Gr - Constitutive relations.

© EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2003