2023 Impact factor 1.8
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


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

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.

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