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 Σ (or strain rate ) and concentration, calculated within the two-fluid, non-local Johnson-Segalman (d-JS-φ) model. We also give results for the macroscopic flow curves Σ(¯,¯φ) for a range of (average) concentrations ¯φ. 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, dΣ/d¯ > 0. As the concentration is reduced, the width of the coexistence regime diminishes and eventually terminates at a non-equilibrium critical point [Σc,¯φc,¯c]. We outline the way in which the flow phase diagram can be reconstructed from a family of such flow curves, Σ(¯,¯φ), measured for several different values of ¯φ. This reconstruction could be used to check new measurements of concentration differences between the coexisting bands. Our d-JS-φ 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 ξ for equilibrium concentration-fluctuations. We show that the phase diagrams (and so also the flow curves) depend on the ratio r ≡ l /ξ, 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 ξ) at the critical point.
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Received: 20 December 2002 / Accepted: 24 April 2003 / Published online: 11 June 2003
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ID="a"e-mail: physf@irc.leeds.ac.uk
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ID="b"e-mail: p.d.olmsted@leeds.ac.uk
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Fielding, S., Olmsted, P. Flow phase diagrams for concentration-coupled shear banding. Eur Phys J E 11, 65–83 (2003). https://doi.org/10.1140/epje/i2002-10128-7
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DOI: https://doi.org/10.1140/epje/i2002-10128-7