Constitutive equations for extensional flow of wormlike micelles : stability analysis of the Bautista-Manero model

E.S. Boek, J.T. Padding, V.J. Anderson, P.M.J. Tardy, J.P. Crawshaw, J.R.A. Pearson

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    Abstract

    We carry out a stability analysis of the Bautista-Manero (B-M) constitutive equations for extensional flow of wormlike micelles. We show that all solutions for the steady-state extensional viscosity ¿E are unstable when the elongational rates e exceed some critical value. In some cases the only real solution for the extensional viscosity is negative at intermediate values of the elongational rate. This critical elongational rate is not unfeasibly large, e.g., 250 s-1 for a typical EHAC solution. We note that the extension rates at which enhanced pressure drop is observed experimentally in porous media flow is generally well below the onset of the instability in the B-M model. However, the extension rates presented here are only average values for the porous media in question and at the pore scale a wide range of values will be encountered. For this reason, we require an improved rheological equation of state. We first separate the contributions to the viscosity of the solution and the wormlike micelles. Then, we remove the term containing the retardation time ¿J. We now find that the extensional flow behaviour is well defined for both the transient and steady-state cases. © 2005 Elsevier B.V. All rights reserved.
    Original languageEnglish
    Pages (from-to)39-46
    Number of pages8
    JournalJournal of Non-Newtonian Fluid Mechanics
    Volume126
    Issue number1
    DOIs
    Publication statusPublished - 2005

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    Micelles
    constitutive equations
    Constitutive Equation
    Constitutive equations
    Stability Analysis
    micelles
    Viscosity
    Porous materials
    viscosity
    Flow in Porous Media
    Transient State
    Pressure Drop
    Equation of State
    Porous Media
    Critical value
    Well-defined
    Exceed
    Unstable
    Equations of state
    Model

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    Boek, E.S. ; Padding, J.T. ; Anderson, V.J. ; Tardy, P.M.J. ; Crawshaw, J.P. ; Pearson, J.R.A. / Constitutive equations for extensional flow of wormlike micelles : stability analysis of the Bautista-Manero model. In: Journal of Non-Newtonian Fluid Mechanics. 2005 ; Vol. 126, No. 1. pp. 39-46.
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    title = "Constitutive equations for extensional flow of wormlike micelles : stability analysis of the Bautista-Manero model",
    abstract = "We carry out a stability analysis of the Bautista-Manero (B-M) constitutive equations for extensional flow of wormlike micelles. We show that all solutions for the steady-state extensional viscosity ¿E are unstable when the elongational rates e exceed some critical value. In some cases the only real solution for the extensional viscosity is negative at intermediate values of the elongational rate. This critical elongational rate is not unfeasibly large, e.g., 250 s-1 for a typical EHAC solution. We note that the extension rates at which enhanced pressure drop is observed experimentally in porous media flow is generally well below the onset of the instability in the B-M model. However, the extension rates presented here are only average values for the porous media in question and at the pore scale a wide range of values will be encountered. For this reason, we require an improved rheological equation of state. We first separate the contributions to the viscosity of the solution and the wormlike micelles. Then, we remove the term containing the retardation time ¿J. We now find that the extensional flow behaviour is well defined for both the transient and steady-state cases. {\circledC} 2005 Elsevier B.V. All rights reserved.",
    author = "E.S. Boek and J.T. Padding and V.J. Anderson and P.M.J. Tardy and J.P. Crawshaw and J.R.A. Pearson",
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    Constitutive equations for extensional flow of wormlike micelles : stability analysis of the Bautista-Manero model. / Boek, E.S.; Padding, J.T.; Anderson, V.J.; Tardy, P.M.J.; Crawshaw, J.P.; Pearson, J.R.A.

    In: Journal of Non-Newtonian Fluid Mechanics, Vol. 126, No. 1, 2005, p. 39-46.

    Research output: Contribution to journalArticleAcademicpeer-review

    TY - JOUR

    T1 - Constitutive equations for extensional flow of wormlike micelles : stability analysis of the Bautista-Manero model

    AU - Boek, E.S.

    AU - Padding, J.T.

    AU - Anderson, V.J.

    AU - Tardy, P.M.J.

    AU - Crawshaw, J.P.

    AU - Pearson, J.R.A.

    PY - 2005

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    N2 - We carry out a stability analysis of the Bautista-Manero (B-M) constitutive equations for extensional flow of wormlike micelles. We show that all solutions for the steady-state extensional viscosity ¿E are unstable when the elongational rates e exceed some critical value. In some cases the only real solution for the extensional viscosity is negative at intermediate values of the elongational rate. This critical elongational rate is not unfeasibly large, e.g., 250 s-1 for a typical EHAC solution. We note that the extension rates at which enhanced pressure drop is observed experimentally in porous media flow is generally well below the onset of the instability in the B-M model. However, the extension rates presented here are only average values for the porous media in question and at the pore scale a wide range of values will be encountered. For this reason, we require an improved rheological equation of state. We first separate the contributions to the viscosity of the solution and the wormlike micelles. Then, we remove the term containing the retardation time ¿J. We now find that the extensional flow behaviour is well defined for both the transient and steady-state cases. © 2005 Elsevier B.V. All rights reserved.

    AB - We carry out a stability analysis of the Bautista-Manero (B-M) constitutive equations for extensional flow of wormlike micelles. We show that all solutions for the steady-state extensional viscosity ¿E are unstable when the elongational rates e exceed some critical value. In some cases the only real solution for the extensional viscosity is negative at intermediate values of the elongational rate. This critical elongational rate is not unfeasibly large, e.g., 250 s-1 for a typical EHAC solution. We note that the extension rates at which enhanced pressure drop is observed experimentally in porous media flow is generally well below the onset of the instability in the B-M model. However, the extension rates presented here are only average values for the porous media in question and at the pore scale a wide range of values will be encountered. For this reason, we require an improved rheological equation of state. We first separate the contributions to the viscosity of the solution and the wormlike micelles. Then, we remove the term containing the retardation time ¿J. We now find that the extensional flow behaviour is well defined for both the transient and steady-state cases. © 2005 Elsevier B.V. All rights reserved.

    U2 - 10.1016/j.jnnfm.2005.01.001

    DO - 10.1016/j.jnnfm.2005.01.001

    M3 - Article

    VL - 126

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    EP - 46

    JO - Journal of Non-Newtonian Fluid Mechanics

    JF - Journal of Non-Newtonian Fluid Mechanics

    SN - 0377-0257

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    ER -