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A new interpretation for the dynamic behaviour of complex fluids at the sol–gel transition using the fractional calculus

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Abstract

We propose to analyse power law shear stress relaxation modulus observed at the sol–gel transition (SGT) in many gelling systems in terms of fractional calculus. We show that the critical gel (gel at SGT) can be associated to a single fractional element and the gel in the post-SGT state to a fractional Kelvin–Voigt model. In this case, it is possible to give a physical interpretation to the fractional derivative order. It is associated to the power law exponent of the shear modulus related to the fractal dimension of the critical gel. A preliminary experimental application to silica alkoxide-based systems is given.

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Notes

  1. When the lower limit is − ∞ in Eq. 7, the equation is named Weyl integral.

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  1. Laboratoire Matière et Systèmes Complexes UMR 7057, Université Paris Diderot-Paris 7, Bâtiment Condorcet CC 7056 10 rue Alice Domon et Léonie Duquet, Paris Cedex 13, 75205, France

    Stéphane Warlus & Alain Ponton

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  1. Stéphane Warlus
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  2. Alain Ponton
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Correspondence to Alain Ponton.

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Warlus, S., Ponton, A. A new interpretation for the dynamic behaviour of complex fluids at the sol–gel transition using the fractional calculus. Rheol Acta 48, 51–58 (2009). https://doi.org/10.1007/s00397-008-0306-z

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