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Author: search.filters.author.Poungthong, PongthepSubject: search.filters.subject.Gleissle mirror relations

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    Viscosity functions of shear flows for fractional maxwell fluids
    (2026-06-01)
    Promjariyakoon, Rattanaporn
    ;
    Poungthong, Pongthep
    ;
    Kolitawong, Chanyut
    ;
    Giacomin, Alan J.
    Fractional calculus is applied increasingly to fluid dynamics. We derive exact analytical solutions for shear stress growth rheological responses of the fractional Maxwell fluid (FMF) in extra-stress tensor form. We do so by using the Laplace transform and its inverse. By shear stress growth, we mean the sudden inception of steady shear flow. We first determine the shear stress growth viscosity, then extend this to the steady shear viscosity using empirical Gleissle mirror relations. We choose to explore the FMF because of its four-parameter versatility and because it describes fluid elasticity measurements accurately. We compare with the ordinary non-fractional Maxwell fluid (OMF) in shear stress growth. Our FMF exact solution agrees well with available measurements on aqueous xanthan gum solutions, so long as the initial residual stresses in the sample are accounted for. We discover that, in practice, positive initial residual shear stress shifts the viscosity in shear stress growth downward. Finally, we construct concentration master curves for our xanthan gum solution shear stress growth rheological functions. We do so to generalize predictions of viscosity under varying conditions. Our worked examples illustrate how to use this dimensionless master curve.
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    Viscosity functions of shear flows for fractional Jeffreys fluids
    (2026-04-01)
    Promjariyakoon, Rattanaporn
    ;
    Poungthong, Pongthep
    ;
    Kolitawong, Chanyut
    ;
    Giacomin, Alan J.
    In our previous work (Promjariyakoon 2025; Promjariyakoon et al. 2026), we derive exact analytical solutions for (1) steady shear viscosity, and (2) shear stress growth rheological responses of the fractional Maxwell fluid (FMF) generalized to tensor form. By shear stress growth, we mean the sudden inception of steady shear flow. We found good agreement with experimental observation, though this left some room for improvement. In this work, following our previous method, we improve upon the FMF by adding one more fractional derivative for retardation to get the fractional Jeffreys model (FJM), a fractional Kelvin-Voigt model arranged in series with a spring-pot. We determine (1) complex viscosity, (2) the shear stress growth viscosity function, (3) then extend these to the steady shear viscosity between the stress and the local properties of theusing Gleissle mirror relations, and (4) shear stress relaxation following cessation of steady shear flow. Our FJM exact solution improves significantly upon the FMF, agreeing well with available measurements on aqueous xanthan gum solutions, so long as the initial residual stresses in the sample are accounted for. We show that its material functions are experimentally measurable and physically interpretable quantities. Finally, we construct temperature master curves for a low-density polyethylene melt. We do so to generalize predictions of viscosity under varying temperatures. Our worked example illustrates how to use our main results.