Modeling of nonlinear effects in the theory of the flow of polymer liquids when superposition periodic oscillations on a stationary shear flow

Rudakov, G.O.; Laas, A.A.; Makarova, M.A.; Malygina, A.S.; Pyshnograi, G. V.

doi:10.1063/5.0060935

AIP Conference Proceedings

2021

DOI: 10.1063/5.0060935

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Modeling of nonlinear effects in the theory of the flow of polymer liquids when superposition periodic oscillations on a stationary shear flow

G.O. Rudakov

A.A. Laas

M.A. Makarova

et al.

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2024

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Cited by 2 publications

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Parallel superposition of small-amplitude oscillatory shear flow upon steady shear flow from rotarance theory

Pak,

Giacomin

2024

Physics of Fluids

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The power of a macromolecular theory for the transport properties of a polymeric liquid increases with the number of analytical expressions for its most important material functions. In this work, we add another of these canonical function to our recent series of material function derivations for rotarance theory. By rotarance theory, we mean the explanation of the elasticity of polymeric liquids by use of (i) the diffusion equation to get the orientation distribution in Euler coordinates, and (ii) the integration in phase space using this distribution to get the target material function. In this paper, we target parallel superposition of oscillatory shear flow upon steady shear flow. We arrive at analytical expressions for both parts of the complex viscosity in parallel superposition. We find that these explain the classic experimental observations in parallel superposition: (a) the maximum in the real part of the complex viscosity, and (b) the negative values of minus its imaginary part, and (c) the independence of the steady mean shear stress from the superposed oscillation.

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Parallel superposition of small-amplitude oscillatory shear flow upon steady shear flow from rotarance theory

Pak,

Giacomin

2024

Physics of Fluids

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Superposition of steady shear flow upon orthogonal small-amplitude oscillation from a rotarance theory

Pak,

Kang,

Giacomin

2024

Physics of Fluids

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The novelty of this work is in its prediction of the non-Newtonian behavior of polymeric liquids in the orthogonal superposition of small-amplitude oscillatory shear flow upon steady shear flow. We do so using rotarance theory, namely, by considering only the orientability of the macromolecules in suspension. We arrive at explicit analytical solutions for the complex viscosity as a function of the steady shear rate and of the frequency of the superposed oscillation. Our results explain the canonical laboratory observations of orthogonal superposition: (α) the real part of the complex viscosity as a function of frequency decreases with increasing steady shear rate, (β) the curves of minus the imaginary part as a function of frequency go through a maximum, and (γ) the independence of the steady mean shear stress from the superposed oscillation. We compare our predictions with those of parallel superposition and discover that the further the macromolecular structure from axisymmetric, I3/I1=1, the greater the difference between parallel and superposition. In other words, studying both directions of superposition of either part of the complex viscosity uncovers the most important feature of macromolecular structure, the moment ratio, I3/I1, and thus, the macromolecular orientability.

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Modeling of nonlinear effects in the theory of the flow of polymer liquids when superposition periodic oscillations on a stationary shear flow

Cited by 2 publications

References 9 publications

Parallel superposition of small-amplitude oscillatory shear flow upon steady shear flow from rotarance theory

Parallel superposition of small-amplitude oscillatory shear flow upon steady shear flow from rotarance theory

Superposition of steady shear flow upon orthogonal small-amplitude oscillation from a rotarance theory

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