On the consistent modeling of shear-thickening polymer solutions

Abstract

During the past few decades, the interest in understanding the peculiar rheological behavior of shear-thickening fluids has increased due to their potential use in various commercial applications. In such an endeavor, the optimal design of these fluids is essential, which necessitates our in-depth understanding of their properties from a modeling perspective. We herein introduce a continuum model to predict the rheological behavior of shear-thickening polymer solutions using non-equilibrium thermodynamics that guarantees, by construction, consistency with the laws of thermodynamics as extended to handle non-equilibrium systems. This is made possible by using a scalar structural variable that characterizes the formation of the shear-induced structure at sufficiently high shear rates, and a conformation tensor that characterizes the deformation of the polymer segments. The model predicts the exhibition of a shear-thickening behavior for all steady shear flow material functions (shear viscosity and normal stress coefficients), which is then followed by a shear-thinning behavior if finite extensibility or anisotropic effects are considered. We further document that these model predictions are in line with available shear viscosity rheological data for shear-thickening polymer solutions.

On the Use of a Non-Constant Non-Affine or Slip Parameter in Polymer Rheology Constitutive Modeling

“…We now proceed to modify the Stephanou et al [22] model by considering a variable slip parameter. To this end, we simply propose here an expression for the evolution equation of 𝜉𝜉 bearing in mind our previous work concerning the scalar structural variable 𝜆𝜆 [31][32][33]:…”

“…Although other constitutive models have considered a variety of mechanisms to accommodate the tumbling of polymer chains under shear, such as the use of a "tumbling" function by Costanzo et al [17] or the explicit consideration of rotational diffusion by Stephanou et al [28][29][30], the necessity to have a variable slip parameter remains. In this work, we will generalize the constitutive model for unentangled polymer melts of Stephanou et al [22] to accommodate a variable slip parameter by including an additional evolution equation for 𝜉𝜉, following our recent work on the use of a scalar structural variable [31][32][33].…”

Non-equilibrium thermodynamics modelling of the stress-strain relationship in soft two-phase elastic-viscoelastic materials

“…Motivated by the previous studies, and more specifically by the modelling approach of Deplace et al [6], in the present work we resort to the rigorous formalism of non-equilibrium thermodynamics (NET) to formulate a more general class of constitutive models capable of addressing the rheological behavior and mechanical response of materials that are characterized by the presence of two distinct phases: a viscoelastic and a purely elastic one. In particular, we make use of the Generalized bracket formalism [10] of NET [10][11][12][13][14] by means of which a large variety of microstructured systems have been successfully addressed over the years, including, among others, complex immiscible fluids [15][16][17][18][19], polymer melts and solutions [10][11][12][13][20][21][22], polymer nanocomposites [23][24][25][26], blood [27][28][29][30], and shear-thickening fluids [31]. The formalism guarantees that the developed constitutive model is consistent with the laws of thermodynamics for systems far away from equilibrium and possesses the required mathematical structure.…”