Non-affine motion and selection of slip coefficient in constitutive modeling of polymeric solutions using a mixed derivative

Abstract

Constitutive models for the dynamics of polymer solutions traditionally rely on closure relations for the extra stress or related microstructural variables (e.g., conformation tensor) linking them to flow history. In this work, we study the eigendynamics of the conformation tensor within the GENERIC framework in mesoscopic computer simulations of polymer solutions to separate the effects of nonaffine motion from other sources of non-Newtonian behavior. We observe that nonaffine motion or slip increases with both the polymer concentration and the polymer chain length. Our analysis allows to uniquely calibrate a mixed derivative of the Gordon–Schowalter type in macroscopic models based on a micro-macromapping of the dynamics of the polymeric system. The presented approach paves the way for better polymer constitutive modeling in multiscale simulations of polymer solutions, where different sources of non-Newtonian behavior are modelled independently.

Molecular Processes Leading to Shear Banding in Entangled Polymeric Solutions

“…In recent experimental and theoretical studies, it has been suggested that shear banding in solutions is induced by fluctuations in polymer concentration [ 35 , 36 , 76 ]. It is therefore critical to investigate the complex interaction between flow-driven entanglement network inhomogeneity and concentration fluctuations in order to understand the dynamic origins of shear-banded structures in greater detail.…”

Generalized Lagrangian heterogeneous multiscale modelling of complex fluids

“…This condition is suitable for dispersed systems in a Newtonian matrix undergoing affine deformations. However, when 0, the ideal contributions are fully accounted for at microscales, making this condition the most general, and thus could be relevant in most complex cases considering non-Newtonian materials (Einarsson et al 2018) or non-affine polymer deformations (Simavilla et al 2023). However, there is a major limitation associated with using only microscopic simulations to determine both ideal and non-ideal contributions ( = 0).…”

“…As a result, our method is theoretically capable of retrieving the ideal solvent stress contribution from microscales as well. Although this would not be needed for dispersed systems in Newtonian media undergoing affine deformations, it could be relevant in most complex cases considering non-Newtonian materials (Einarsson, Yang & Shaqfeh 2018) or non-affine polymer deformations (Simavilla, Espanol & Ellero 2023).…”

“…2018) or non-affine polymer deformations (Simavilla et al. 2023). However, there is a major limitation associated with using only microscopic simulations to determine both ideal and non-ideal contributions ().…”