Modeling the Rheology of Polymer Melts and Solutions

Abstract

We review constitutive modeling of solutions and melts of linear polymers, focusing on changes in rheological behavior in shear and extensional flow as the concentration increases from unentangled dilute, to entangled, to dense melt. The rheological changes are captured by constitutive equations, prototypes of which are the FENE-P model for unentangled solutions and the DEMG model for entangled solutions and melts. From these equations, and supporting experimental data, for dilute solutions, the extensional viscosity increases with the strain rate from the low–strain rate to the high–strain rate asymptote, but in the densely entangled state, the high–strain rate viscosity is lower than the low–shear rate value, especially when orientation-dependent friction is accounted for. In shearing flow, shear thinning increases dramatically as the entanglement density increases, which can eventually lead to a shear-banding inhomogeneity. Recent improvements in constitutive modeling are paving the way for robust and accurate numerical simulations of polymer fluid mechanics and industrial processing of polymers.

The Rheology behind Stress-Induced Solidification in Native Silk Feedstocks

“…Although these changes in shear stress were considerably larger and faster than those observed at 1 s −1 , they may have originated from similar effects: stress overshoot and changes in sample distribution in the geometry are often observed to be more pronounced at higher shear-rates [83,84,85,86,87]. On the other hand, errors due to “wall slip” or “edge fracture” [89] could be more significant at the higher shear rate.…”

Analytic solutions of the Rolie Poly model in time-dependent shear

“…Lateral movement is inhibited within the tube but the test chain is free to move diffusively along its contour; chain ends that have escaped the tube are free to explore any configuration. Both the motion of the tube and the chain within it are modelled as a random walk, with Z steps (or segments) at equilibrium [2]. The ensuing incarnations of the Tube Model are complex constitutive equations but are all still built on the simple basic idea of two types of relaxation acting on the chain in the tube: a) relaxation of polymer stretch, occurring along the contour with a timescale of the chain Rouse time τ R and b) relaxation of the polymer orientation, which occurs at a much slower timescale of the reptation time τ d ≈ 3Zτ R [2].…”

“…Both the motion of the tube and the chain within it are modelled as a random walk, with Z steps (or segments) at equilibrium [2]. The ensuing incarnations of the Tube Model are complex constitutive equations but are all still built on the simple basic idea of two types of relaxation acting on the chain in the tube: a) relaxation of polymer stretch, occurring along the contour with a timescale of the chain Rouse time τ R and b) relaxation of the polymer orientation, which occurs at a much slower timescale of the reptation time τ d ≈ 3Zτ R [2]. In recent years a wide range of modelling and simulation techniques, across many length and timescales, have been developed that both implement the tube idea and enable microscopic testing of its founding assumptions.…”

Complex Fluids in Energy Dissipating Systems

“…Typically, polymeric liquids exhibit viscoelasticy. In opposition to STFs, VEFs enjoy reasonably accurate constitutive models that allow for meaningful numerical simulations in complex flow conditions [152][153][154][155]. Traditionally, the viscoelastic behavior has been characterized rheologically in a rotational rheometer by means of the measurement of the viscoelastic moduli (G and G ) within the linear viscoelastic regime (SAOS), based on a solid theoretical background.…”