Paper Number
SM40 

Session
Polymer Solutions and Melts

Title
The nonlinear rheology of multiscale complex fluids: Deriving empirical rules in rheology from fractional constitutive equations

Presentation Date and Time
October 8, 2014 (Wednesday) 3:10

Track / Room
Track 3 / Commonwealth C

Authors (Click on name to view author profile)

1. Jaishankar, Aditya (Massachusetts Institute of Technology, Department of Mechanical Engineering)
2. McKinley, Gareth H. (Massachusetts Institute of Technology, Department of Mechanical Engineering)

Author and Affiliation Lines (in printed abstract book)
Aditya Jaishankar and Gareth H. McKinley
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139-4307

Speaker / Presenter 
Jaishankar, Aditya

Text of Abstract
The relaxation processes of a wide variety of soft materials frequently contain one or more broad regions of power law-like relaxation in time and frequency. Fractional constitutive equations have been shown to be excellent models for capturing the linear viscoelastic behavior of such materials. However, these fractional constitutive models cannot describe the non-linear behavior of such power-law materials. We show how predictions of non-linear viscometric properties such as shear thinning in the viscosity and in the first normal stress coefficient can be quantitatively described in terms a nonlinear fractional constitutive model. We adopt an integral K-BKZ framework and modify it for power law materials exhibiting Mittag-Leffler type relaxation dynamics at small strains. Only one additional parameter is needed to predict nonlinear rheology, which is introduced through an experimentally measured damping function. Empirical rules such as the Cox-Merz rule are frequently used to estimate the nonlinear response of complex fluids from linear response. We use the fractional model framework to assess the performance of such heuristic rules and quantify the systematic offsets that can be observed between experimental data and the predicted nonlinear response. We also demonstrate how an appropriate choice of fractional constitutive model and damping function results in a nonlinear viscoelastic constitutive model that predicts a flow curve identical to the elastic Herschel-Bulkley model. This new constitutive equation satisfies the Rutgers-Delaware rule that is appropriate for yielding materials. This K-BKZ framework can be used to generate canonical three-element mechanical models that provide nonlinear viscoelastic generalizations of other empirical inelastic models such as the Cross model. In addition to describing nonlinear viscometric responses, we are also able to provide accurate expressions for the linear viscoelastic behavior of materials that exhibit shear-thinning Cross-type or Carreau-type flow curve.