A sequence of physical processes determined and quantified in large-amplitude oscillatory shear (LAOS): Application to theoretical nonlinear models

Abstract

The nonlinear yielding responses of three theoretical models, including the Bingham, a modified Bingham, and Giesekus models, to large-amplitude oscillatory shear are investigated under the framework proposed recently by Rogers et al. (2011). Under this framework, basis states are allowed to wax and wane throughout an oscillation, an approach that conflicts directly with the assumptions of all Fourier-like linear algebraic approaches. More physical yielding descriptions of the nonlinear waveforms are attained by viewing the responses as representing purely elastic to purely viscous sequences of physical processes. These interpretations are compared with, and contrasted with, results obtained from linear algebraic analysis methods: Fourier-transform rheology; and the Chebyshev description of the so-called elastic and viscous stress components r 0 and r 00. Further, we show that the discrepancies between the built-in model responses and parameters, and the interpretations of the Chebyshev and Fourier coefficients are directly related to misinterpretations of r 0 and r 00 as being the elastic and viscous stress contributions. We extend these ideas and discuss how every linear algebraic analysis is likely to conflate information from predominantly elastic and viscous processes when a material yields. V

Shear banding in large amplitude oscillatory shear (LAOStrain and LAOStress) of polymers and wormlike micelles

“…In that sense, this work is closest in spirit to the SPP approach of [69,70] (which did not, however, explicitly consider heterogeneous response). In particular, we seek to interpret the emergence of shear banding in LAOS on the basis of the existing criteria for the onset of banding in the simpler timedependent protocols of shear startup and step stress [47].…”

“…These include Fourier transform rheology [63]; measures for quantifying Lissajous-Bowditch curves (defined below) in their elastic representation of stress versus strain, or viscous representation of stress versus strain rate [64]; a decomposition into characteristic sine, square, and triangular wave prototypical response functions [65,66]; decomposition into elastic and viscous stress contributions using symmetry arguments [67]; Chebyshev series expansions of these elastic and viscous contributions [68]; and interpretations of the LAOS cycle in terms of a sequence of physical processes (SPP) [69,70].…”

Rheological characterizations of wormlike micellar solutions containing cationic surfactant and anionic hydrotropic salt

“…Although linear viscoelasticity is useful for understanding the relationship between the microstructure and rheological properties of complex fluids, the linear viscoelastic moduli (G 0 and G 00 ) are limited by the first harmonic Fourier coefficients of G 0 and G 00 , which are insufficient to describe the nonlinear material response with a distorted sinusoidal stress response. The LAOS procedure has been employed to provide more detailed information on the viscoelastic response of materials under nonlinear regimes, by capturing higher harmonic Fourier coefficients or Chebyshev coefficients [Ewoldt (2013); Ewoldt et al (2008)] of stress responses, or fitting experimental data with different viscoelastic models [Blackwell and Ewoldt (2014); Giacomin and Dealy (1998); Gurnon and Wagner (2012); Hyun et al (2002); Rogers and Lettinga (2012)], by applying different flow procedures [Ewoldt (2013); Rogers (2012); Rogers et al (2011)].…”

Reversibility and hysteresis of the sharp yielding transition of a colloidal glass under oscillatory shear

“…By measuring the stress response to sinusoidal strain, one determines the linear elastic and viscous moduli G and G from the harmonic in and out of phase response, respectively, all the way from the linear to the nonlinear response regime [25][26][27][28][29]. These measurements provide insight into the yielding [30][31][32], caging and relaxation processes of glasses [33][34][35] as a function of strain amplitude and frequency. The sinusoidal strain avoids the continuous accumulation of strain and allows frequency-dependent steady states [36] to be probed.…”