Large-amplitude oscillatory shear flow from the corotational Maxwell model

Giacomin, A. Jeffrey; Bird, R. Byron; Johnson, L. M.; Mix, A. W.

doi:10.1016/j.jnnfm.2011.04.002

Cited by 142 publications

(131 citation statements)

References 44 publications

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“…(87) of their paper) to make the equation dimensionally consistent. Much closer agreement with the Cox-Merz rule is recovered, however, when the co-rotational Maxwell model is generalized to include a spectrum of relaxation times (Giacomin et al 2011). This model is arguably the simplest canonical nonlinear viscoelastic equation of state that incorporates linear viscoelasticity, rheological invariance as well as shear-thinning material functions.…”

Section: Discussion and Outlookmentioning

confidence: 66%

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An intriguing empirical rule for computing the first normal stress difference from steady shear viscosity data for concentrated polymer solutions and melts

Sharma

McKinley

2012

Rheol Acta

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The Cox-Merz rule and Laun's rule are two empirical relations that allow the estimation of steady shear viscosity and first normal stress difference respectively using small amplitude oscillatory shear measurements. The validity of the Cox-Merz rule and Laun's rule imply an agreement between the linear viscoelastic response measured in small amplitude oscillatory shear and the nonlinear response measured in steady shear flow measurements. We show that by using a lesser known relationship also proposed by Cox and Merz, in conjunction with Laun's rule, a relationship between the rate-dependent steady shear viscosity and the first normal stress difference can be deduced. The new empirical relation enables a priori estimation of the first normal stress difference using only the steady flow curve (i. e. viscosity vs shear rate data). Comparison of the estimated first normal stress difference with the measured values for six different polymer solutions and melts show that the empirical rule provides values that are in reasonable agreement with measurements over a wide range of shear rates; thus deepening the intriguing connection between linear and nonlinear viscoelastic response of polymeric materials.2

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Section: Discussion and Outlookmentioning

confidence: 66%

“…(12) given above should replace the eq. (87) in the paper by Giacomin and coworkers (Giacomin et al 2011), as η 0 is required in denominator on the both sides (in eq. (87) of their paper) to make the equation dimensionally consistent.…”

Section: Discussion and Outlookmentioning

confidence: 99%

An intriguing empirical rule for computing the first normal stress difference from steady shear viscosity data for concentrated polymer solutions and melts

Sharma

McKinley

2012

Rheol Acta

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“…There have already been several examples in the rheology literature of studies focused on using LAOS to determine model parameters and test the predictive performance of constitutive models (Giacomin et al, 1993;Zhou et al, 2010;Calin et al, 2010;Ng et al, 2011;Giacomin et al, 2011;Gurnon and Wagner, 2012). Similarly, in the solid mechanics and plasticity community, experiments very similar to LAOS are frequently used to probe material behavior.…”

Section: Introductionmentioning

confidence: 99%

Describing and prescribing the constitutive response of yield stress fluids using large amplitude oscillatory shear stress (LAOStress)

Dimitriou

Ewoldt²,

McKinley

2013

Journal of Rheology

242

160

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Large Amplitude Oscillatory Shear (LAOS) is used as a tool to probe the nonlinear rheological response of a model elasto-viscoplastic material (a Carbopol microgel). In contrast to most recent studies, these large amplitude measurements are carried out in a stress-controlled manner. We outline a descriptive framework of characterization measures for nonlinear rheology under stress-controlled LAOS, and this is contrasted experimentally to the strain-controlled framework that is more commonly used. We show that this stress-controlled methodology allows for a physically intuitive interpretation of the yielding behavior of elasto-viscoplastic materials. The insight gained into the material behavior through these nonlinear measures is then used to develop two constitutive models that prescribe the rheological response of the Carbopol microgel. We show that these two successively more sophisticated constitutive models, which are based on the idea of strain decomposition, capture in a compact manner the important features of the nonlinear rheology of the microgel. The second constitutive model, which incorporates the concept of kinematic hardening, embodies all of the the essential behaviors exhibited by Carbopol. These include elasto-viscoplastic creep and time-dependent viscosity plateaus below a critical stress, a viscosity bifurcation at the critical stress, and Herschel-Bulkley flow behavior at large stresses.

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“…Many models have been used to examine the LAOS response, which include upper convected Maxwell, Giesekus [20,31], transient network model (TNM) [32], Leonov [33], molecular stress function (MSF) [34], corotational Maxwell [35] and Doi Edwards model [36]. A single relaxation mode as well as the relaxation spectrum has been used.…”

Section: Materials Models Relevant For Laosmentioning

confidence: 99%