Combined simple and sinusoidal shearing in elastic liquids

Tanner, Roger I.; Simmons, J. M.

doi:10.1016/0009-2509(67)80211-2

Cited by 112 publications

(29 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We are now interested in determining the response of such a FKVM constitutive model under a steady shear rateγ. To find the steady state response for the springpot, we use a K-BKZ approach as before, along with a damping function h(γ) given by Tanner and Simmons (1967) …”

Section: The Delaware-rutgers Rule For Power-law Materialsmentioning

confidence: 99%

“…These materials appear gel-like or solid-like at rest and yield or flow at large strains. We use the Fractional Kelvin-Voigt Model (FKVM) that characterize the linear viscoelastic properties of solid-like power-law gels, along with a damping function proposed by Tanner and Simmons (1967) to derive the Herschel-Bulkley equation for flow of a yielding material under steady shear. For this nonlinear fractional…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A fractional K-BKZ constitutive formulation for describing the nonlinear rheology of multiscale complex fluids

Jaishankar

McKinley

2014

Journal of Rheology

103

134

View full text Add to dashboard Cite

The relaxation processes of a wide variety of soft materials frequently contain one or more broad regions of power-law-like or stretched exponential relaxation in time and frequency. Fractional constitutive equations have been shown to be excellent models for capturing the linear viscoelastic behavior of such materials, and their relaxation modulus can be quantitatively described very generally in terms of a Mittag-Leffler function. However, these fractional constitutive models cannot describe the nonlinear behavior of such power-law materials. We use the example of Xanthan gum to 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 suitably modify it for power-law materials exhibiting MittagLeffler 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 and Gleissle mirror relations are frequently used to estimate the nonlinear response of complex fluids from linear rheological data. We use the fractional model framework to assess the performance of such heuristic rules and quantify the systematic offsets, or shift factors, 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 complex materials that exhibit strongly shearthinning Cross-type or Carreau-type flow curve. The findings in this work provide a coherent and quantitative way of translating between the linear and nonlinear rheology of multiscale materials, using a constitutive modeling approach that involves only a few material parameters.

show abstract

Section: The Delaware-rutgers Rule For Power-law Materialsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A fractional K-BKZ constitutive formulation for describing the nonlinear rheology of multiscale complex fluids

Jaishankar

McKinley

2014

Journal of Rheology

103

134

View full text Add to dashboard Cite

show abstract

“…Flow induced anisotropy may make the spectral nature of the response anisotropic, which is not captured by the simple Yamamoto analysis. Superposition moduli can help designing or evaluating constitutive models, by assessing the effects of flow on the spectra in a direct and elegant manner [40,41].…”

Section: Methodsmentioning

confidence: 99%

Superposition rheology and anisotropy in rheological properties of sheared colloidal gels

Colombo

Kim

Schweizer

et al. 2017

Journal of Rheology

View full text Add to dashboard Cite

Gelling colloidal suspensions represent an important class of soft materials. Their mechanical response is characterized by a solid-to-liquid transition at a given shear stress level. Moreover, they often exhibit a complex time-dependent rheological behavior known as thixotropy. The viscosity changes find their origin in the microstructure, which depends on flow history. Yet, the structural response of colloidal gels to flow differs fundamentally from most complex fluids, where flow induces orientation. Upon yielding, low to intermediate volume fraction gels break down in a spatially anisotropic way. Bonds in the velocity-velocity gradient plane are broken, whereas microstructural features in other planes are less affected. The subsequent flow-induced microstructural anisotropy is characterized by typical butterfly scattering patterns. However, as yet there was no evidence for the pertinence of this anisotropy for the rheological properties of these systems. In the present work, orthogonal superposition rheometry was first used to evaluate how the flow-induced microstructure affects the viscoelastic properties. It was shown to retain significant elasticity in the velocity-vorticity plane, even when the structure liquefied. Further, the shearinduced mechanical anisotropy was measured using two-dimensional small amplitude oscillatory shear, exploiting the fact that for suitable thixotropic samples the recovery after arresting the flow is relatively slow. It was hence possible to measure the anisotropy of the moduli upon cessation of flow. The mechanical anisotropy was shown to be spectacular, with the storage moduli in perpendicular directions differing by as much as 2 orders of magnitude. V C 2017 The Society of Rheology. [http://dx

show abstract

“…We call the resulting model a modified Tanner model because if we choose ~1, t -t' < sc, (26) instead of using eq. (20), the original Tanner "rupture" model [4,20] is recovered.…”

Section: Li/~~7--3 T-t'<=sùmentioning

confidence: 99%

“…These last results are a direct consequence of the assumption that the rates of creation and loss of segments are independent of the flow history. The effects of flow history on the rates of creation and loss of segments will surely arise at large enough deformations or stresses, and empirical extensions of Lodge's model to allow for these effects have been made [3][4][5][6][7][8][9], which lead to constitutive *) This paper is dedicated to Alan H. Crossland whose "constrained-chain" theory of rubber elasticity provides the foundation for the work presented here. His untimely death at the age of 38 is a tragic loss for his family, for those of us who knew hirn as a eolleague and for the field of polymer rheology which has lost a gifted researcher.…”

Section: Introductionmentioning

confidence: 99%

A ?constrained-chain? network model for viscoelastic fluids

Chan

Macdonald

1983

Rheol Acta

View full text Add to dashboard Cite

The "constrained-chain" theory of rubber elasticity proposed by Crossland and van der Hoffwas found by them to predict quantitatively many salient features of experimental studies.The present work utilized the "constrained-chain" strain-energy function in a development parallel to that of the "rubberlike liquid" model of Lodge to arrive at a naturally strain-dependent integral constitutive equat_ion for viscoelastic fluids. It can be considered as a particular case of the K-BKZ model with part of the memory function arising from a molecular model. The memory function contains the only nonlinear parameter of the model, the maximum extensibility of a network chain. The model gives a singularity in the stress integral when a network chain is streched to its maximum extensibility. To eliminate this singularity, an assumption has been made which reduces the number of fully extended network chains to zero. Alternative approaches are discussed briefly.

show abstract

Combined simple and sinusoidal shearing in elastic liquids

Cited by 112 publications

References 23 publications

A fractional K-BKZ constitutive formulation for describing the nonlinear rheology of multiscale complex fluids

A fractional K-BKZ constitutive formulation for describing the nonlinear rheology of multiscale complex fluids

Superposition rheology and anisotropy in rheological properties of sheared colloidal gels

A ?constrained-chain? network model for viscoelastic fluids

Contact Info

Product

Resources

About