Medium amplitude parallel superposition (MAPS) rheology. Part 2: Experimental protocols and data analysis

Lennon, Kyle R.; Geri, Michela; McKinley, Gareth H.; Swan, James W.

doi:10.1122/8.0000104

Title: Medium amplitude parallel superposition (MAPS) rheology. Part 2: Experimental protocols and data analysis

Abstract

An experimental protocol is developed to directly measure the new material functions revealed by medium amplitude parallel superposition (MAPS) rheology. This protocol measures the medium amplitude response of a material to a simple shear deformation composed of three sine waves at different frequencies, revealing a rich dataset consisting of up to 19 measurements of the third-order complex modulus at distinct three-frequency coordinates. We discuss how the choice of input frequencies influences the features of the MAPS domain studied by the experiment. A polynomial interpolation method for reducing the bias of measured values from spectral leakage and reducing variance due to noise is discussed, including a derivation of the optimal range of amplitudes for the input signal. This leads to the conclusion that conducting the experiment in a stress-controlled fashion possesses a distinct advantage to the strain-controlled mode. The experimental protocol is demonstrated through measurements of the MAPS response of a model complex fluid: a surfactant solution of wormlike micelles. The resulting dataset is indeed large and feature-rich, while still acquired in a time comparable to similar medium amplitude oscillatory shear (MAOS) experiments. We demonstrate that the data represent measurements of an intrinsic material function by studying its internal consistency, compatibilitymore »« less

Authors:

^[1];

^[2];

^[2]; Swan, James W. ^[1]

Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02142
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139

Publication Date:: 2020-09-01

Sponsoring Org.:: USDOE

OSTI Identifier:: 1659531

Grant/Contract Number:: SC0020347

Resource Type:: Publisher's Accepted Manuscript

Journal Name:: Journal of Rheology

Additional Journal Information:: Journal Name: Journal of Rheology Journal Volume: 64 Journal Issue: 5; Journal ID: ISSN 0148-6055

Publisher:: Society of Rheology

Country of Publication:: United States

Language:: English

Citation Formats


                    Lennon, Kyle R., Geri, Michela, McKinley, Gareth H., and Swan, James W. Medium amplitude parallel superposition (MAPS) rheology. Part 2: Experimental protocols and data analysis.  United States: N. p., 2020. 
Web.  doi:10.1122/8.0000104.

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                    Lennon, Kyle R., Geri, Michela, McKinley, Gareth H., & Swan, James W. Medium amplitude parallel superposition (MAPS) rheology. Part 2: Experimental protocols and data analysis.  United States.  https://doi.org/10.1122/8.0000104

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                    Lennon, Kyle R., Geri, Michela, McKinley, Gareth H., and Swan, James W. Tue .  
"Medium amplitude parallel superposition (MAPS) rheology. Part 2: Experimental protocols and data analysis".  United States.  https://doi.org/10.1122/8.0000104.

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@article{osti_1659531,

  title        = {Medium amplitude parallel superposition (MAPS) rheology. Part 2: Experimental protocols and data analysis},

  author       = {Lennon, Kyle R. and Geri, Michela and McKinley, Gareth H. and Swan, James W.},

  abstractNote = {An experimental protocol is developed to directly measure the new material functions revealed by medium amplitude parallel superposition (MAPS) rheology. This protocol measures the medium amplitude response of a material to a simple shear deformation composed of three sine waves at different frequencies, revealing a rich dataset consisting of up to 19 measurements of the third-order complex modulus at distinct three-frequency coordinates. We discuss how the choice of input frequencies influences the features of the MAPS domain studied by the experiment. A polynomial interpolation method for reducing the bias of measured values from spectral leakage and reducing variance due to noise is discussed, including a derivation of the optimal range of amplitudes for the input signal. This leads to the conclusion that conducting the experiment in a stress-controlled fashion possesses a distinct advantage to the strain-controlled mode. The experimental protocol is demonstrated through measurements of the MAPS response of a model complex fluid: a surfactant solution of wormlike micelles. The resulting dataset is indeed large and feature-rich, while still acquired in a time comparable to similar medium amplitude oscillatory shear (MAOS) experiments. We demonstrate that the data represent measurements of an intrinsic material function by studying its internal consistency, compatibility with low-frequency predictions for Coleman–Noll simple fluids, and agreement with data obtained via MAOS amplitude sweeps. Finally, the data are compared to predictions from the corotational Maxwell model to demonstrate the power of MAPS rheology in determining whether a constitutive model is consistent with a material’s time-dependent response.},

  doi          = {10.1122/8.0000104},

  journal      = {Journal of Rheology},

  number       = 5,

  volume       = 64,

  place        = {United States},

  year         = {2020},

  month        = {9}

}

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Title: Medium amplitude parallel superposition (MAPS) rheology. Part 2: Experimental protocols and data analysis

Abstract

Citation Formats

Intermodulation atomic force microscopy journal, April 2008

A Rheological Equation of State which Predicts Non‐Newtonian Viscosity, Normal Stresses, and Dynamic Moduli journal, July 1955

Medium amplitude parallel superposition (MAPS) rheology. Part 1: Mathematical framework and theoretical examples journal, May 2020

Evaluating predictability of various constitutive equations for MAOS behavior of entangled polymer solutions journal, May 2020

Nonlinear viscoelasticity of wormlike micelles (and other reversibly breakable polymers) journal, January 1990

Global crack detection using bispectral analysis journal, February 2006

A review of nonlinear oscillatory shear tests: Analysis and application of large amplitude oscillatory shear (LAOS) journal, December 2011

On the steady simple shear flows of the one-mode Giesekus fluid journal, January 1989

Nonlinear shear and extensional flow dynamics of wormlike surfactant solutions journal, February 2006

Nonlinear Continuum Mechanics of Viscoelastic Fluids journal, January 1971

Foundations of Linear Viscoelasticity journal, April 1961

Large amplitude oscillatory shear (LAOS) measurements to obtain constitutive equation model parameters: Giesekus model of banding and nonbanding wormlike micelles journal, March 2012

Superposition rheometry of a wormlike micellar fluid journal, June 2013

Measuring volterra kernels (II) journal, April 1989

Fourier transform mechanical spectroscopy of viscoelastic materials with transient structure journal, January 1988

Orthogonal versus parallel superposition measurements journal, November 1998

Time-strain separability in medium-amplitude oscillatory shear journal, February 2019

Detection and classification of flaws in concrete structure using bispectra and neural networks journal, January 2002

New measures for characterizing nonlinear viscoelasticity in large amplitude oscillatory shear journal, November 2008

The mechanics of non-linear materials with memory journal, January 1959

The Vandermonde Matrix journal, May 1967

Shear-banding in surfactant wormlike micelles: elastic instabilities and wall slip journal, January 2012

Frequency-sweep medium-amplitude oscillatory shear (MAOS) journal, January 2018

Deviation of Velocity Gradient Profiles from the “Gap Loading” and “Surface Loading” Limits in Dynamic Simple Shear Experiments journal, September 1977

On the generation of nonlinear damage resonance intermodulation for elastic wave spectroscopy journal, April 2017

The general low-frequency prediction for asymptotically nonlinear material functions in oscillatory shear journal, July 2014

Detection of structural damage of aluminum alloy 6082 using elastic wave modulation spectroscopy journal, October 2008

Velocity Profiles in Shear-Banding Wormlike Micelles journal, June 2003

Multitone signals with low crest factor journal, January 1997

Viscoelastic surfactant solutions: model systems for rheological research journal, December 1991

Phase imaging with intermodulation atomic force microscopy journal, May 2010

Polynomial operators in non-linear systems theory journal, July 1971

Low-dimensional intrinsic material functions for nonlinear viscoelasticity journal, March 2013

Rate‐Dependent Relaxation Spectra and Their Determination journal, July 1971

A mathematical theory of the mechanical behavior of continuous media journal, January 1958

First-Order and Third-Order Nonlinearities from Medium-Amplitude Oscillatory Shearing of Hydrogen-Bonded Polymers and Other Viscoelastic Materials journal, November 2019

Time-Resolved Mechanical Spectroscopy of Soft Materials via Optimally Windowed Chirps journal, December 2018

A simple constitutive equation for polymer fluids based on the concept of deformation-dependent tensorial mobility journal, January 1982

Multitone signals with low crest factor journal, October 1986

The mechanics of non-linear materials with memory: Part I journal, January 1957

Measuring Volterra kernels journal, August 1983

Large-amplitude oscillatory shear flow from the corotational Maxwell model journal, October 2011

Small Finite Deformations of Viscoelastic Solids journal, October 1964

Shear banding in time-dependent flows of polymers and wormlike micelles journal, January 2014

Factors affecting the ultrasonic intermodulation crack detection technique using bispectral analysis journal, April 2008

Bulk rheometry at high frequencies: a review of experimental approaches journal, November 2019

Comparative Studies of Some Simple Viscoelastic Theories journal, March 1968

Nonlinear Dynamic Mechanical Moduli for Polycarbonate and PMMA journal, February 1978

Intermodulation atomic force microscopy
journal, April 2008

A Rheological Equation of State which Predicts Non‐Newtonian Viscosity, Normal Stresses, and Dynamic Moduli
journal, July 1955

Medium amplitude parallel superposition (MAPS) rheology. Part 1: Mathematical framework and theoretical examples
journal, May 2020

Evaluating predictability of various constitutive equations for MAOS behavior of entangled polymer solutions
journal, May 2020

Nonlinear viscoelasticity of wormlike micelles (and other reversibly breakable polymers)
journal, January 1990

Global crack detection using bispectral analysis
journal, February 2006

A review of nonlinear oscillatory shear tests: Analysis and application of large amplitude oscillatory shear (LAOS)
journal, December 2011

On the steady simple shear flows of the one-mode Giesekus fluid
journal, January 1989

Nonlinear shear and extensional flow dynamics of wormlike surfactant solutions
journal, February 2006

Nonlinear Continuum Mechanics of Viscoelastic Fluids
journal, January 1971

Foundations of Linear Viscoelasticity
journal, April 1961

Large amplitude oscillatory shear (LAOS) measurements to obtain constitutive equation model parameters: Giesekus model of banding and nonbanding wormlike micelles
journal, March 2012

Superposition rheometry of a wormlike micellar fluid
journal, June 2013

Measuring volterra kernels (II)
journal, April 1989

Fourier transform mechanical spectroscopy of viscoelastic materials with transient structure
journal, January 1988

Orthogonal versus parallel superposition measurements
journal, November 1998

Time-strain separability in medium-amplitude oscillatory shear
journal, February 2019

Detection and classification of flaws in concrete structure using bispectra and neural networks
journal, January 2002

New measures for characterizing nonlinear viscoelasticity in large amplitude oscillatory shear
journal, November 2008

The mechanics of non-linear materials with memory
journal, January 1959

The Vandermonde Matrix
journal, May 1967

Shear-banding in surfactant wormlike micelles: elastic instabilities and wall slip
journal, January 2012

Frequency-sweep medium-amplitude oscillatory shear (MAOS)
journal, January 2018

Deviation of Velocity Gradient Profiles from the “Gap Loading” and “Surface Loading” Limits in Dynamic Simple Shear Experiments
journal, September 1977

On the generation of nonlinear damage resonance intermodulation for elastic wave spectroscopy
journal, April 2017

The general low-frequency prediction for asymptotically nonlinear material functions in oscillatory shear
journal, July 2014

Detection of structural damage of aluminum alloy 6082 using elastic wave modulation spectroscopy
journal, October 2008

Velocity Profiles in Shear-Banding Wormlike Micelles
journal, June 2003

Multitone signals with low crest factor
journal, January 1997

Viscoelastic surfactant solutions: model systems for rheological research
journal, December 1991

Phase imaging with intermodulation atomic force microscopy
journal, May 2010

Polynomial operators in non-linear systems theory
journal, July 1971

Low-dimensional intrinsic material functions for nonlinear viscoelasticity
journal, March 2013

Rate‐Dependent Relaxation Spectra and Their Determination
journal, July 1971

A mathematical theory of the mechanical behavior of continuous media
journal, January 1958

First-Order and Third-Order Nonlinearities from Medium-Amplitude Oscillatory Shearing of Hydrogen-Bonded Polymers and Other Viscoelastic Materials
journal, November 2019

Time-Resolved Mechanical Spectroscopy of Soft Materials via Optimally Windowed Chirps
journal, December 2018

A simple constitutive equation for polymer fluids based on the concept of deformation-dependent tensorial mobility
journal, January 1982

Multitone signals with low crest factor
journal, October 1986

The mechanics of non-linear materials with memory: Part I
journal, January 1957

Measuring Volterra kernels
journal, August 1983

Large-amplitude oscillatory shear flow from the corotational Maxwell model
journal, October 2011

Small Finite Deformations of Viscoelastic Solids
journal, October 1964

Shear banding in time-dependent flows of polymers and wormlike micelles
journal, January 2014

Factors affecting the ultrasonic intermodulation crack detection technique using bispectral analysis
journal, April 2008

Bulk rheometry at high frequencies: a review of experimental approaches
journal, November 2019

Comparative Studies of Some Simple Viscoelastic Theories
journal, March 1968

Nonlinear Dynamic Mechanical Moduli for Polycarbonate and PMMA
journal, February 1978