Single-point parallel disk correction for asymptotically nonlinear oscillatory shear

Bharadwaj, N. Ashwin; Ewoldt, Randy H.

doi:10.1007/s00397-014-0824-9

Title: Single-point parallel disk correction for asymptotically nonlinear oscillatory shear

Journal Article · Thu Jan 15 00:00:00 EST 2015 · Rheologica Acta

DOI:https://doi.org/10.1007/s00397-014-0824-9· OSTI ID:1876189

Bharadwaj, N. Ashwin ^[1]; Ewoldt, Randy H. ^[1]

Univ. of Illinois at Urbana-Champaign, IL (United States)

We derive exact single-point corrections for parallel disk measurements of all four asymptotically nonlinear measures under strain-controlled oscillatory shear. In this regime, sometimes called medium-amplitude oscillatory shear (MAOS), the derivatives appearing in the general stress correction are constant over the range of interest. This enables an exact single-point correction of all four shear stress components and material functions in the asymptotically nonlinear regime. This greatly simplifies the data processing and allows convenient measurements of true nonlinear material functions with parallel disk geometries. We use a strain amplitude expansion for the stress response, introducing a general non-integer strain amplitude scaling for the leading order nonlinearity, σ ~ γ ^α, where typically α = 3 has been assumed in the past. The stress corrections are a multiplicative amplification by a factor f(α) = α+3/4, shown for the first time for all four asymptotically nonlinear coefficients. Experimental measurements are presented for the four asymptotically nonlinear signals on an entangled polymer melt of cis-1,4-polyisoprene, using both parallel disk and cone fixtures. The polymer melt follows a cubic (α = 3) strain amplitude scaling in the MAOS regime. Furthermore, the theoretical corrections indicate a 50 % amplification of the apparent signals measured with the parallel disk fixture. The corrected (amplified) signals match the measurements with the cone.

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Research Organization:: Univ. of Illinois at Urbana-Champaign, IL (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division

Grant/Contract Number:: FG02-07ER46471

OSTI ID:: 1876189

Journal Information:: Rheologica Acta, Vol. 54, Issue 3; ISSN 0035-4511

Publisher:: SpringerCopyright Statement

Country of Publication:: United States

Language:: English

References (43)

The general low-frequency prediction for asymptotically nonlinear material functions in oscillatory shear Bharadwaj, N. Ashwin; Ewoldt, Randy H. Journal of Rheology, Vol. 58, Issue 4 https://doi.org/10.1122/1.4874344	journal	July 2014
Large amplitude oscillatory shear behavior of entangled polymer solutions: Particle tracking velocimetric investigation Ravindranath, Sham; Wang, Shi-Qing Journal of Rheology, Vol. 52, Issue 2 https://doi.org/10.1122/1.2833453	journal	March 2008
Control on the topological structure of polyolefin elastomer by reactive processing Liu, Jianye; Yu, Wei; Zhou, Wei Polymer, Vol. 50, Issue 2 https://doi.org/10.1016/j.polymer.2008.11.030	journal	January 2009
Analysis of medium amplitude oscillatory shear data of entangled linear and model comb polymers Wagner, Manfred H.; Rolón-Garrido, Víctor Hugo; Hyun, Kyu Journal of Rheology, Vol. 55, Issue 3 https://doi.org/10.1122/1.3553031	journal	May 2011
Differences between stress and strain control in the non-linear behavior of complex fluids Läuger, Jörg; Stettin, Heiko Rheologica Acta, Vol. 49, Issue 9 https://doi.org/10.1007/s00397-010-0450-0	journal	April 2010
Defining nonlinear rheological material functions for oscillatory shear Ewoldt, Randy H. Journal of Rheology, Vol. 57, Issue 1 https://doi.org/10.1122/1.4764498	journal	January 2013
Rheological behavior of fiber-filled polymers under large amplitude oscillatory shear flow Férec, J.; Heuzey, M. C.; Ausias, G. Journal of Non-Newtonian Fluid Mechanics, Vol. 151, Issue 1-3 https://doi.org/10.1016/j.jnnfm.2008.01.002	journal	May 2008
Response of an elastic Bingham fluid to oscillatory shear Yoshimura, A. S.; Prud'homme, R. K. Rheologica Acta, Vol. 26, Issue 5 https://doi.org/10.1007/BF01333843	journal	September 1987
Rheology of non-Newtonian fluids: A new flow equation for pseudoplastic systems Cross, Malcolm M. Journal of Colloid Science, Vol. 20, Issue 5 https://doi.org/10.1016/0095-8522(65)90022-X	journal	June 1965
Viscous dissipation with fluid inertia in oscillatory shear flow Ding, Fan; Jeffrey Giacomin, A.; Byron Bird, R. Journal of Non-Newtonian Fluid Mechanics, Vol. 86, Issue 3 https://doi.org/10.1016/S0377-0257(99)00004-X	journal	September 1999
A review of nonlinear oscillatory shear tests: Analysis and application of large amplitude oscillatory shear (LAOS) Hyun, Kyu; Wilhelm, Manfred; Klein, Christopher O. Progress in Polymer Science, Vol. 36, Issue 12 https://doi.org/10.1016/j.progpolymsci.2011.02.002	journal	December 2011
Large Step Shear Strain Experiments with Parallel‐Disk Rotational Rheometers Soskey, Paul R.; Winter, H. Henning Journal of Rheology, Vol. 28, Issue 5 https://doi.org/10.1122/1.549770	journal	October 1984
Low-dimensional intrinsic material functions for nonlinear viscoelasticity Ewoldt, Randy H.; Bharadwaj, N. Ashwin Rheologica Acta, Vol. 52, Issue 3 https://doi.org/10.1007/s00397-013-0686-6	journal	March 2013
Directed self-assembly of suspensions by large amplitude oscillatory shear flow McMullan, Jason M.; Wagner, Norman J. Journal of Rheology, Vol. 53, Issue 3 https://doi.org/10.1122/1.3088848	journal	May 2009
Analysis of the edge fracture process in oscillation for polystyrene melts Mattes, K. M.; Vogt, R.; Friedrich, C. Rheologica Acta, Vol. 47, Issue 8 https://doi.org/10.1007/s00397-008-0286-z	journal	June 2008
Prediction of normal stresses under large amplitude oscillatory shear flow Nam, Jung Gun; Hyun, Kyu; Ahn, Kyung Hyun Journal of Non-Newtonian Fluid Mechanics, Vol. 150, Issue 1 https://doi.org/10.1016/j.jnnfm.2007.10.002	journal	March 2008
Behavior of concentrated polystyrene solutions in large-amplitude oscillating shear fields Pearson, Dale S.; Rochefort, Willie E. Journal of Polymer Science: Polymer Physics Edition, Vol. 20, Issue 1 https://doi.org/10.1002/pol.1982.180200107	journal	January 1982
Describing and prescribing the constitutive response of yield stress fluids using large amplitude oscillatory shear stress (LAOStress) Dimitriou, Christopher J.; Ewoldt, Randy H.; McKinley, Gareth H. Journal of Rheology, Vol. 57, Issue 1 https://doi.org/10.1122/1.4754023	journal	January 2013
A kinetic theory for polymer melts VI. calculation of additional material functions Fan, Xi-Jun; Byron Bird, R. Journal of Non-Newtonian Fluid Mechanics, Vol. 15, Issue 3 https://doi.org/10.1016/0377-0257(84)80018-X	journal	January 1984
Intrinsic nonlinearity from LAOStrain—experiments on various strain- and stress-controlled rheometers: a quantitative comparison Merger, Dimitri; Wilhelm, Manfred Rheologica Acta, Vol. 53, Issue 8 https://doi.org/10.1007/s00397-014-0781-3	journal	July 2014
Constitutive model fingerprints in medium-amplitude oscillatory shear Bharadwaj, N. Ashwin; Ewoldt, Randy H. Journal of Rheology, Vol. 59, Issue 2 https://doi.org/10.1122/1.4903346	journal	March 2015
A simple thixotropic–viscoelastic constitutive model produces unique signatures in large-amplitude oscillatory shear (LAOS) Blackwell, Brendan C.; Ewoldt, Randy H. Journal of Non-Newtonian Fluid Mechanics, Vol. 208-209 https://doi.org/10.1016/j.jnnfm.2014.03.006	journal	June 2014
Large amplitude oscillatory shear (LAOS) measurements to obtain constitutive equation model parameters: Giesekus model of banding and nonbanding wormlike micelles Kate Gurnon, A.; Wagner, Norman J. Journal of Rheology, Vol. 56, Issue 2 https://doi.org/10.1122/1.3684751	journal	March 2012
Response of elastoviscoplastic materials to large amplitude oscillatory shear flow in the parallel-plate and cylindrical-Couette geometries Stickel, Jonathan J.; Knutsen, Jeffrey S.; Liberatore, Matthew W. Journal of Rheology, Vol. 57, Issue 6 https://doi.org/10.1122/1.4820495	journal	November 2013
Large amplitude oscillatory shear of pseudoplastic and elastoviscoplastic materials Ewoldt, Randy H.; Winter, Peter; Maxey, Jason Rheologica Acta, Vol. 49, Issue 2 https://doi.org/10.1007/s00397-009-0403-7	journal	December 2009
How polymeric solvents control shear inhomogeneity in large deformations of entangled polymer mixtures Ravindranath, Sham; Wang, Shi-Qing; Olechnowicz, M. Rheologica Acta, Vol. 50, Issue 2 https://doi.org/10.1007/s00397-010-0507-0	journal	December 2010
A new approach for calculating the true stress response from large amplitude oscillatory shear (LAOS) measurements using parallel plates Fahimi, Zahra; Broedersz, Chase P.; van Kempen, Thomas H. S. Rheologica Acta, Vol. 53, Issue 1 https://doi.org/10.1007/s00397-013-0738-y	journal	November 2013
Non-linear oscillatory flow of a soft solid-like viscoelastic material Phan-Thien, Nhan; Newberry, Marcus; Tanner, Roger I. Journal of Non-Newtonian Fluid Mechanics, Vol. 92, Issue 1 https://doi.org/10.1016/S0377-0257(99)00110-X	journal	August 2000
Analysis of shear rheometry of yield stress materials and apparent yield stress materials Brunn, Peter; Asoud, Hesham Rheologica Acta, Vol. 41, Issue 6 https://doi.org/10.1007/s00397-002-0234-2	journal	January 2002
Single‐point correction for parallel disks rheometry Carvalho, M. S.; Padmanabhan, M.; Macosko, C. W. Journal of Rheology, Vol. 38, Issue 6 https://doi.org/10.1122/1.550532	journal	November 1994
Large amplitude oscillatory shear flow of gluten dough: A model power-law gel Ng, Trevor S. K.; McKinley, Gareth H.; Ewoldt, Randy H. Journal of Rheology, Vol. 55, Issue 3 https://doi.org/10.1122/1.3570340	journal	May 2011
Non‐Linear Behavior of Viscoelastic Materials. I. Disperse Systems of Polystyrene Solution and Carbon Black Onogi, Shigeharu; Masuda, Toshiro; Matsumoto, Takayoshi Transactions of the Society of Rheology, Vol. 14, Issue 2 https://doi.org/10.1122/1.549190	journal	July 1970
A general method for obtaining shear stress and normal stress functions from parallel disk rheometry data Yeow, Y. Leong; Chandra, Dolly; Sardjono, Albert A. Rheologica Acta, Vol. 44, Issue 3 https://doi.org/10.1007/s00397-004-0407-2	journal	August 2004
Large-amplitude oscillatory shear flow from the corotational Maxwell model Giacomin, A. J.; Bird, R. B.; Johnson, L. M. Journal of Non-Newtonian Fluid Mechanics, Vol. 166, Issue 19-20 https://doi.org/10.1016/j.jnnfm.2011.04.002	journal	October 2011
The quasilinear large-amplitude viscoelastic regime and its significance in the rheological characterization of soft matter de Souza Mendes, Paulo R.; Thompson, Roney L.; Alicke, Alexandra A. Journal of Rheology, Vol. 58, Issue 2 https://doi.org/10.1122/1.4865695	journal	March 2014
Calculation of the nonlinear stress of polymers in oscillatory shear fields Helfand, Eugene; Pearson, Dale S. Journal of Polymer Science: Polymer Physics Edition, Vol. 20, Issue 7 https://doi.org/10.1002/pol.1982.180200711	journal	July 1982
Establishing a New Mechanical Nonlinear Coefficient Q from FT-Rheology: First Investigation of Entangled Linear and Comb Polymer Model Systems Hyun, Kyu; Wilhelm, Manfred Macromolecules, Vol. 42, Issue 1 https://doi.org/10.1021/ma8017266	journal	January 2009
Nonlinear Dynamic Mechanical Moduli for Polycarbonate and PMMA Davis, W. M.; Macosko, C. W. Journal of Rheology, Vol. 22, Issue 1 https://doi.org/10.1122/1.549500	journal	February 1978
Vibrational Measurements with Large Amplitudes Philippoff, W. Transactions of the Society of Rheology, Vol. 10, Issue 1 https://doi.org/10.1122/1.549049	journal	March 1966
Deviation of Velocity Gradient Profiles from the “Gap Loading” and “Surface Loading” Limits in Dynamic Simple Shear Experiments Schrag, John L. Transactions of the Society of Rheology, Vol. 21, Issue 3 https://doi.org/10.1122/1.549445	journal	September 1977
Large-amplitude oscillatory shear rheology of dilute active suspensions Bozorgi, Yaser; Underhill, Patrick T. Rheologica Acta, Vol. 53, Issue 12 https://doi.org/10.1007/s00397-014-0806-y	journal	October 2014
Single-point Determination of Nonlinear Rheological Data from Parallel-Plate Torsional Flow Shaw, Montgomery T.; Liu, Zhizhong Z. Applied Rheology, Vol. 16, Issue 2 https://doi.org/10.1515/arh-2006-0004	journal	April 2006
Simple procedures for obtaining viscosity/shear rate data from a parallel disc viscometer Cross, M. M.; Kaye, A. Polymer, Vol. 28, Issue 3 https://doi.org/10.1016/0032-3861(87)90196-0	journal	March 1987

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Parallel disk rheometry
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