Strain-rate frequency superposition in large-amplitude oscillatory shear

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 81, Issue 3, 2010, Pages

  Kalelkar, Chirag ^a   Lele, Ashish ^a   Kamble, Samruddhi ^a  

^a NATIONAL CHEMICAL LABORATORY   (India)

Author keywords

[No Author keywords available]

Indexed keywords

ENERGY DISSIPATION RATE; FIRST HARMONIC; FREQUENCY SWEEP MEASUREMENT; HIGHER HARMONICS; LARGE STRAINS; LINEAR VISCOELASTIC; LOW FREQUENCY; MASTER CURVE; MONODISPERSE; NONLINEAR VISCO-ELASTIC; OSCILLATORY SHEAR; PER UNIT VOLUME; SHIFT FACTORS; SOFT-SOLID; STRAIN-AMPLITUDE; SURFACE PLOTS; SWEEP TESTS;

ENERGY DISSIPATION; HARMONIC ANALYSIS; HYDROGELS; SHEAR STRESS; SUSPENSIONS (FLUIDS);

STRAIN RATE;

EID: 77749298147     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.81.031401     Document Type: Article

References (37)

1. J. Ferry, Viscoelastic Properties of Polymers (John Wiley, New York, 1980).
2. W. Philippoff, Trans. Soc. Rheol. 10, 317 (1966). 10.1122/1.549049
3. S. Onogi, T. Masuda, and T. Matsumoto, Trans. Soc. Rheol. 14, 275 (1970). 10.1122/1.549190
4. I. Krieger and T. Niu, Rheol. Acta 12, 567 (1973). 10.1007/BF01525599
5. T. Tee and J. Dealy, Trans. Soc. Rheol. 19, 595 (1975). 10.1122/1.549387
6. W. Davis and C. Macosko, J. Rheol. 22, 53 (1978) 10.1122/1.549500
7. D. Pearson and W. Rochefort, J. Polym. Sci., Polym. Phys. Ed. 20, 83 (1982) 10.1002/pol.1982.180200107
8. W. MacSporran and R. Spiers, Rheol. Acta 23, 90 (1984) 10.1007/BF01333880
9. M. Wilhelm, Macromol. Mater. Eng. 287, 83 (2002). 10.1002/1439- 2054(20020201)287:2<83::AID-MAME83>3.0.CO;2-B
10. S. Ganeriwala and C. Rotz, Polym. Eng. Sci. 27, 165 (1987). 10.1002/pen.760270211
11. D. Gamota, A. Wineman, and F. Filisko, J. Rheol. 37, 919 (1993). 10.1122/1.550403
12. M. Reimers and J. Dealy, J. Rheol. 40, 167 (1996). 10.1122/1.550738
13. A. Collyer and D. Clegg, Rheological Measurement (Springer, New York, 1998).
14. R. Ewoldt, A. Hosoi, and G. McKinley, J. Rheol. 52, 1427 (2008). 10.1122/1.2970095
15. J. Meissner, Pure Appl. Chem. 42, 551 (1975). 10.1351/pac197542040551
16. H. M. Wyss, K. Miyazaki, J. Mattsson, Z. Hu, D. R. Reichman, and D. A. Weitz, Phys. Rev. Lett. 98, 238303 (2007). 10.1103/PhysRevLett.98.238303
17. R. Di Leonardo, F. Ianni, and G. Ruocco, Phys. Rev. E 71, 011505 (2005). 10.1103/PhysRevE.71.011505
18. P. Sollich, F. Lequeux, P. Hébraud, and M. E. Cates, Phys. Rev. Lett. 78, 2020 (1997). 10.1103/PhysRevLett.78.2020
19. P. H. Mohan and R. Bandyopadhyay, Phys. Rev. E 77, 041803 (2008). 10.1103/PhysRevE.77.041803
20. S. Marze, R. Guillermic, and A. Saint-Jalmes, Soft Matter 5, 1937 (2009). 10.1039/b817543h
21. K. Desai, S. Lele, and A. Lele, AIP Conf. Proc., 1027, 1226 (2008). 10.1063/1.2964524
22. By design, in a cone-plate measuring system the stresses and strains or strain rates are uniform across the plate gap.
23. The sampling rate is well beyond the Nyquist rate of our experiments, aliasing effects are therefore neglected.
24. W. Press, S. Teukolsky, W. Vetterling, and B. Flannery, Numerical Recipies: The Art of Scientific Computing (Cambridge University Press, Cambridge, 2007).
25. The torque transducer Autoranging feature was disabled to prevent changes in torque scaling during the course of the experiments.
26. H. Senff and W. Richtering, Colloid Polym. Sci. 278, 830 (2000). 10.1007/s003960000329
27. R. Christensen, Theory of Viscoelasticity (Dover, New York, 2003).
28. For the real-valued time series h (t) with Fourier coefficients H (ω), the amplitude spectrum is defined as 2 | H (ω) |. The sign of the moduli G n ′, G n ″ are determined by the phase angles Φ n.
29. The sinc function is defined as sinc (t) = 1 for t = 0, sin (π t) / (π t) for other values of t.
30. J. Kauppinen and J. Partanen, Fourier Transforms in Spectroscopy (Wiley-VCH, Berlin, 2001). 10.1002/3527600299
31. D. van Dusschoten and M. Wilhelm, Rheol. Acta 40, 395 (2001). 10.1007/s003970000158
32. The highest value of the ratio of the third to the first harmonic stress amplitude I (3 ω) / I (ω) ≡ σ 3 / σ 1 in our experiments was found to equal 0.22, consistent with machine limitations.
33. D. Adrian and A. Giacomin, J. Rheol. 36, 1227 (1992). 10.1122/1.550309
34. A. J. Liu, S. Ramaswamy, T. G. Mason, H. Gang, and D. A. Weitz, Phys. Rev. Lett. 76, 3017 (1996). 10.1103/PhysRevLett.76.3017
35. Chirag Kalelkar (private communication).
36. The odd-order Green-Rivlin equation in one dimension is σ (t) = ∫∞t K 1 (t - t 1) γ (t 1) d t 1 + ∫∞t ∫∞t ∫∞t K 3 (t - t 1, t - t 2, t - t 3) γ (t 1) γ (t 2) γ (t 3) d t 1 d t 2 d t 3 +..., where K 1, K 3,... are stress-relaxation moduli (see Ref. for the definition).
37. The area bounded by the stress-strain curve may be found by applying Green's theorem, viz. ∫ C (f d x + g d y) = ∫ ∫ D ( x g - y f) d x d y where the plane region D is bounded by the simple, closed curve C with f (x, y), g (x, y) defined on an open region containing D and having continuous partial derivatives there. For f = 0, g = x, the theorem reduces to ∫ C x d y = ∫ ∫ D d x d y.