Complex viscosity vs. frequency

Figure 26. Complex viscosity vs. frequency, if vs. u, for System 1 (top) and 2. Points are experimental, lines computed from the frequency relaxation spectrum.

Figure 8.1(a) Effect of strain on the complex viscosity vs. frequency curves for NA-250 low density polyethylene with 50vol% of spherical stainless steel particles at 160°C. (Reprinted from Ref. 44 with kind permission from Society of Plastics Engineers Inc., Connecticut, USA.)... 

Complex viscosity vs. frequency data would show that viscosity increase would be the highest for fibrous fillers and lowest for spherical fillers whereas particulate and platelet fillers would lie in between. Further rigid fillers would show higher complex viscosity than flexible fillers at the same frequency if their dimensions were similar. 

The smaller the size of the filler, the greater the particle-particle interaction and this reflects greatly on the unsteady shear viscoelastic properties. In the case of complex viscosity vs. frequency curves, it would be natural to expect yield stress with decreasing particle size as... 

The complex viscosity vs. frequency behavior on different t) es of filler is qualitatively the same as fhat of shear viscosity vs. shear rate. Only the extent of the viscosity increases due to ttie filler addition would be different for the unsteady and steady state because the Cox-Mertz rule is known to fail for filled pol5mtier systems. 

Figure 11.13 Double logariflimic plot of storage modulus G loss modulus G", and the magnitude of the complex viscosity > vs. frequency / for a vesicle phase of 90 mM C14DMAO, 10 mM Ci4TMABr, 220 mM QOH, and water at 25 °C.

Figure 7 Apparent viscosity vs. shear rate and the absolute value of the complex viscosity vs. frequency for the 70% neutralized sodium salt of copoly(ethylene/methacrylic acid) (4.1 mol % acid)...

Figure 1. Effect of amount of TGIC on PBT complex viscosity vs. frequency curves (250"C).

Figure 11 The real modulus and complex viscosity vs. the particle volume fraction for oxidi/.ed polyacrylonitrile/silicone oil suspensions. The applied electric field = 1.5 kV/mm. The strain amplitude = 200%, frequency = 2 Hz. Redrawn with permission from T. Hao, Y. Chen, Z. Xu, Y. Xu and Y. Huang, Chin. J. Polym. Sci., 12(1994)97...

Gortemaker (et al.), 1976). In Fig. 15.12, the dynamic moduli are plotted vs. reduced angular frequency. From these results the complex viscosity rf and its components // and rf were calculated. They were plotted vs angular frequency in Fig. 15.13, where also experimental values of the steady shear viscosity are shown. The agreement between rj q) and rf co) is clearly visible. This relationship between steady shear and sinusoidal experiments... 

FIG. 15.13 Non-Newtonian shear viscosity r/(q) at 170 °C vs. shear rate, q, for the polystyrene mentioned in Fig. 15.12, measured in a cone and plate rheometer (O) and in a capillary rheometer ( and ) and the dynamic and complex viscosities, rj (w) (dotted line), rj (w) (dashed line) and i (< ) (full line), respectively, as functions of angular frequency, as calculated from Fig. 15.12. From Gortemaker (1976) and Gortemaker et al. (1976). Courtesy Springer Verlag. 

Figure 8. Complex viscosity, storage modulus (G ) and loss modulus (G") vs. frequency for poly(pheny1-1,4-phenylene terephthalate) (polyester nr. A). G and G" correspond to the 4 days dried sample. Parallel plates. Strain = 3% and Temp. = 355°C.

Figure 11. Complex viscosity, storage modulus and loss modulus vs. frequency at 290°C. Polyester 4,4 -0 = 0.15 (nr. BB1). Strain = 5%.

Figure 9.19. Complex viscosity of talc filled PP vs. frequency. [Data from Chang Ho Suh, White J L, J. Non-Newtonian Fluid Mechanics, 62, Nos.2/3, 1996, 175-206.]...

Figure 9.21. Complex viscosity of calcium carbonate filled PP vs. frequency. [Adapted, by permission, from Johnson K C, Antec 96. Volume III. Conference proceedings, Indianapolis, 5th-10th May 1996, 3545-9.]...

Figure 9.22. Complex viscosity of 31% TiO2 in polybutene vs. frequency. [Data from Carreau P J, Lavoie P A, Bagassi M, Macromol. Symp., 108, 1996, 111-26.]...

Fig. Dsmamic modnh, G and G", and complex viscosity, tj vs angular frequency on (knible logarithmic scales fora9wt% PBLG-BAgelat28 Cand 1% strain. Reproduced from Mym Eng Sci [Ref. 410] by the courteqr of the authors and of The Society of Plastics EngineMS, Brookfield, UK...

Figure 24 The imaginary part of a complex viscosity, normalized by the zero shear viscosity, vs, the mechanical oscillation frequency without an applied electric field (I) and at 2000 V/mm strength (2) for an organogel contains 250 mg/mL lecithin and 0.9 mol of glycerol per mole of lecithin in fl-decane. Reproduced with permission from Yu. A. Shchipunov, T. Durrschmidt, and H. Hoffmann, Langmuir 16(2000)297...

Figure 46 Complex viscosity of oxidized polyacrylonitrile/silicone oil suspension vs. the particle volume fraction at different electric fields. The mechanical strain is 1 and frequency is 5 s. Reproduced with permission from Y. Xu, R. Liang, J. Rheol. 35 (1991) 1355.

Figure 31 The storage modulus G, loss modulus G", and absolute value of the complex viscosity i] vs. strain at the mechanical oscillatory frequency...

Figure 11.4a Double logarithmic plot of storage modulus G, loss modulus G", and complex viscosity n vs. frequency /for a solution with 100 mM CPyCl and 60 mM NaSal at 25 °C. The solution behaves like a Maxwell fluid with a single shear modulus G° and a single structural relaxation time t.

Figure 11.20 Double logarithmic plot of shear viscosity t] vs. shear rate y and of the magnitude of the complex viscosity >j vs. angular frequency to for two different vesicle phases at 25 °C.

Figure 4 Viscosity master curve [absolute value of the complex viscosity ( ri ) vs. frequency x shift factor (oa, rad s" )] for copoly(ethylene/methacrylic acid (3.5 mol % acid, = 86 000, A = 9400) (reproduced by permission of John Wiley Sons, Inc. from T. R. Earnest, Jr., and W. J. MacKnight, J. Polym. ScL, Polym. Phys. Ed., 1978, 16, 143)...

A viscoelastic material also possesses a complex dynamic viscosity, rj = rj - - iv( and it can be shown that r = G jiuj-, rj = G juj and rj = G ju), where CO is the angular frequency. The parameter Tj is useful for many viscoelastic fluids in that a plot of its absolute value Tj vs angular frequency in radians/s is often numerically similar to a plot of shear viscosity Tj vs shear rate. This correspondence is known as the Cox-Merz empirical relationship. The parameter Tj is called the dynamic viscosity and is related to G the loss modulus the parameter Tj does not deal with viscosity, but is a measure of elasticity. 

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