A concentric-cylinder rheometer for polymer melts

Dealy, John M.; Petersen, J. F.; Tee, Tiam‐Ting

doi:10.1007/bf01525596

Cited by 30 publications

(8 citation statements)

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“…where m is the power of each term in the series and k m C n and s m S n are given up to Wi 16 in Tables 3 and 4. Equation (31) (with Equations (32) and (33), Tables 3 and 4 (up to Wi 16 )) is the main result of this paper. To our knowledge, Equation (31) is new.…”

Section: Discussionmentioning

confidence: 82%

“…We arrive at an expression for the region of usefulness, so long as Wi=De < 7 2 , for the special cases of the corotational Jeffreys and corotational Maxwell fluids. We also arrive at a power series in the shear rate amplitude for h 0 1 v; _ g 0 À Á and h 00 1 v; _ g 0 À Á , the sweep material functions for the first harmonic, Equations (34) and (35), by extracting the leading terms from our main result, Equation (31). The advantage of using our power series over the exact solution is computational economy.…”

Section: Resultsmentioning

confidence: 99%

“…Figures 5-8 illustrate each of these l 2 =l 1 conditions using an Ewoldt grid of shear stress versus shear rate loop. [31][32][33] Each of the dimensionless loops is constructed for a specific ordered pair of conditions (De, Wi). When miniaturized and mapped into rows and columns onto Pipkin space, that is, onto a map of Wi versus De (see Figure 2 of Saengow et al [11] ), we call the result an Ewoldt grid (see Figures 4 and 8 of Ewoldt et al, [34] Figures 4-4-4-6 in Ewoldt, [35] Figure 1 in Giacomin and Saengow, [36] and Figure 2 of Saengow et al [37] ).…”

Section: Ewoldt Gridsmentioning

confidence: 99%

“…[32,33] Tee and Dealy report one frequency sweep, comprising ten SAOS measurements over the ranges 0:38 < v < 24 rad=s and 0:076 < _ g 0 < 4:8 s À1 , performed using oscillatory cone-plate flow (the Wi De ¼ 0:2 set of points in Figure 12 of Saengow and Giacomin [13] ). [31,32,33] Tee and Dealy also report a set of thirty LAOS measurements, comprising 5 frequency sweeps over the ranges 0:96 < v < 25 rad=s and 2:6 < _ g 0 < 250 s À1 , performed on a concentric cylinder rheometer specially designed for LAOS (the 2:67 Wi De 10 sets of points in Figure 12 of Saengow and Giacomin [13] ). [31,32,33] Specifically, they report frequency sweeps of t 0 v; _ g 0 À Á = _ g 0 , where t 0 is the peak shear stress in LAOS.…”

Section: Applicationmentioning

confidence: 99%

“…[31,32,33] Tee and Dealy also report a set of thirty LAOS measurements, comprising 5 frequency sweeps over the ranges 0:96 < v < 25 rad=s and 2:6 < _ g 0 < 250 s À1 , performed on a concentric cylinder rheometer specially designed for LAOS (the 2:67 Wi De 10 sets of points in Figure 12 of Saengow and Giacomin [13] ). [31,32,33] Specifically, they report frequency sweeps of t 0 v; _ g 0 À Á = _ g 0 , where t 0 is the peak shear stress in LAOS. Since the higher harmonics normally affect loop shapes while hardly affecting t 0 :…”

Section: Applicationmentioning

confidence: 99%

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Series expansion for shear stress in large‐amplitude oscillatory shear flow from oldroyd 8‐constant framework

et al. 2019

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When polymeric liquids undergo large-amplitude oscillatory shear flow, the shear stress responds as a Fourier series, the higher harmonics of which are caused by the fluid nonlinearity, and the first harmonic of which is a nonlinear function of both the frequency and the shear rate amplitude. The Oldroyd 8-constant framework for continuum constitutive theory contains a rich diversity of popular special cases for polymeric liquids. The shear stress response for the Oldroyd 8-constant framework has recently yielded to exact analytical solution. However, in its closed form, Bessel functions appear 24 times, each within infinite summations. In this paper, to simplify the exact solution, we expand it in a Taylor series. We truncate the series after its 16th power of the shear rate amplitude. Our main result reduces to the well known expression for the corotational Jeffreys and corotational Maxwell fluids. Whereas these special cases yielded to the Goddard integral expansion (GIE), the more general Oldroyd 8-constant framework does not. We use Ewoldt grids to show our main result to be highly accurate, for the corotational Jeffreys and corotational Maxwell fluids. For these two special cases, our solutions agree closely with the exact solutions so long as Wi=De < 7 2 . We apply our main result for the special case of the Johnson-Segalman fluid to describe the measured frequency sweep and shear rate amplitude sweep responses of molten atactic polystyrene. For this, we use the Spriggs relations to generalize our main result to multimode, which then agrees closely with the measured responses.

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Section: Discussionmentioning

confidence: 82%

Section: Resultsmentioning

confidence: 99%