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A sequence of physical processes determined and quantified in LAOS: An instantaneous local 2D/3D approach
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10.1122/1.4726083
/content/sor/journal/jor2/56/5/10.1122/1.4726083
http://aip.metastore.ingenta.com/content/sor/journal/jor2/56/5/10.1122/1.4726083
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

A linear viscoelastic response plotted in the 3D space defined by the strain, rate, and stress axes. 2D projections of the periodic orbit are displayed as a plan and elevations on the left, and in perspective 3D on the right. Curved arrows indicate the direction of orbit. The negative binormal vector, −B, and reference vectors s1 and s2 (see text) are indicated.

Image of FIG. 2.
FIG. 2.

A purely elastic response (a) and a purely viscous response (b). In each case, the gradient is equal to the tangent of the angle between the negative binormal vector and the reference vector s2.

Image of FIG. 3.
FIG. 3.

The response of the Bingham model with an elastic modulus , plastic viscosity , and yield strain showing (a) the time trace of the stress for a complete period, (b) the phase angle as a function of time, (c) the magnitude of the complex modulus as a function of time, (d) the elastic Lissajous projection, (e) the viscous Lissajous projection, and (f) the full 3D orbit.

Image of FIG. 4.
FIG. 4.

Full 3D orbits of power-law fluid responses for various values of the power-law index n. The perfect plastic response corresponds to a power-law index of zero, so that the stress is a signum function of the shear rate.

Image of FIG. 5.
FIG. 5.

The response of a power-law fluid of consistency K = 1 and power-law index n = 0.5 showing (a) the time trace of the stress for a complete period, (b) the phase angle as a function of time, (c) the magnitude of the complex modulus as a function of time, (d) the elastic Lissajous projection, (e) the viscous Lissajous projection, and (f) the full 3D orbit.

Image of FIG. 6.
FIG. 6.

The response of the Herschel–Bulkley model with modulus G = 2, consistency K = 0.5, and power-law index n = 0.5 showing (a) the time trace of the stress for a complete period, (b) the phase angle as a function of time, (c) the magnitude of the complex modulus as a function of time, (d) the elastic Lissajous projection, (e)the viscous Lissajous projection, and (f) the full 3D orbit.

Image of FIG. 7.
FIG. 7.

The linear-regime relaxation spectrum of the Giesekus model with parameters as quoted in the text. The angular frequencies are normalized by the relaxation time λ1 = 1 s.

Image of FIG. 8.
FIG. 8.

Results of a strain sweep experiment are normally displayed in terms of G′ and G″. These reduce the information from an entire period to two points. Shown here are the calculated values from the response of the Giesekus model for three representative frequencies.

Image of FIG. 9.
FIG. 9.

The strain dependence [(a) and (b)] and strain-rate dependence [(c) and (d)] on strain amplitude and time throughout an oscillation for an applied angular frequency of 0.1 rad s−1.

Image of FIG. 10.
FIG. 10.

The results of strain sweeps must be shown as surfaces using the new analysis method. Here, the grey/blue surface represents the loss modulus and the white/red surface represents the storage modulus to an input frequency of De = 0.1.

Image of FIG. 11.
FIG. 11.

The storage (white/red) and loss (grey/blue) moduli as functions of strain amplitude and time throughout an oscillation at an input frequency of De = 1 for the Giesekus model. The double peaks in R″ around times t/T ∼ 0.5 and 1 are artifacts of the interpolation scheme of the plotting software.

Image of FIG. 12.
FIG. 12.

The storage (white/red) and loss (grey/blue) moduli as functions of strain amplitude and time throughout an oscillation at an input frequency of De = 10 for the Giesekus model.

Image of FIG. 13.
FIG. 13.

The data of Figs. 10–12 are displayed as viewed from “above looking down.” Yielding can be determined from the points where R′ > R″ changes to R″ > R′. This is equivalent to moving vertically upward along the time axis and going from a light to a dark region. The minimum yielding amplitude is the smallest amplitude that displays this behavior and is marked with vertical dashed lines at each frequency.

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/content/sor/journal/jor2/56/5/10.1122/1.4726083
2012-06-19
2014-04-24
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: A sequence of physical processes determined and quantified in LAOS: An instantaneous local 2D/3D approach
http://aip.metastore.ingenta.com/content/sor/journal/jor2/56/5/10.1122/1.4726083
10.1122/1.4726083
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