From a theoretical point of view, the LE model of transient shear rheology predicts
periodic damped stress oscillations for shear start-up and flow reversal that are in
perfect agreement with stress measurements for a low-molar mass non-aligning
thermotropic N C material (Han and Rey 1994a, b). Figure 8 shows a characteristic
flow-reversal stress calculation.
The kinematics in flow reversal involves a reverse motion in the upper plate
instantaneously at t = t v which can be expresses as the apparent shear rate Á:
_
γ ¼ 8 1 À 2Η t À t v
ð
Þ
½
s
À1
À Á
(21)
In Eq. 21, H(t À t v ) denotes the Heaviside unit step function. Figure 8 shows the
shear stress as a function of time(s) during flow reversal, for six increasing reversal
times t v = 4.94 (solid line), 9.63 (dot dash line), 16.35 (long dash line), 20.11 (triple
dot dash line), and 27.79 (s) (dotted line). Figure 8 shows that (i) double peaks
reappear for earlier reversal times, and (ii) when the flow is reversed earlier in time,
larger amplitude oscillatory behaviors are predicted.
Fig. 6 Computed Schlieren textures for different orientations of the cross-polarizers indicated by
the cross. The charge of the wedge disclinations enumerated on the left panel are: (1) À1, (2) +1,
(3) À1/2, (4) À1, (5) +1/2, (6) À1/2
Fig. 7 Computed visualization based on the LdG model of texture generation by the Kibble
mechanism and coarsening through defect annihilation. The top is the polarized light intensity
and the bottom the +1/2 and À1/2 disclinations. (Adapted from Tsuji and Rey 1998)
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A. D. Rey et al.
periodic damped stress oscillations for shear start-up and flow reversal that are in
perfect agreement with stress measurements for a low-molar mass non-aligning
thermotropic N C material (Han and Rey 1994a, b). Figure 8 shows a characteristic
flow-reversal stress calculation.
The kinematics in flow reversal involves a reverse motion in the upper plate
instantaneously at t = t v which can be expresses as the apparent shear rate Á:
_
γ ¼ 8 1 À 2Η t À t v
ð
Þ
½
s
À1
À Á
(21)
In Eq. 21, H(t À t v ) denotes the Heaviside unit step function. Figure 8 shows the
shear stress as a function of time(s) during flow reversal, for six increasing reversal
times t v = 4.94 (solid line), 9.63 (dot dash line), 16.35 (long dash line), 20.11 (triple
dot dash line), and 27.79 (s) (dotted line). Figure 8 shows that (i) double peaks
reappear for earlier reversal times, and (ii) when the flow is reversed earlier in time,
larger amplitude oscillatory behaviors are predicted.
Fig. 6 Computed Schlieren textures for different orientations of the cross-polarizers indicated by
the cross. The charge of the wedge disclinations enumerated on the left panel are: (1) À1, (2) +1,
(3) À1/2, (4) À1, (5) +1/2, (6) À1/2
Fig. 7 Computed visualization based on the LdG model of texture generation by the Kibble
mechanism and coarsening through defect annihilation. The top is the polarized light intensity
and the bottom the +1/2 and À1/2 disclinations. (Adapted from Tsuji and Rey 1998)
292
A. D. Rey et al.