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Dynamic defect morphology and hydrodynamics of sheared nematic polymers in two space dimensions
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10.1122/1.3089622
/content/sor/journal/jor2/53/3/10.1122/1.3089622
http://aip.metastore.ingenta.com/content/sor/journal/jor2/53/3/10.1122/1.3089622
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Sketch of the initial condition of ellipsoids and velocity profile (arrows). The right color bar is based on the level set values of the oblate defect metric , which is consistent (~0.8) for the uniform initial conditions on orientation chosen here. The same color scale is applied throughout the paper.

Image of FIG. 2.
FIG. 2.

2D steady roll-cell morphology: secondary flow and orientational correlation. Top: The absolute value of the out-of-plane primary director angle superimposed with the secondary flow . Bottom: The ellipsoids color-coded by level set values of the oblate defect metric of , indicating a negative test for defects.

Image of FIG. 3.
FIG. 3.

2D steady roll-cell morphology: order parameter defect diagnostics. Left: The steady isotropic defect metric . Right: The steady oblate defect metric . Note that each defect metric is color-coded with blue for the minimum value and red for the maximum value. Both metrics are bounded far from the zero value indicative of defects.

Image of FIG. 4.
FIG. 4.

2D steady roll-cell morphology: full 2D velocity and pressure profiles, where , (a) , (b) , (c) , (d) , and (e) . The color code for each quantity is blue for the minimum value and red for the maximum value.

Image of FIG. 5.
FIG. 5.

Unsteady regime of roll-cell breakup: Top row: Snapshots of the absolute value of the out-of-plane angle superimposed on the secondary flow profiles at , 17, and 50. Bottom row: Local blow up of the regions in each snapshot where a strong gradient occurs. In all six figures, the color-coding is based on the values of , where dark red = 90 degrees for vorticity (z-axis) alignment and dark blue = 0 degrees for alignment somewhere in the shear (x,y) plane.

Image of FIG. 6.
FIG. 6.

Unsteady regime of roll-cell breakup: primary and secondary flow and pressure profiles at (top row), (middle row), and (bottom row). The color-coding in each figure interpolates between dark red for the maximum value and dark blue for the minimum of each respective function.

Image of FIG. 7.
FIG. 7.

Unsteady regime of roll-cell breakup. Order parameter diagnostics for isotropic defects (column 1) and oblate defects, (column 2), and tensor ellipsoids color coded by level set values of the oblate defect metric (column 3), at (row 1), (row 2), and (row 3). N.B. Dark blue signals oblate defect domains of the level set , which we conclude from the isotropic defect metric that remains well above zero.

Image of FIG. 8.
FIG. 8.

Unsteady regime of roll-cell breakup: post-diction topological evaluation of defects from the snapshot in Fig. 7. The two distinct defect domain structures near the top plate are amplified: , , in panels (a)–(c) and , in panels (d)–(f). Column 1: fourfold magnification of the ellipsoid texture together with the projection of the major ellipsoid axis onto the texture plane. Column 2: 16-fold magnification of the major director topology, superimposed with color coding by the level sets of the oblate defect metric . Column 3: 16-fold magnification of the secondary flow profile, superimposed with color coding by the level sets of the oblate defect metric . Topological defects are identified and labeled according to degree: (square) and (tripod) defects share one oblate defect core; −1 (cross) and (circle) defects share the other oblate defect core. (a) , , (b) , , (c) , , (d) −1, , (e) −1, , and (f) −1, .

Image of FIG. 9.
FIG. 9.

Diagnostics of defect merger, annihilation of topology, and persistence of oblate domains: Two defects at , their merger ( to 98.25), and topological annihilation , seen through full orientational ellipsoid textures. (a) , (b) , (c) , (d) , (e) , and (f) .

Image of FIG. 10.
FIG. 10.

Diagnostics of defect merger, annihilation of topology, and persistence of oblate domains: seen through projection of the director field superimposed with color-coded level sets of the oblate metric . Topological defects: (square); (tripod); −1 (cross), and (circle). (a) , (b) , (c) , (d) , (e) , and (f) .

Image of FIG. 11.
FIG. 11.

Diagnostics of defect merger, annihilation of topology, and persistence of oblate domains: seen through the secondary flow field superimposed with color-coded level sets of the director angle with respect to the shear plane. (a) , (b) , (c) , (d) , (e) , and (f) .

Image of FIG. 12.
FIG. 12.

Diagnostics of oblate defect splitting and reformation of topological degree: seen through the full orientational ellipsoid textures between and . (a) , (b) , (c) , (d) , (e) , and (f) .

Image of FIG. 13.
FIG. 13.

Diagnostics of oblate defect splitting and reformation of topological degree: seen through the projection of the major director and the color-coded level sets of the oblate defect metric between and . Topological defects: (square); (tripod); −1 (cross), and (circle). (a) , (b) , (c) , (d) , (e) , and (f) .

Image of FIG. 14.
FIG. 14.

Diagnostics of oblate defect splitting and reformation of topological degree: seen through the secondary flow field superimposed with color-coded level set values of the out-of-plane director angle . (a) , (b) , (c) , (d) , (e) , and (f) .

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/content/sor/journal/jor2/53/3/10.1122/1.3089622
2009-05-01
2014-04-24
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Dynamic defect morphology and hydrodynamics of sheared nematic polymers in two space dimensions
http://aip.metastore.ingenta.com/content/sor/journal/jor2/53/3/10.1122/1.3089622
10.1122/1.3089622
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