Anisotropic viscous effects of local flow by a rotating microparticle in nematic liquid crystal

The presented study opens a perspective to investigate the effects of local flow on nematic liquid crystals. A particle rotated in nematic fluids typically generates a rotationally symmetric local flow, which causes a change in the director orientation. The director above the threshold velocity has a particular angle determined by the ratio of Leslie coefficients, ${\alpha }_2/{\alpha }_3$. In 5CB liquid crystals, this director angle with respect to the flow is approximately ${13}^{\circ }$. The angle is calculated through Ericksen-Leslie theory. The angle is not dependent on rotation frequency or particle size but temperature. The area of the influenced region increases with the rotation frequency and particle size. The changes in radius of the influenced region are calculated theoretically using Ericksen number. Further, an interference pattern appears at the edge of the influenced region by the refractive indexes mismatch between the influenced region and the rest. We experimentally obtain the thickness of the influenced region analyzing intervals of the pattern.

Figure 1

(a) Schematic diagram of the sample structure. (b) Schematic diagram of the stage in which an in-plane rotating magnetic field can be applied to samples. TEC represents a thermoelectric cooler. (c) Plot of the direction of the magnetic field as a function of time.

Figure 2

Images from (a) counterclockwise or (b) clockwise rotating particle under crossed polarizers. An oblique dark cross dependent on the rotation direction appears. (c) Image with a schematic diagram of the director (blue lines) overlaid around the rotating particle. (d) Images from rotating crossed polarizers from 0 to ${90}^{\circ }$. The director is aligned parallel with the polarizer or analyzer in the dark cross in each image. (e) Images obtained by rotating the polarizer with no analyzer from 0 to ${180}^{\circ }$. Because scattering is strong at the position where the orientation of the director coincides with the polarization direction of light, the director is aligned parallel with the polarizer in the dark cross. The particle in (d) and (e) rotates counterclockwise.

Figure 3

(a) Schematic diagram of the velocity distribution around a counterclockwise rotating particle. The red arrows indicate velocity vectors. The flow has a tangential velocity that decreases further from the particle. (b) Schematic diagram of the orientation of the director.

Figure 4

(a) Images with changing rotation frequencies of a particle with a 30-$\mu \mathrm{m}$ diameter. (b) Images from rotating particles with diameters of 10, 20, and $30\mu \mathrm{m}$. The degree of obliqueness of the dark cross is not dependent on the frequency or diameter of the particle.

Figure 5

Images from a counterclockwise rotating particle (a) at room temperature and (b) near the transition temperature. We modified the brightness and contrast to increase clarity.

Figure 6

(a) Textures around a counterclockwise rotating particle with increasing frequency. The region where the alignment changes grows with frequency. (b), (c) Plots of the radius of the region where the alignment changes as a function of frequency and particle radius. We normalized all the length scale with the radius of particle to clarify the characterization of the relative length change. The coat radii in (b) and (c), and particle radius in (c) are normalized by the general particle size we used, $15\mu \mathrm{m}$. The coat radii in (b) and (c) are observed, respectively, with fixed particle size $15\mu \mathrm{m}$ and at fixed frequency 2 Hz. The black squares and red line are the experimental and calculated results, respectively.

Figure 7

(a) Images obtained through horizontally polarized light. An interference pattern is observed around the edge of the region affected by the flow. The particle rotates counterclockwise. In the right enlarged image, the interference pattern in the blue dashed circle is blurred because of a refractive index match. (b) Images obtained under crossed polarizers. The interference pattern in the images is easier to analyze than in (a) due to the clear contrast. (c) Graph of the thickness of the region where the director changes as a function of distance analyzed through the interference pattern.