Levitation, Lift, and Bidirectional Motion of Colloidal Particles in an Electrically Driven Nematic Liquid Crystal

We study electric-field-induced dynamics of colloids in a nematic cell, experimentally and by computer simulations. Solid particles in the nematic bulk create director distortions of dipolar type. Elastic repulsion from the walls keeps the particles in the middle of cell. The ac electric field reorients the dipoles and lifts them to top or bottom, depending on dipole orientation. Once near the walls, the colloids are carried along two antiparallel horizontal directions by nematic backflow. Computer simulations of the backflow agree with the experiment.

Figure 1

Elastic dipoles formed by colloids 1 (a) and 2 (b) in the cell with $h=19\mu \mathrm{m}$, and their FCPM textures (d), (e). Part (c) shows the experimental and theoretical (solid line) shift $\delta$ of the particles from $z=h/2$ as a function of $h$. The ac field reorients $\widehat{\mathbf{n}}$ and pushes particle 1 to the bottom (f) and particle 2 to the top (g). In FCPM textures (d)–(g), light polarization is normal to the plane of figures.

Figure 2

Electric-field-induced bidirectional motion of particles 1 and 2: (a) initial state, $U=0$, particles at $z=h/2$; (b)–(e) bidirectional motion driven by $U=10\mathrm{V}$, $f=10\mathrm{kHz}$, $f_m=10\mathrm{Hz}$. Particle 1, near the bottom wall, migrates to the left ($-x$), while particle 2, near the top, moves to the right ($+x$). The particles of type 1 and 2 are well separated along the $z$ axis and do not trap each other; $t$ is the time since voltage application.

Figure 3

(a) Average particle velocity $⟨v_p⟩$ vs $f_m$ for $f=10\mathrm{kHz}$ (filled symbols) and $f=1\mathrm{kHz}$ (open symbols). The lines show the simulated average backflow velocity $⟨v⟩(f_m)$, at $z=2\mu \mathrm{m}$ and $5\mu \mathrm{m}$. The inset shows the enlarged plot for $0<f_m\le 10\mathrm{Hz}$; (b) simulated displacement following the switch on ($s_{\mathrm{on}}$), switch off ($s_{\mathrm{off}}$), and during an entire cycle, $\mathrm{on}+\mathrm{off}$ ($s_{\mathrm{total}}$), for $z=2\mu \mathrm{m}$.

Figure 4

Computer-simulated dynamics of the director tilt (b) and instantaneous velocity $v$ (c) of backflow caused by a voltage $U=10\mathrm{V}$, $f=10\mathrm{kHz}$, $f_m=10\mathrm{Hz}$ (a).