Dynamics of colloidal particles in electrohydrodynamic convection of nematic liquid crystal

We have studied the dynamics of micrometer-sized colloidal particles in electrohydrodynamic convection of nematic liquid crystal. Above the onset voltage of electroconvection, the parallel array of convection rolls appears to be perpendicular to the nematic field at first. The particles are forced to rotate by convection flow and are trapped within a single roll in this voltage regime. A slow glide motion along the roll axis is also observed. The frequency of rotational motion and the glide velocity increase with the applied voltage. Under a much larger voltage where the roll axis temporally fluctuates, the particles occasionally hop to the neighbor rolls. In this voltage regime, the motion of the particles becomes two-dimensional. The motion perpendicular to the roll axis exhibits diffusion behavior at a long time period. The effective diffusion constant is ${10}^3–{10}^4$ times larger than the molecular one. The observed behavior is compared with the result obtained by a simple stochastic model for the transport of the particles in convection. The enhancement of diffusion can be quantitatively described well by the rotation frequency in a roll, the width of the roll, and the hopping probability to the neighbor rolls.

Figure 1

Shadowgraph image of EHD patterns and silica particles (left) and the trajectories of the dispersed silica particles (right). (a) Williams domain: stationary array of convection rolls. (b) Fluctuating Williams domain: convection rolls fluctuate their roll axis, and the defects of rolls appear.

Figure 2

Dependence of the oscillation frequency $f$ on the control parameter $\varepsilon$. The solid curve is the best fit of ${\varepsilon }^{0.5}$.

Figure 3

Dependence of the glide velocity of the particles along the roll axis $v_g$ on the control parameter $\varepsilon$. The rate of the increase of the velocity changes around $\varepsilon =0.26$.

Figure 4

Dependence of the averaged MSD of a particle vertical to the roll axis on the elapsed time $t$. The different symbols are averaged data of 80 particles obtained for different $\varepsilon$.

Figure 5

Dependence of the effective diffusion constant $D$ on the control parameter $\varepsilon$. The solid curve is the best fit of ${(\varepsilon -0.22)}^{0.75}$ to the data.

Figure 6

Dependence of the simulated MSD on the elapsed time $t$ by varying the transition probability $p$. The respective curves are averaged for 50 samples. The upper schematic explains the situation of our simulation: A particle rotates in a roll with a constant angular velocity $\Omega$. The particle hops to the neighbor roll with the transition probability $p$ and remains with the same roll with probability $1-p$. The time period of the rotation is fixed to $T=2\pi /\Omega =40$, and the radius of a roll $a$ is set to 1. The inset graph shows the dependence of the effective diffusion constant $D$ on $p$. The best-fit curve in the inset is $D=Cp/(1-p)$ ($C$ is constant).

Figure 7

Temporal change of MSD obtained experimentally in the reduced unit for the various control parameters $\varepsilon$. The MSD is plotted in units of $D/f$. The time $t$ is plotted in units of $1/f$. The solid line is simulated for $p=0.3$.

Figure 8

Dependence of the evaluated transition probability $p$ on the control parameter $\varepsilon$. The value of $p$ rapidly increases at the onset $\varepsilon$ from WD to FWD.