Self-Propulsion of Nematic Drops: Novel Phase Separation Dynamics in Impurity-Doped Nematogens

We report a novel phase separation dynamics, mediated by self-propelled motion of the nucleated drops, in a mixture of a nematogen and an isotropic dopant. We show that surface flow, induced by the gradient in the concentration of the dopant expelled by the growing drops, provides the driving force for the propulsion of nematic droplets. While the liquid crystal-isotropic transition is used here to demonstrate the phenomenon, self-propulsion should be observable in many other systems in which the dynamics of a conserved order parameter is coupled to a nonconserved order parameter.

Figure 1

(a) Image sequence ($6\mathrm{s}/\mathrm{\text{frame}}$) showing radial drift of small nematic droplets toward a big drop, in a sample with radial concentration gradients, when cooled at $0.2°\mathrm{C}/\min $. The scale bar is $50\mu \mathrm{m}$. (b) The radial drift and growth of droplets is illustrated by stacking the detected boundaries of drops from a sequence of images. (c) A typical plot of the variation of the projected area and velocity of drops for cooling rates of 0.2 and $0.5°\mathrm{C}/\min $.

Figure 2

(a) Fluorescence images (in pseudocolor) showing a nematic domain with surrounding droplets (0 s) and the diffusion of the dopant after the sample was heated to its isotropic state ($t>0\mathrm{s}$). (b) Evolution of the angular-averaged radial intensity distribution after the central domain was melted. An almost linear gradient is set up after a sufficiently long time. The intensity dip for the 0 s curve, just outside the interface, is largely due to the small droplets around it. (c) Stack of detected boundaries of droplets moving in an almost unidirectional gradient obtained using a contact preparation (see text). The droplets move away from the pure dopant side (above) and towards the slowly advancing $I\mathrm{\text{−}}N$ interface.

Figure 3

(a) Pseudocolor fluorescence image obtained using labeled polystyrene oligomer as the dopant. The sample was cooled from a state with arbitrary concentration gradients. The dopant concentration has a local maximum close to the drop interface, which is asymmetric in the case of moving drops. The arrows indicate directions of motion. (b),(c) Gray-scale and pseudocolor images of drops which are about to coalesce. The concentration profiles overlap at short distances even before the interfaces coalesce. (d) Sequence of images ($4\mathrm{s}/\mathrm{\text{frame}}$) showing the motion of a dust particle along the surface of a moving drop. The arrow indicates the direction of motion of the drop. The dust particle flows only when in contact with the interface due to surface flow.

Figure 4

Results from the numerical solution of the equations of motion with ${\sigma }_0=40$, ${\sigma }_1=-20$, ${\varphi }_c=1.0$, $a_0=18$, $a_1=3$, $w=20$, and $u=w-a_0[{\varphi }_c-\tanh (a_1)]$. (a) The variation of the order parameter $S$ and the dopant concentration along a line through the center of the drop in the direction of motion (left to right). (b) The velocity field in and around the moving drop (red circle) for ${\sigma }_1=1$. (c) Drop velocity for two values of the dopant diffusivity: Slower diffusion results in faster motion. (d) The drop size vs time showing growth rate is smaller when the dopant diffusion is small. We also verify that the interfacial tension is larger at the back on the drop than the front (data not shown).