Recirculatory\nSolvotaxis of a Nematic Droplet on Water\nSurface Enabling Miniaturization

Self-organized contact line instabilities (CLI) of a\nmacroscopic\nliquid crystal (LC) droplet can be an ingenious pathway to generate\na large collection of miniaturized LC drops. For example, when a larger\ndrop of volatile solvent (e.g., hexane) is dispensed near a smaller\nLC drop resting on a soft and slippery surface of a nonsolvent (e.g.,\nwater), unique self-organized locomotion in the form of a twin vortex\nhas been observed within the droplets. This phenomenon is driven by\nthe rapid counter diffusion of hexane and LC between the two droplets,\nresulting in the formation of a pair of vortices within the droplets\nbefore instigating a CLI at the three-phase contact line (TPCL) of\nthe LC droplet. Initially, the higher Laplace pressure inside the\nLC droplet (<i>P</i><sub>L,5CB</sub>) due to a net pressure\ngradient, <i>P</i><sub>L,5CB</sub> > <i>P</i><sub>L,Hex</sub>, drives the LC toward hexane. However, as the volatile\nsolvent droplet shrinks due to rapid evaporation, a flow reversal\nhappens owing to <i>P</i><sub>L,5CB</sub> < <i>P</i><sub>L,Hex</sub>. Subsequently, the diffusion of hexane into the\nLC droplet and its subsequent evaporation manifest a periodic oscillatory\nCLI expansion and retraction at the TPCL, which in turn form periodic\nfinger-like structures. Following this, the fingers with a higher\naspect ratio break into an array of miniaturized satellite LC droplets\nundergoing Rayleigh–Plateau instability (RPI). The observed\ndeviation in the normalized satellite droplet spacingλ/R5CB∼3.152π compared to theoretical value ∼22π affirm the stabilizing influence of LC\nelasticity in such fingers, where λ and <i>R</i><sub>5CB</sub> are experimentally calculated droplet spacing and 5CB droplet\nradius. Control experiments elucidate the specific contributions of\ncapillary, drag, solutal Marangoni, and osmotic forces to the 5CB\ndroplet locomotion phenomena. The experimentally and analytically\nconsistent demonstration also supports and predicts pressure drop-induced\ndroplet velocities as <i>v</i> ∼ <i>t</i><sup>1.16</sup>.