Recirculatory Solvotaxis of a Nematic Droplet on Water Surface Enabling Miniaturization

Self-organized contact line instabilities (CLI) of a macroscopic liquid crystal (LC) droplet can be an ingenious pathway to generate a large collection of miniaturized LC drops. For example, when a larger drop of volatile solvent (e.g., hexane) is dispensed near a smaller LC drop resting on a soft and slippery surface of a nonsolvent (e.g., water), unique self-organized locomotion in the form of a twin vortex has been observed within the droplets. This phenomenon is driven by the rapid counter diffusion of hexane and LC between the two droplets, resulting in the formation of a pair of vortices within the droplets before instigating a CLI at the three-phase contact line (TPCL) of the LC droplet. Initially, the higher Laplace pressure inside the LC droplet (<i>P</i>_L,5CB) due to a net pressure gradient, <i>P</i>_L,5CB > <i>P</i>_L,Hex, drives the LC toward hexane. However, as the volatile solvent droplet shrinks due to rapid evaporation, a flow reversal happens owing to <i>P</i>_L,5CB < <i>P</i>_L,Hex. Subsequently, the diffusion of hexane into the LC droplet and its subsequent evaporation manifest a periodic oscillatory CLI expansion and retraction at the TPCL, which in turn form periodic finger-like structures. Following this, the fingers with a higher aspect ratio break into an array of miniaturized satellite LC droplets undergoing Rayleigh-Plateau instability (RPI). The observed deviation in the normalized satellite droplet spacing<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>λ</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mn>5</mml:mn><mml:mi>CB</mml:mi></mml:mrow></mml:msub><mml:mo>∼</mml:mo><mml:mn>3.15</mml:mn><mml:msqrt><mml:mn>2</mml:mn></mml:msqrt><mml:mi>π</mml:mi></mml:math> compared to theoretical value <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mo>∼</mml:mo><mml:mn>2</mml:mn><mml:msqrt><mml:mn>2</mml:mn></mml:msqrt><mml:mi>π</mml:mi></mml:math> affirm the stabilizing influence of LC elasticity in such fingers, where λ and <i>R</i>_5CB are experimentally calculated droplet spacing and 5CB droplet radius. Control experiments elucidate the specific contributions of capillary, drag, solutal Marangoni, and osmotic forces to the 5CB droplet locomotion phenomena. The experimentally and analytically consistent demonstration also supports and predicts pressure drop-induced droplet velocities as <i>v</i> ∼ <i>t</i>^1.16.