Topological Stabilization and Dynamics of Self-Propelling Nematic Shells

Liquid shells (e.g., double emulsions, vesicles, etc.) are susceptible to interfacial instability and rupturing when driven out of mechanical equilibrium. This poses a significant challenge for the design of liquid-shell-based micromachines, where the goal is to maintain stability and dynamical control in combination with motility. Here, we present our solution to this problem with controllable self-propelling liquid shells, which we have stabilized using the soft topological constraints imposed by a nematogen oil. We demonstrate, through experiments and simulations, that anisotropic elasticity can counterbalance the destabilizing effect of viscous drag induced by shell motility and inhibit rupturing. We analyze their propulsion dynamics and identify a peculiar meandering behavior driven by a combination of topological and chemical spontaneously broken symmetries. Based on our understanding of these symmetry breaking mechanisms, we provide routes to control shell motion via topology, chemical signaling, and hydrodynamic interactions.

Figure 1

Droplet production and setup schematics. (a) Double emulsion production via microfluidic flow junctions. (b) Droplet propulsion via a self-sustaining Marangoni gradient in the interface. (c) Microfluidic cell and inverted microscope setup for quasi-2D observation. All schematics are not to scale; spherical shells and micelles are represented by their 2D cross section.

Figure 2

Life stages of active shells. (a) Polarized images of resting and swimming shells. (b) Video stills of droplet life stages. (c) Example trajectory colored by shell radius $R_s$, recorded over 40 min. The sudden change of color from blue to red corresponds to the burst moment. (d) Average speed $V$ (dotted, red) and radius $R_s$ (solid, blue) for 13 shells, with time $t$ relative to bursting time $t_b$ (scatter plots: values for all experiments).

Figure 3

Stabilization of the active shells. (a) Burst statistics (number of bursts $N_B$ normalized to initial number of shells $N_0$) for shells below and above the clearing point, plotted against time $t$ normalized to final time $t_f$ with no remaining shells [$t_f(24°\mathrm{C})\approx 45\min$, $t_f(39°\mathrm{C})\approx 10\min$, initial $R_s=30\mu \mathrm{m}$, $R_c=18\mu \mathrm{m}$]. (b) Elastic energy $E/E_c$ ($E_c$: core at center of droplet) as a function of core displacement $d/d_{\max }$, with $d_{\max }=R_s-R_c-100\mathrm{nm}$, for two different ratios $R_s/R_c$. (c) Ratio of elastic energies $E_i/E_c$ ($E_i$: core droplet close to outer shell interface) against ratio of radii $R_s/R_c$, using $R_c=25\mu \mathrm{m}$ and $R_s$ shrinking from $125\mu \mathrm{m}$ to $25.6\mu \mathrm{m}$. Schematics are illustrative, and illustrated radius values do not directly correspond to the simulation parameters.

Figure 4

Swimming behavior. (a) Top: PIV data for flow at the outer interface and in the core. Bottom: Schematic of core and flow arrangement. (b) Top: Shark-fin meandering of swimming trajectory over 2 minutes ($R_s=36\mu \mathrm{m}$); the shell switches periodically between clockwise and anticlockwise turns. Bottom: Zoomed-in view of the shell-core alignment with the swimming trajectory, with superimposed core flow fields and color-coded circulation. (c) Core circulation $\mathrm{\Gamma }/{\mathrm{\Gamma }}_{\max }$, local curvature $\kappa$, and shell speed $V$ vs time over four meandering periods. (d)–(f) Nematic structure (top, polarized images of the droplets at rest with overlaid director field schematic) and 3D swimming trajectories (bottom, multiple exposure micrograph captured over 60 s) for a no-core droplet (d), a single-core droplet (e), and a two-core droplet (f). See Movie S8 in Ref. [16].

Figure 5

Control of shell dynamics. Micrographs of shells with two cores, showing (a) long-time stability and (b) no meandering in 2D confinement (multiple exposure micrographs at two shell thicknesses). Because of the larger initial volume of the oil phase, survival times are increased compared to Fig. 2. (c) Topographical guidance by walls. Multiple exposure micrograph taken over 65 seconds at 3 second intervals. (d) Chemotaxis: Diffusing surfactant guides shells to the left (trajectories colored by shell speed $V$).