Crowding and confinement of mesoscale swimmers in living droplets

Abstract

Droplets encapsulating active or living matter provide controllable platforms for studying collective dynamics and active interfacial actuation. However, prior work has largely focused on quasi-2D confinement, microscopic swimmers, or externally driven, non-living droplets. Here, we introduce living droplets internally activated by tens of enclosed mesoscale swimmers to study crowding and confinement in 3D with swimmer sizes comparable to the droplet radius. In large droplets with few swimmers, the droplet oscillation frequencies collapse onto the classical sessile-drop frequency-volume scaling. By increasing the number of swimmers or decreasing the droplet size, crowding and confinement alter the droplet oscillation frequencies and amplitudes as many-body or swimmer-droplet interactions start dominating. We develop a scaling-law framework linking the oscillation amplitude to swimmer speed through collision probability and momentum transfer, enabling indirect 3D velocimetry in the opaque, crowded droplets. Complementary quasi-2D experiments with direct tracking reveal dimensionality-dependent crowding effects, which we successfully describe with a kinetic theory-based model. We show distinct crossovers and strong-crowding asymptotic scalings of the swimmer speed with the dimensionless swimmer density, $U_{\mathrm{crowd}}\sim (N^{\ast }{)}^{-1}$ in 3D and $U_{\mathrm{crowd}}\sim (N^{\ast }{)}^{-1/2}$ in quasi-2D. Our results connect mesoswimmer encounter dynamics to macroscopic droplet mechanics and inform the design of bio-inspired micromachines, fluidic control, and sensing technologies.

arXiv comment*Authors with equal contribution