Living Droplets with Mesoscale Swimmers

Abstract

We study the activity of "living" droplets, which confine 1-6 mesoswimmers in 3D using a superhydrophobic substrate. The swimmers induce oscillations of the droplets at their inherent resonant frequencies, regardless of swimmer size and number. In contrast, the droplet oscillation amplitude is strongly affected by crowding, which we successfully model with a new scaling law and show that crowding reduces the speed of the swimmers. These fundamental living matter physics results reveal mechanisms for bio-inspired droplet actuation with implications for mesoscale robotics, fluidics, and sensing.

Figures (3)

• Figure 1: Experimental micrographs of living droplets supported by a superhydrophobic black silicon substrate, exhibiting an average contact angle $\theta$, with (a) $N=1$ and (b) $N=6$Artemia swimmers of length $L=490\pm20\ \mu$m. Images are shown for droplet volumes $V= 3-13.5\ \mu$L, corresponding to radii $R= 895-1550\ \mu$m and $L/R= 0.30-0.57$. Droplet deflections are measured along the $x$ direction. Scale bar $200 \ \mu$m.
• Figure 2: Oscillatory signal, frequency response and characterization. (a) Deflection versus time plot shows a typical oscillatory signal for an experimental case of $N=6$Artemia swimmers ($48$ h old) inside a droplet of volume $\ V\sim 4 \ \mu$L. $A$ (dashed line) denotes the root-mean-square of the time-varying amplitude. Inset shows a zoomed-in view of an oscillation envelope. (b) Fourier transform of the oscillatory signal in (a), showing two different responses: $f_{\mathrm{1}}$ and $f_{\mathrm{2}}$ which denote the resonant and the envelope frequencies, respectively. (c) $f_{\mathrm{1}}$ plotted as a function of droplet volume for varying $N$ and age of Artemia as well as a few experiments with a copepod ($N=1$). The best experimental fit to the data ($f_{\mathrm{1}}=18.7\ V^{-0.5}$) is found to be in good agreement with the CK model ($f_{\mathrm{1}}=22.7\ V^{-0.5}$) Celestini2006Sakakeeny2021.
• Figure 3: Theoretical prediction of droplet amplitude and characterization of crowded swimmer velocity. (a) Schematic drawing of two Artemia swimmers ($L^*=0.4$) moving with a velocity, $U_{\mathrm{c}}$ and impacting the droplet interface while swimming within distance $L$ from the periphery characterized by peripheral volume, $V_{\mathrm{p}}$. (b) Comparison of average experimental amplitude, $A$ and theoretical amplitude, $A_{\mathrm{t}}$ (Eq. \ref{['eq:At']}) for the case of unconfined ($L^*<0.4$) and uncrowded ($N^*<0.03$) swimmers. The least crowded cases with $N=1$ are indicated. The solid line is $A=1.8A_{\mathrm{t}}$, indicating an excellent agreement between the experimental data and theory. (c) The crowded swimmer velocity, $U_c$ normalized with the average swimmer velocity in the least crowded case, $U_{\mathrm{0}}$ (average of $N=1$ and $L^*<0.4$ data, filled markers) plotted against the dimensionless swimmer density, $N^*$. The experimental data of robotic fish confined in 2D Boudet2025 is shown as a comparison in red. An empirical scaling of $U_{\mathrm{c}}/U_{\mathrm{0}} \sim {N^*}^{-0.7}$ is found for our experiments as opposed to $U_{\mathrm{c}}/U_{\mathrm{0}} \sim {N^*}^{-0.4}$ for the 2D robotic fish, indicated by black and red lines, respectively.