Collective bacterial motion drives interfacial waves and shape dynamics in phase-separated droplets

Abstract

Liquid-liquid phase separation is important across biology, physics, and materials science. Although usually studied at equilibrium, active components - such as motor proteins, enzymes, and synthetic microswimmers - are increasingly recognized as key players in reshaping phase separation dynamics. Here, we encapsulate motile bacteria inside phase-separated aqueous droplets to investigate how internal activity alters interfacial behavior. By varying bacterial density, we control the active stress at the droplet interface. At low activity, we observe scale-dependent interfacial fluctuations that propagate as waves. In this low Reynolds number regime, these waves arise from an effective inertial response, generated when active bacterial stresses balance passive viscous damping of the interface. At higher activity, droplets deform strongly - exceeding the Plateau-Rayleigh instability threshold - and even form cell-sized filaments - a morphology without a passive counterpart. Enhanced droplet motility and accelerated coarsening accompany these shape changes. Our work shows how active stresses can reshape the morphology and dynamics of multiphase systems, offering new insight into the physics of internally driven phase-separated fluids.

Figures (5)

• Figure 1: Phase separation and sedimentation dynamics. (a) Schematic illustration of an active bacterial droplet. (b--d) Confocal images at the initial ($T = 1~\text{min}$, top) and final ($T = 36~\text{min}$, bottom) stages of coarsening and sedimentation for (b) the control case without bacteria, (c) the low-activity case ($\varphi_\text{b} = 20\%$), and (d) the high-activity case ($\varphi_\text{b} = 35\%$). Field of view: $330~\mu\text{m} \times 330~\mu\text{m} \times 200~\mu\text{m}$. Fluorescence highlights the dextran-rich phase. (e) Time evolution of the volume fraction of the droplet in bulk, excluding those touching the substrate. See SI for measurements of liquid densities, viscosities, contact angles, and surface tension.
• Figure 2: Shape dynamics of active droplets measured in experiments (top) and simulations (bottom). (a,b) Experimental bacterial flow fields measured on the equatorial plane in two droplets with different radii: (a) $R = 39.6~\mu$m and (b) $R = 273~\mu$m. (c) Fluctuation spectra, $S(k)$, measured in four droplets. The horizontal axis is normalized by the corresponding flow correlation lengths, $\ell_{v}$; the dashed line marks $k\ell_{v}=1$. (d) Normalized dynamic structure factor, $S_{n}(k,\omega)$, measured in a droplet with $R = 226~\mu$m. The dashed line marks the cutoff wavevector $k_c$. (e,f) Numerical bacterial flow fields measured on the equatorial plane in two simulated droplets with different radii (in simulation units): (e) $R = 12$ and (f) $R = 32$. (g) Fluctuation spectra, $S(k)$, obtained from simulations of four droplets. Inset: Mean interfacial energy $E_{\ell}$ as a function of $\ell/R\cdot \ell_v$, averaged over $m$. The dashed lines mark $k\ell_{v}=1$. (h) Normalized dynamic structure factor, $S_{n}(k,\omega)$, for a simulated droplet with $R = 32$. The dashed line marks the cutoff wavevector $k_c$. Red dots denote characteristic frequencies extracted from simulations with specific initial conditions (see Fig. 3) and stars correspond to the two curves with $\ell=5,m=0$ (blue) and $\ell=13,m=0$ (orange) in Fig. 3(b). The zero frequency points correspond to damping conditions. All experimental data are obtained in droplets with $\varphi_\text{b} = 20\%$, and all simulation parameters are described in SI Sec. S2.
• Figure 3: Oscillatory and wave dynamics from simulations of a spherical (top) and flat (bottom) interface. (a) Interface evolution and associated flow field resulting from an initial perturbation with a spherical harmonic mode $(\ell=5,m=0)$ on a spherical interface. The blue dashed line indicates the unperturbed shape. One-fifth of the droplet is shown for clarity. (b) Temporal evolution of the amplitudes of the $(\ell=5,m=0)$ and $(\ell=13,m=0)$ modes. The black dot denotes the corresponding frequency appearing in Fig. \ref{['fig:2']}h. (c) Fluctuation spectra, $S(k)$, obtained from 2D simulations of four flat interfaces. Inset: Mean interfacial energy $E_{k}$ as a function of $k \ell_v$. The dashed lines mark $k\ell_v=1$. The expression of $E_{k}$ is procided in Sec. S3 of the SI. (d) Normalized dynamic structure factor $S_{n}(k,\omega)$ measured from a flat interface. The orange and red dashed lines represent the analytical results in Eq. \ref{['eq:oscillator']} without and with the inclusion of higher-order viscosity, respectively; the black dashed line marks the threshold beyond which propagating modes disappear. The yellow dots denote characteristic frequencies extracted from simulations with specific initial conditions. All simulation parameters are given in Sec. S2 in the SI.
• Figure 4: Shape and dynamics of strongly deformed droplets. (a) Bacterial flow field in an elongating droplet. (b) Temporal evolution of the droplet aspect ratio in experiment (red) and simulation (blue). (c) Representative image of a droplet exhibiting a complex, highly non-spherical shape. (d) Filament-like protrusions extending from the droplet interface. (e) Normalized surface area as a function of droplet size, $R_\mathrm{eff}$, under low-activity (blue) and high-activity (red) conditions. $R_\mathrm{eff}$ is defined as $R_\mathrm{eff} = (3V/4\pi)^{1/3}$, where $V$ is the droplet volume. All experimental data correspond to droplets with $\varphi_\text{b}=35\%$, except for the low-activity data in (e). The simulation curve in (b) corresponds to the snapshots and parameters in Fig. S23.
• Figure 5: Droplet motion and coarsening near the substrate. (a) Side view of a low-activity droplet with $\varphi_\mathrm{b} = 20\%$. The red contour marks the substrate position. (b) Contact line corresponding to the droplet in (a). (c) Trajectory of the droplet’s center of mass in the $x$–$y$ plane; points are spaced by $4.7~\mathrm{s}$. (d) Side view of a high-activity droplet with $\varphi_\mathrm{b} = 35\%$, showing enhanced interfacial deformation. The red contour marks the substrate position. (e) Contact line corresponding to the droplet in (d). (f) Trajectory of the droplet’s center of mass with a temporal spacing of $0.87~\mathrm{s}$. (g) Time evolution of the characteristic length of the dextran phase, $\xi(t)$, within a $40~\mu\mathrm{m}$ region above the substrate for the zero-, low-, and high-activity conditions. (h) Droplet size distributions at $T = 36\,\mathrm{min}$ for the zero-, low-, and high-activity groups.