Bicontinuity in active phase separation

TL;DR

This work demonstrates that active stresses can continuously arrest coarsening in a three-dimensional phase-separating mixture, producing steady-state bicontinuous networks dominated by sheet-like interfaces. By coupling a Cahn–Hilliard description with active nematodynamics and validating with 3D experiments using MT–KSA–driven activity in a PEO–dextran mixture, the authors show that the bicontinuous morphology is tunable via activity and surface tension and persists over the active lifetime. A key finding is the scaling of the active width $w_a$ with a collapse $w_a \sim \big((|\oldsymbol{\alpha}|-\boldsymbol{\alpha_c})/\gamma^{2/3}\big)^\nu$ with $\nu \approx -1.36$, indicating sheet-like structures with $d_f \approx 1.1$. Curvature analyses confirm the predominance of near-zero Gaussian curvature in active interfaces, contrasting with saddle-like interfaces in passive coarsening. Together, these results reveal a robust, tunable pathway to reconfigurable bicontinuous morphologies with potential implications for biomimetic materials and controlled interfacial architectures.

Abstract

We study phase separation between coexisting active and passive fluids in three-dimensions, using numerical simulation and experiments. Chaotic flows of the active phase drive giant interfacial deformations, causing the co-existing phases to interpenetrate and generate a continuously reconfiguring bicontinuous morphology which persists over the lifetime of the active fluid. Active bicontinuous structures are dominated by sheet-like interfaces, in marked difference from passive liquid-liquid phase separation which is controlled by saddle-like surfaces. Activity and surface tension control the length scale of the bicontinuous structure. These results demonstrate how active stresses suppress the coarsening of conventional phase separation, generating steady-state reconfigurable morphologies not accessible with conventional surface-modifying agents or through quenching of transient phase separated structures.

Figures (11)

• Figure 1: Active 3D phase separation yields a percolating network-like structure. (A-B) Morphology of active phase separation in computer simulations from the early state to the steady state. Red represents the active phase ($\phi>0.5$). Simulation parameters: activity $|\alpha|=1.30,$ surface tension $\gamma=1.0,$ and active fraction $\phi_a = 0.40$. (C) Experimental morphology of the active phase (red) at steady state. (D) An $x$-$y$ cross-section of a phase-separating experimental sample. The white arrows indicate the active flows in the dextran phase (red), obtained from Particle Imaging Velocimetry. (E) MTs (cyan) partition into the dextran phase (red). (F) MTs in the dextran phase form bundles due to the depletion effect. Kinesin clusters (KSA) bind to MT bundles driving their extension. The experimental samples (C-E) contain 1.8% PEO and 1.8% dextran, $\phi_a=0.37$, and are imaged at time $t=1.5$ h. The KSA concentration is 183 nM (C) and 92 nM (D, E).
• Figure 2: Bicontinuous morphology persists over a wide range of volume fractions. (A) Connected active (red) and passive phase (blue) in simulations, with $\phi_a = 0.40$ (B) Connectedness factor $f_c$ of the active and passive phases as a function of the volume fraction of the active phase $\phi_a$. The range where $f_c \approx 1$ for both phases highlighted in pink indicates bicontinuity. Simulation parameters: $|\alpha| = 0.70, \gamma=1.0$. (C) Morphology of the connected active (red) and passive phase (blue) in the experiment. $\phi_a = 0.37$. (D) The connectedness fraction $f_c \approx 1$ for intermediate values of $\phi_a$, indicating bicontinuity. Experimental samples initially contain 183 nM KSA, 1.8% PEO, and 1.8% dextran.
• Figure 3: Active width $w_a$ decreases with activity and increases with surface tension. (A-B) $w_a$ decreases with activity $|\alpha|$ in simulations and with KSA concentration in experiments. (C-D) $w_a$ increases with surface tension $\gamma$ in simulations and with capillary length in experiments. In (A-D) the color of the dots represents the volume fraction $\phi_a$ of the active phase (see color bar) and shows that $w_a$ is essentially independent of $\phi_a$. (E-G) 3D visualization of the dextran phase (red) in experiments with increasing KSA concentration, showing a corresponding decrease of $w_a$. (H-J) 3D visualization of the dextran phase (red) in experiments with increasing capillary length, showing a corresponding increase of $w_a$. The experimental samples (B, E-G) contain 1.8% PEO and 1.8% dextran. KSA concentrations are increased from 42 nM (E), 92 nM (F), to 183 nM (G). Samples (D, H-J) contain 183 nM KSA. PEO and dextran concentrations are both increased from 1.8% (H), 1.9% (I), to 2.0% (J).
• Figure 4: Scaling law for the width $w_a$ in simulations. Steady state width $w_a= \text{Volume}/\text{Surface Area}$ of the connected active domain in the bicontinuous region as a function of activity $|\alpha|$ and equilibrium surface tension $\gamma$, for a fixed active fraction $\phi_a=0.40$. The main figure shows that the data collapse when plotted versus $(|\alpha|-\alpha_c)/\gamma^{2/3}$ (Eq. \ref{['eq:scalingLaw']}). The black dashed line shows the best fit (via linear regression) to $w_a \sim (|\alpha|-\alpha_c)/\gamma^{2/3})^\nu$ for $\nu = -1.36 \pm 0.04$. The inset shows the unscaled active width as a function of activity, for various values of $\gamma$. Fixed parameters: $K = 24.0, \alpha_c = 2\eta r/\lambda \Gamma =0.2$.
• Figure 5: Comparing the interface morphology in passive and active bicontinuous structures. (A) The two principal curvatures $\kappa_1$ and $\kappa_2$ are calculated everywhere on the interface. (B-D) 3D visualization of the normalized Gaussian curvature $\kappa_1\kappa_2w_a^2$ of the interface from experiment (B), simulations of the active/passive mixture(C) and simulations of the passive Cahn-Hilliard equation (D). The color indicates the value of the Gaussian curvature. (E-H) Distribution $\rho(\kappa_1,\kappa_2)$ of normalized principal curvatures $\kappa_1w_a$ and $\kappa_2w_a$. Different values of $\kappa_1$ and $\kappa_2$ correspond to different geometries (E). $\rho$ peaks at small values of $\kappa_1$ and $\kappa_2$ in experiments (F) and simulations (G), indicating sheet-like interfaces. $\rho$ peaks at $\kappa_1 \ll 0, \kappa_2 \gg 0$ in simulations of the Cahn-Hilliard equation (H), indicating a saddle-like interface. The experimental sample (B,F) contains 92 nM KSA, 1.8% PEO, 1.8% dextran, and $\phi_a=0.37$. Simulation parameters (C,G): $|\alpha|=1.30, \gamma=1.0,$ and $\phi_a=0.40$.