🔬 condensed matter

Self-organized flows break morphological symmetry in active/passive systems

Numerical simulations demonstrate that self-organized flows within the active regions of a phase-separating active/passive fluid mixture drive an inverse energy cascade and vortex formation, which break the morphological symmetry of the resulting bicontinuous emulsion through a tight coupling between flow dynamics and interfacial fluctuations.

Original authors: Rainer Backofen, Axel Voigt

Published 2026-01-22

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CC BY 4.0

Original authors: Rainer Backofen, Axel Voigt

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a pot of soup where two types of ingredients are trying to separate: one part is "lazy" and just sits there (passive), while the other part is "hyperactive" and constantly wiggling, pushing, and pulling itself around (active). Usually, when you let oil and water separate, they form big, smooth blobs. But in this study, the authors discovered that when you add a "hyperactive" ingredient, the separation doesn't happen smoothly. Instead, it creates a chaotic, dancing mess where the shapes of the blobs become strangely lopsided.

Here is the simple breakdown of what they found, using some everyday analogies:

1. The "Turbulent Dance Floor"

Think of the active part of the mixture like a crowded dance floor where everyone is moving wildly. The authors found that this chaos isn't random noise; it organizes itself. Just like how a crowd might spontaneously form a giant circle dance, the active fluid creates swirling "vortices" (mini-tornadoes).

In a normal, calm fluid, these swirls would just die out. But in this active soup, the energy from the tiny wiggles of the bacteria or cells piles up into bigger and bigger swirls. This is called an "inverse energy cascade." It's like if you started clapping your hands softly, but somehow that energy traveled up to make the whole room shake.

2. The "Room Size" Rule

Here is the most important discovery: The size of the swirls depends entirely on how much empty space is available.

Imagine the active fluid is a group of dancers.

If they are in a wide-open ballroom, they can form a massive, slow-moving circle dance (a large vortex).
If they are squeezed into a narrow hallway or a tiny corner, they can only do a small, frantic jig (a tiny vortex).

The paper shows that the active fluid "senses" the shape of the space it occupies. If the active region is wide and open, it builds up a lot of energy and creates huge, powerful swirls. If the active region is squeezed into a thin, narrow bridge, it can't build up much energy, and the swirls stay small and weak.

3. Why the Shapes Are Lopsided (The "Pinch-Off" Effect)

This is where the magic happens. The mixture separates into two types of droplets:

Passive droplets (the lazy blobs) floating inside the active soup.
Active droplets (the wiggly blobs) floating inside the lazy soup.

The authors found that there are way more passive droplets than active ones. Why?

The Passive Droplet Scenario: Imagine a lazy blob (passive) sticking out into the active soup. Because it's surrounded by the active fluid, the active fluid has a lot of "room" to move around it. This allows the active fluid to build up huge, powerful swirls. These powerful swirls slap against the lazy blob, shaking it so hard that it gets ripped apart into smaller pieces.
The Active Droplet Scenario: Now imagine a wiggly blob (active) sticking out into the lazy soup. The wiggly blob is surrounded by the lazy fluid, which doesn't move. The active fluid is trapped in a narrow, thin shape. Because it's squeezed, it can't build up big, powerful swirls. It's like trying to dance a giant circle dance in a closet. Without that big, powerful energy, it doesn't shake the blob enough to rip it apart.

The Result: The lazy blobs get ripped apart easily, creating many small passive droplets. The wiggly blobs stay mostly whole, forming long, connected, snake-like structures.

4. The Big Picture

The paper claims that you don't need complex biological rules (like specific cell structures) to get this lopsided shape. You just need fluid motion. The self-organized flow of the active part creates a feedback loop:

The shape of the fluid determines how big the swirls can get.
The size of the swirls determines how hard the fluid shakes the boundaries.
The shaking breaks the boundaries in specific ways, creating more "lazy" droplets and fewer "wiggly" ones.

Why Does This Matter?

The authors suggest this mechanism explains how nature might create complex, uneven shapes in soft materials without needing special instructions. It's like a self-organizing sculptor: the fluid's own movement carves the shape, breaking symmetry and creating a specific, uneven pattern. They propose this could be a way to control the texture of "smart" soft materials in the future, simply by adjusting how active the fluid is.

In short: The active fluid creates its own weather. Where the weather is wild and open, it tears things apart. Where the weather is cramped and weak, things stay together. This creates a world where the "lazy" parts get shredded into tiny pieces, while the "active" parts stay connected in long, winding shapes.

Technical Summary: Self-organized flows break morphological symmetry in active/passive systems

Problem Statement
Interfaces in phase-separating fluid mixtures dictate morphology, a critical factor in creating functional soft materials in biology and physics. While previous research has utilized interfacial modifications (e.g., chemical reactions, jamming) or bulk properties to control morphology, recent studies on mixtures of active and passive fluids have shown that bulk activity can arrest phase separation and induce asymmetric dynamic emulsions. Specifically, experiments with active microtubule-based liquid crystals and passive isotropic fluids demonstrated that activity arrests coarsening and enhances interfacial fluctuations, leading to a predominance of passive droplets within the active material. This asymmetry was previously attributed to nematic elasticity arising from liquid crystalline degrees of freedom. The central question addressed in this work is whether such morphological asymmetry requires explicit liquid crystalline order, or if it can be explained solely by self-organized hydrodynamic flows within the active region.

Methodology
The authors investigate a two-phase system consisting of one active and one passive fluid region using a momentum-conserving extension of the Navier-Stokes equations, known as the Generalized Navier-Stokes (GNS) equations, coupled with Cahn-Hilliard (CH) equations.

Model Formulation: The system is modeled by the Cahn-Hilliard-Generalized-Navier-Stokes (CHGNS) equations. The effective stress tensor $\sigma$ includes passive viscous contributions and active contributions driven by an activity parameter $\alpha_{act}$ . The active stress is defined via an effective viscosity $\nu_{eff}$ that depends on the phase field $c$ , distinguishing between active ( $c \approx 1$ ), passive ( $c \approx -1$ ), and interfacial ( $c \approx 0$ ) regions.
Active Stress Mechanism: The active viscosity is modeled in reciprocal space to inject energy at a specific activity band ( $k_0 \le k \le k_1$ ), mimicking the energy injection in bacterial suspensions. This setup allows for the study of isotropic active stress without requiring nematic order.
Numerical Approach: Two-dimensional numerical simulations are performed under periodic boundary conditions with a symmetric initial condition ( $\int c dx = 0$ ). The system is evolved from random noise to explore the transition from spinodal decomposition to dynamic equilibrium. The study focuses on the "arrested coarsening" regime where the system reaches a dynamic equilibrium state characterized by fluctuating interfaces.

Key Contributions and Results
The study reveals that self-organized flows in the active region are sufficient to break morphological symmetry, without invoking liquid crystalline elasticity.

Arrested Coarsening and Dynamic Emulsion:
- As activity ( $\alpha_{act}$ ) increases, the standard coarsening process (where interface length decreases over time) is arrested. The system settles into a dynamic equilibrium state characterized by a constant mean interface length and fluctuating kinetic energy.
- This state forms a dominantly bicontinuous dynamic emulsion with occasional droplets formed via pinch-off events.
- The mean interface length and kinetic energy density in the arrested state increase approximately linearly with activity.
Inverse Energy Cascade and Condensate Formation:
- Similar to inertial turbulence, the active region exhibits an inverse energy cascade where energy injected at the activity scale ( $K$ ) transfers to larger scales.
- This leads to the formation of mesoscopic vortices (condensates). Unlike single-phase systems where condensate size is limited by the domain size, in this two-phase system, the size of these vortices is determined by the locally available space within the active region.
- The energy spectrum shows a peak at wavenumbers smaller than the forcing scale, indicating the emergence of flow structures larger than the activity scale.
Morphological and Topological Asymmetry:
- Droplet Count: There is a significant asymmetry in the number of droplets: the system contains more passive droplets within the active region than active droplets within the passive region.
- Connectivity: The active region remains dominantly bicontinuous (high connectivity), while the passive region becomes more fragmented with increasing activity.
- Geometry: Passive regions tend to form more compact, larger domains, whereas active regions exhibit more elongated structures and protrusions.
Mechanism of Symmetry Breaking:
- The authors propose a mechanism linking flow structure to interface fluctuations. The kinetic energy density in the active region is positively correlated with the locally available space (quantified by the radius of the maximal inscribed circle, $r_{MIC}$ ).
- Active Protrusions: In narrow active protrusions, the available space is small, suppressing the formation of large, energetic vortices. Consequently, interface fluctuations are weak, making pinch-off events (droplet formation) less likely.
- Passive Protrusions: Passive protrusions are surrounded by active regions with potentially larger available space. This allows for the formation of larger, higher-energy vortices, generating stronger interface fluctuations that promote pinch-off.
- Result: This differential fluctuation strength leads to a preferential formation of passive droplets, breaking the geometric and topological symmetry.

Significance and Claims
The paper claims that the observed morphological asymmetry in active/passive emulsions does not strictly require nematic elasticity or liquid crystalline order. Instead, it can be fully explained by the self-organization of hydrodynamic flows and the coupling between the flow field and the dynamic morphology.

Generalization: The proposed mechanism is presented as a general principle applicable to heterogeneous active systems with long-ranged hydrodynamic flows, such as suspensions of different bacterial types or mixtures of different cell types with internal boundaries.
Control: The findings suggest a pathway to control the morphology of functional soft materials by tuning activity and the resulting flow-morphology coupling, rather than relying solely on interfacial chemistry or elastic properties.
Theoretical Context: The work bridges the gap between active turbulence and two-phase systems, demonstrating that while the inverse cascade and hyperuniformity characteristics of vorticity fields resemble inertial turbulence, the specific coupling to the interface introduces unique asymmetries distinct from classical coarsening or active Model B/H extensions.

The authors conclude that this mechanism offers a potential explanation for the coupling between active processes and the self-organization of biomolecular condensates in cell biology, though they note that experimental validation is required to confirm the mechanism in biological contexts.