Collective behavior of squirmers in thin films

This study employs the squirmer model and dissipative particle dynamics to investigate how swimmer shape, volume fraction, hydrodynamic interactions, and rotlet dipoles influence the collective behaviors—ranging from gas-like phases to swarming and motility-induced phase separation—of bacteria in confined thin films, revealing asymmetric structural formation and the mitigating effect of rotlet dipoles on differences between swimmer types.

The Gist

Imagine a crowded dance floor, but instead of people, the dancers are microscopic bacteria. These aren't just any dancers; they are "self-propelled," meaning they have their own little engines and can swim around on their own. Scientists call these "squirmers."

This paper is like a high-tech observation of what happens when you pack a lot of these swimming bacteria into a very thin, flat sandwich of water—so thin that they can only really move in two layers, like a double-decker bus, but with enough room to spin around.

Here is what the researchers found, explained simply:

1. The Three Types of Dancers

The researchers studied three different "personalities" of these swimming bacteria, based on how they push water to move:

• The Pushers (like E. coli): They push water away from their tails to move forward. Think of them as people shoving a crowd to get through a door.
• The Pullers: They pull water toward their heads to move forward. Think of them as people using a rope to pull themselves through a crowd.
• The Neutrals: They just glide without pushing or pulling the water much.

2. The "Thin Film" Dance Floor

The scientists put these swimmers in a narrow gap between two walls.

• The Result: The bacteria naturally formed two layers, one near the top wall and one near the bottom wall. They didn't stack up into a tall tower; they stayed in these two flat sheets.
• The Orientation: Most of the time, the bacteria swam parallel to the walls, like cars driving on a highway. However, the "Pullers" were a bit rebellious; at low crowds, they liked to stand almost perpendicular (upright) to the walls, like flowers growing out of a pot.

3. How Crowds Change the Dance

The researchers changed how many bacteria were in the box (the "volume fraction") to see how the crowd behaved:

• Low Crowd (The Gas Phase): When there were few bacteria, they just swam around randomly, like people milling about in a large, empty park.
• Medium Crowd (Swarming): As they added more bacteria, they started forming mobile groups that moved together. This is called "swarming." It's like a school of fish or a flock of birds moving in unison.
  • The Twist: The "Pushers" and bacteria with a special spinning feature (called a "rotlet dipole") were great at swarming. The "Pullers" without that spinning feature didn't swarm as well; they preferred to stick together in tight, stationary blobs.
• High Crowd (The Traffic Jam): When the box was packed tight, the bacteria got stuck in huge, immobile clusters. They couldn't move anymore. This is called "Motility-Induced Phase Separation" (MIPS). It's like a traffic jam where everyone is stuck in a massive, unmoving pile.

4. The "Spinning Top" Effect (The Rotlet Dipole)

One of the most interesting findings involved a specific flow field called a "rotlet dipole." Imagine a bacterium that not only swims forward but also spins its body like a top while it moves.

• The Magic: When the researchers added this spinning motion, it acted like a universal equalizer. It didn't matter if the bacteria were Pushers, Pullers, or Neutrals; they all started behaving the same way.
• The Result: The spinning made them much more active. They stopped forming those tight, stuck blobs and kept moving around. They also started jumping between the top and bottom layers of the "sandwich" much more often, like people switching lanes on a highway to avoid a traffic jam.

5. Why This Matters for Biofilms

Biofilms are the slimy layers of bacteria you find on teeth (dental plaque) or on rocks in a stream. They start as a single layer of bacteria on a surface.

• The Big Question: How do they grow into thick, multi-layered mounds?
• The Answer: The study suggests that if the bacteria are "Pushers" (like E. coli) or if they have that "spinning top" motion, they are very good at jumping from the bottom layer to the top layer. This allows them to build up a multi-layered structure quickly.
• The Exception: The "Pullers" tended to stay stuck in their specific patterns and didn't switch layers as easily, which might slow down how thick their biofilm gets.

Summary

In short, the paper shows that the shape of the bacteria, how they push water, and whether they spin while they swim all determine whether they will form a chaotic crowd, a coordinated swarm, or a stuck traffic jam. The "spinning" feature is particularly powerful because it keeps the bacteria moving and prevents them from getting stuck, helping them build thicker, more complex structures.

Technical Summary

Problem Statement
The collective motion of microswimmers, such as bacteria in biofilms, is a complex phenomenon driven by the interplay of morphological characteristics, propulsive forces, volume fractions, and hydrodynamic and steric interactions. While motility-induced phase separation (MIPS), swarming, and active turbulence are well-documented in quasi-two-dimensional (quasi-2D) monolayers and three-dimensional (3D) periodic systems, the behavior of swimmers in thin films that allow for multi-layered structures remains less understood. Specifically, there is a need to bridge the gap between highly confined quasi-2D systems and bulk 3D systems to understand how bacteria transition from a surface monolayer to multi-layered biofilm structures. Key questions include whether swimmers in thin films prefer orientations parallel or perpendicular to walls, under what conditions they spontaneously leave the wall to form multi-layered structures, and how their collective behavior differs from quasi-2D systems.

Methodology
The authors employ the squirmer model to represent microswimmers and the Dissipative Particle Dynamics (DPD) method for fluid modeling. The system consists of spheroidal squirmers confined between two parallel walls with a film thickness ($L_y$) sufficient to allow full rotational freedom but restricted enough to permit a maximum of a two-layered structure.

• Squirmer Model: The swimmers are modeled as spheroids with an aspect ratio of 2 ($b_z/b_x = 2$), mimicking E. coli. The surface slip velocity includes terms for self-propulsion ($B_1$), active stress ($\beta$) to distinguish between pushers ($\beta < 0$), neutral swimmers ($\beta = 0$), and pullers ($\beta > 0$), and a rotlet dipole term ($\lambda$) to mimic the counter-rotating flow of flagellated bacteria.
• Simulation Setup: The simulations are conducted in a domain with periodic boundary conditions in the $x$ and $z$ directions and confined walls in the $y$ direction. The study varies the volume fraction ($\phi \in \{0.18, 0.35, 0.44, 0.56\}$), active stress ($\beta \in \{-5, 0, 5\}$), and rotlet dipole strength ($\tilde{\lambda} \in \{0, 133.5\}$).
• Analysis: Structural properties are analyzed via cluster size distributions, radial distribution functions, and orientation distributions. Dynamic properties are characterized by effective rotational diffusion, mean-squared displacement (MSD), and average swimmer speed.

Key Contributions and Results
The study identifies distinct collective states—gas-like phases, swarming, and MIPS—as a function of increasing volume fraction and swimmer type.

1. Phase Behavior and Volume Fraction:
   • At low volume fractions ($\phi \approx 0.18$), the system generally exhibits a gas-like phase of small clusters, except for pullers without a rotlet dipole, which form large clusters (MIPS) due to attractive hydrodynamic interactions.
   • At intermediate fractions ($\phi \approx 0.35$), swarming behavior emerges for pushers and swimmers with a rotlet dipole. Pullers without a rotlet dipole tend toward MIPS.
   • At high fractions ($\phi \ge 0.44$), all systems transition to a MIPS phase characterized by large, nearly immobile clusters.
2. Role of Swimmer Type and Wall Interaction:
   • Pushers and Neutral Swimmers: These tend to align parallel to the walls. Pushers frequently switch between the two layers, facilitating the formation of multi-layered structures.
   • Pullers: Without a rotlet dipole, pullers favor a nearly perpendicular orientation to the walls, leading to the formation of "flower-like" structures at low $\phi$ (one central puller perpendicular to the wall surrounded by "petal" pullers). This orientation promotes early cluster nucleation and MIPS. Pullers rarely switch layers spontaneously.
3. Impact of Rotlet Dipole:
   • The presence of a rotlet dipole ($\tilde{\lambda} = 133.5$) significantly mitigates the differences in collective behavior between pushers, neutral, and puller swimmers.
   • With a rotlet dipole, all swimmer types exhibit similar behaviors: they align parallel to the walls, show swarming at intermediate $\phi$, and transition to MIPS at high $\phi$.
   • The rotlet dipole induces circular trajectories near walls and frequent switching between layers, thereby enhancing effective rotational diffusion and mobility even at moderate volume fractions.
4. Structural Asymmetry: The formation of collective structures is not necessarily symmetric with respect to the two walls, particularly in the absence of a rotlet dipole.

Significance
The paper claims to provide the first steps in bridging the gap between very confined quasi-2D systems and less confined 3D collective behaviors. The results highlight the critical importance of swimmer anisotropy, hydrodynamic interactions, and wall interactions in determining collective states. Specifically, the study suggests that:

• The aspect ratio of the swimmer and its hydrodynamic interactions with walls are crucial for the emergence of different collective behaviors.
• A rotlet dipole can homogenize the behavior of different swimmer types, reducing the distinctions between pushers, neutral, and puller swimmers.
• Pusher-like swimmers (analogous to E. coli) are capable of spontaneously transitioning from a monolayer to a multi-layered configuration due to their frequent layer-switching, whereas pullers tend to remain in specific orientations that nucleate clusters.

The authors note that while the squirmer model captures far-field hydrodynamics well, near-field details specific to real bacteria (such as flagellar geometry and tumbling) are simplified. Therefore, direct quantitative comparison with experiments requires calibration, but the simulations offer a robust qualitative characterization of confined active matter.