Using sound to build a wall: how physicists measure pressure in active systems

Original paper: Acoustic trapping of active matter


You know how sometimes you tell to yourself things like “life is complicated”? Theoretical physicists are constantly reminded of this fact when studying living organisms. Recently, a new field of physics has emerged, inspired by the observation of living systems. What forces do cells exert during metastasis in cancer? What are the growth dynamics of biofilms of bacteria? How can a school of fish organize itself and move simultaneously? These are questions raised in the physics of active matter. Active matter is an assembly of objects able to move freely and capable of organizing into complex structures by consuming energy from their environment. Active matter can be composed of living or artificial self-propelled particles.

However, active systems differ from a simple gas or liquid because they are out-of-equilibrium. A system is in equilibrium if there is an energy balance between the system and the environment. When the energy isn’t balanced, the system will evolve toward an equilibrium state. Imagine a ball on a hilltop: it is in an out-of-equilibrium state until it has rolled down and stopped at bottom of the hillside. Now imagine that the ball is an active particle. This means it can consume energy from its environment to propel itself back up the hill, which drives the system out of equilibrium.
But physical notions such as pressure or temperature, are defined in thermodynamics only at equilibrium. This is why bridging the gap between physics and active matter has been a new challenge for theoretical physicists. Today’s paper focuses on the definition of a new quantity called swim pressure and highlights how researchers achieved its experimental measurements using an acoustic trap.

Rather than dealing with living organisms in this study, Sho and his collaborators used a system of artificial self-propelled particles, called Janus particles. They are made of two half faces; one in polystyrene and one in platinum [1]. Once immersed in a liquid, the platinum coating reacts with hydrogen peroxide contained in the liquid. The available energy resulting from this chemical reaction is then converted into motion. Particles move individually and randomly (analogous to an atom’s motion in a gas).

Due to self-propelled motion, active particles exert a mechanical force on their surrounding boundaries. In other words, a particle would naturally swim away in space unless confined by walls. The pressure exerted by active particles on the walls that confine them is the swim pressure. This is analogous to the definition of pressure from a microscopic point of view, which is the result of atoms colliding on a surface. Now that the theory is set, researchers try to measure swim pressure experimentally. But to control, confine and observe micro-particles between walls that you can remove at will is quite a challenge.

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Figure 1. The curves represent two profile of an acoustic wave throughout time. Particles migrate to nodes due to the difference in acoustic pressure between nodes and antinodes.

Sho and his collaborators at California Institute of Technology did not actually use physical walls in their experiment but instead used sound. When an acoustic wave propagates through a material, the deformation of the material causes a local pressure. Using this acoustic pressure, researchers can move objects between specific locations called nodes, which are special locations where the pressure wave is stable in time. The local pressure is minimal at nodes, while pressure is maximal at antinodes (see Figure 1). Since objects move from high to low pressure, the particles become trapped at nodes (see Figure 1). This technique is called an acoustic tweezer, or acoustic trap. Here, researchers built an acoustic trap such that many particles are confined over a large trap area.

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Figure 2: a-c. Snapshot of Janus particles in an acoustic trap (watch movie here). The red spot is the center of the trap and the white dashed line represents the contour of the acoustic trap. d. The figure shows trajectories of Janus particles moving randomly inside the trap (images adapted from Sho and coworkers’ original paper).

The researchers also adjust the size and force of the trap as a function of the velocity of active particles. Over time, more particles get trapped, and a densely packed cluster forms (see Figure 2). Particles can move within the trap area, but cannot exit (see Figure 2d). Then, when the acoustic tweezers are turned off, the cluster explodes! Meaning that free from confinement, active particles spontaneously disperse (see Figure 3). Thus, knowing the acoustic pressure and measuring the dispersion of particles over time allows researchers to measure the swim pressure.

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Figure 3. Snapshots of Janus particles at different times after the acoustic trap has been released (watch movie here). The active cluster explodes, resulting in Janus particle dispersion (Images adapted from Sho and coworkers’ original paper).

When you inflate a soccer ball with a pump, the walls will experience more collisions with the air molecules, meaning pressure increases. Similarly, squeezing the ball reduces space between the molecules and also results in an increase in pressure. These types of pressure changes are analogous to those observed in Sho and collaborators’ experiments. As shown in Figure 4, swim pressure increases over time as more particles get trapped (like pumping air into the soccer ball). Swim pressure also gets stronger for smaller trap area (like squeezing the soccer ball). But despite the analogy, we must not overlook the complexity behind the physics. Swim pressure is different from the pressure we experience every day, which comes from atoms and molecules. Here the classical model of pressure is an inspiration to build a new model. And as Figure 4 illustrates, the theory is consistent with experimental observations and validates this concept of swim pressure.

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Figure 4. Evolution of the swim pressure as a function of time for two different size area. The swim pressure is higher for smaller trap areas. Researchers compare here experimental data with numerical simulations and theory (adapted from Sho and coworkers’ paper).

To conclude, today’s paper shows how classical physics quantities can be redefined to describe a new phenomenon in active matter. Sho and his collaborators used an ingenious device to measure the swim pressure exerted by active particles for different degrees of confinement and different crystal size. Their results confirm experimentally the theory of swim pressure established in a new approach of active matter, and open ways to a better description of the living world (from molecular to cells dynamics, bio-films formation, collective motion…). So indeed, life might be complicated, but from the point of view of scientists, this is what keeps them excited.

[1] these particles were named Janus particles in reference to the Hall-faced Roman God Janus.

From errant to coherent motion

Original paper

Emergence of macroscopic directed motion in populations of motile colloids. By Bricard A., Caussin J-B, Desreumaux N., Dauchot O. & Bartolo D.


Have you ever seen those wide shapes moving in the sky at dawn, made of thousands of starlings, or the swarms of fish swimming in the ocean (see Figure 1)? The ability to organize and move in groups without a leader is called collective motion and has been observed at various spatial scales in the living world, from birds to locusts, cells, and bacteria. Even humans can perform collective motion in some situations, as it has been modeled in crowd movements (for example Mosh pits). Physicists have gazed at this phenomenon over the last couple of decades trying to answer questions such as: How can different organisms exhibit the same behavior? What common features do all these organisms have that allow them to move in such a synchronized way?

The key to the emergence of collective motion is interactions, the ability of individuals to modify their behavior to coordinate their movements with those of their neighbors. The details of these interactions are difficult to model and control in many living or man-made systems, or may even still be unknown. Yet, in today’s paper, Antoine Bricard and colleagues showed how collective motion can arise solely from known physical interactions.

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Figure 1. Examples of collective motion in nature. (a) a flock of starlings (image adapted from howitworksdaily.com), (b) a swarm of fish (image adapted from scielo.br).

One of the first scientists who tackled these questions was Tamas Vicsek in the 90’s. He showed how collective motion can emerge from simple rules using a computer simulation. Although numerous theoretical and numerical studies followed, only few experiments were done. The biggest difficulty in studying collective motion experimentally is gaining control and reproducibility over a living system. Raising thousands of birds in a lab might not be the most convenient way of study, and even simpler biological systems, like bacteria, have problems of their own. Luckily, if you don’t want to deal with a biological system, you can build an artificial one. This is what Antoine Bricard and collaborators did, at Ecole Normale Supérieure de Lyon. To study collective motion, they built an artificial system made of millions of tiny, plastic beads (5 µm diameter) that were able to move freely, interact with their neighbors, and even self-organize as a group.

To put these inert beads in motion, researchers used a phenomenon called Quincke electro-rotation. The idea is to convert electrostatic energy into mechanical rotation. Here, the rotation is triggered by an electric field, $latex E_0$, applied to insulating beads, which are immersed in a conductive liquid. Under this field, small fluctuations in the charge distribution tilt the orientation of the bead. Then, the small rotational perturbation is amplified, resulting in a constant rotation and the bead rolling on the bottom of a pool. The researchers refer to these activated beads as “rollers”. All rollers move at the same speed, directly controlled by $latex E_0$, yet they don’t move in the same direction but rather randomly. As you can see in Figure 2, the beads move individually in different directions and there is no general directed motion. So how can this disordered system switch to an ordered motion?

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Figure 2. (a) The propulsion mechanism of a bead under an electric field, $latex E_0$, inducing an electric polarization, P. When P is tilted, the bead starts to rotate and moves forward at a constant speed, v. (b) A superposition of 10 images taken at successive timesteps showing the trajectories of 4 rollers activated by the Quincke electro-rotation. (Image adapted from the Antoine Bricard and coworkers’ paper.)

Using Quincke electro-rotation, the exact interactions between the rollers were described by the research team mathematically. Firstly, the beads interact through electrostatics, like two magnets, via an interaction that depends on how far they are from each other. Secondly, the beads interact through hydrodynamics, because when a bead moves in a liquid a flow is generated around it. This generates a pull similar to a swimmer who is feeling the flow produced by another swimmer nearby. What’s more, the theory shows that the combination of these two physical interactions tends to align a group of rollers. When two beads are close enough to each other, they slightly change their course to roll in the same orientation and they all eventually move in the same direction.

To study rollers for millions of particle lengths, the researchers chose to put them in a racetrack-shaped area (Figure 3 a). The rollers spontaneously organized, and a large band made of millions of rollers moved around the track. Of course, rollers had to be close enough in order for interactions to be effective. Figures 3 b-d show how the rollers changed behavior as they get more densely packed. In Figure 3 b, the rollers look like they are wandering in random directions because they are too far from each other to interact, while in Figure 3 d high-density rollers move in the same direction. And as more rollers are added in the same area, the interactions between rollers become more effective. This transition from a disordered state to an ordered state is called a phase transition. In most familiar cases, for example, water-to-ice, phase transitions are driven by temperature. Here density is the control parameter, meaning the research team measured what is the minimum density required for a collective motion to emerge. And being able to couple this observation with a theoretical description of the interactions, the key ingredient underpinning of the system, is what got them further than anyone else at the time.

Figure 3
Figure 3. (a) The racetrack band (watch the movie here) made of millions of self-organized rollers circulating around the area. (b-d) Screenshots of rollers at different densities; (b) at low density, (c) at the front of the band, and (d) at high density of rollers (watch the close view here). (Image adapted from the Antoine Bricard and coworkers’ paper.)

Collective motion seems natural in many living organisms but is still poorly understood by scientists. This paper highlights the importance of interactions between individuals in a group during the process of collective motion. Even though this study is specific and does not account for the mechanisms at work in most biological systems, it was a great achievement toward understanding this phenomenon. Comparing these results with the studies of biologists, ethologists, and mathematicians make me wonder: if a scientist working in his/her lab is like a random walker, then, what beautiful picture will emerge from the work of thousands of scientists interacting with each other to understand collective motion?