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.

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.

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.

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.

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.

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