January 6, 2025
Magnetic spinners self-propel, flock, and form new type of fluid
When William Irvine’s team put tiny magnetic particles in a fluid-filled chamber and spun them around, something unexpected happened. They began to flock together, splitting and merging like a school of fish. When they put lots of those particles in to swim, the suspension became a new phase of matter.
Irvine, a professor in the Department of Physics, the James Franck Institute, the Enrico Fermi Institute, and the College, conducts research that spans soft condensed matter, fluid dynamics, turbulence, and topological flow to understand the mechanisms that underpin many natural phenomena.
In a paper published October 8 in Nature Physics, Irvine’s team, with their collaborators in Michael Shelley’s team from the Flatiron Institute and NYU, describe the collective dynamics of these “spinners” under flow conditions between the largest and smallest scales where inertia and viscosity compete. They discovered that a spinner creates a localized three-dimensional region of vorticity, which they termed a “vortlet,” that drives the particle’s motion. When many vortlets interact, flocking behavior emerges. And when enough spinners are added to the fluid, the suspension forms a homogenous, dynamic steady-state: an active chiral fluid representing a new phase of matter.
Irvine’s UChicago team on this research includes physics PhD student Panyu Chen, then-postdoctoral researcher Severine Atis, and Takumi Matsuzawa, PhD’23. We spoke with Irvine about what the behavior of these spinners reveals about fluid dynamics. This interview has been edited and condensed.
What is a “vortlet?”
A vortlet is the name we gave to the flow field generated around a point particle spinning inside a fluid. It’s a new type of building block of flow.
The quintessential building block of all flow is vorticity [a measure of the local rate of rotation of a fluid element]. Vorticity typically comes in the form of closed loops, like smoke rings, or manifests in lines, like tornadoes, because the vorticity field must close on itself. When a point in a fluid is spinning, the generated rotation extends along lines that must connect back to the point or fill space. You can’t just have a point rotating in the middle of the fluid. So when we put these point particles inside the fluid and spun them, we challenged the fluid to react to this supposedly impossible scenario. The fluid responded by generating a vortlet—this complex flow around a particle like a vortex but a point vortex.
What surprised you most about this research?
As soon as we started experimenting with these spinners, they spontaneously formed flocks that propagated up and down the flow chamber like birds or schools of fish. They would move at different speeds, sometimes to the left and sometimes to the right. We were confused for a long time.
So we took a reductive approach, making a flock of 100 particles, then 50 particles, then 20 particles, and then down to one particle. That one particle started swimming. We spent all this time thinking about how three particles moving in some particular way could cause them to self-propel, and instead, the building block itself was moving on its own.
We looked at the laser-cut particles under a microscope and noticed they weren’t perfect cylinders. They’re a bit like a truncated cone. The asymmetry was very slight but sufficient to give rise to propulsion at the individual particle level.
How did that shape lead to propulsion?
We had already been working with our long-time collaborators, Mike Shelley and his former student and then postdoc, Scott Weady, from New York University and Flatiron, who deeply understand flows in this intermediate regime, numerically and theoretically. Once we realized these particles could propel at the single particle level, Scott produced a numerical code to capture that behavior and the flow field around it. Armed with that code, we could derive a mechanistic explanation of why a single particle spins.
One of the most beautiful moments in a course on fluid mechanics is when you put the high Reynolds number worlds together with the low Reynolds number worlds. Reynolds numbers indicate the ratio of the role of inertial forces to viscous forces. With large-scale flows—such as those behind an airplane or boat—inertia is key. Viscosity is almost irrelevant in determining those dynamics [high Reynolds numbers]. But on extremely small scales, like inside cells, viscosity is everything [low Reynolds numbers].
At some point, these two worlds are incompatible. So, what happens when you try to put them together? If I’m studying the flow past an airplane wing, in the world of high Reynolds numbers, it just slips past the wing. In the world of low Reynolds numbers, the flow is not allowed to slip at the wing surface. It seems like a contradiction, but it’s resolved through the concept of a boundary layer: a super thin region that hugs the object in which the flow goes from no velocity at the wing’s surface to a very fast stream of velocity a little bit above the wing.
These boundary layers are magic; they have dynamics of their own. We realized that a boundary layer forms on the surface of our truncated cone, and the pressure drop in that boundary layer makes it move.
The spinners (~9,500 shown here) are roughly 1 mm in diameter and 0.6 mm thick, crafted from PDMS polymer, laser-cut, and magnetized. Wound around the fluid- and particle-filled flow chamber are magnetic coils through which electric current runs, generating a rotating magnetic field that spins the discs. When the spinners are suspended in a fluid with a density that matches the discs, rendering them neutrally buoyant, they form a homogeneous 3D chiral fluid. When the density is mismatched, they self-organize into eruptions of cohesive flocks. Playback speed is 4x real time.
Why is it important to understand how these vortlets behave and interact?
Understanding what flow is made of is a fundamental question. We’re surrounded by flows. We have atmospheric-scale flows. Many animals flow in the way they fly or swim. We have flows in the air around us. We have flows inside us. Our cells are filled with flows.
A fair amount of understanding has been developed on large-scale, purely inertial flows. On the other end of the spectrum, scientists have been trying to understand how collective flows emerge from lots of little active agents.
For anything to happen at small scales where viscosity reigns, like inside cells, you need “engines” that generate and sustain the flow, such as flagella. Three types of agents have gained a lot of interest. One type is called active nematics, which are perhaps most like the agents inside your cells—a crowded environment of rods that push and pull on each other to generate flow. Another group is rollers: particles near a substrate that move at constant velocity in random directions. They tend to self-organize themselves to move collectively. And finally, there are spinners, which are collections of point-like particles at tiny scales and slow rotation speeds that come together and form active phases where everything is spinning and pushing off each other, generating large flows.
That’s a very brief summary of just over two decades of research. What has not yet been explored is the regime between the largest and smallest flow scales, between whales and bacteria, where both viscosity and inertia come into play and compete with each other. There’s no experimental platform of non-sentient beings to explore the physics occurring there. So we went to fill that gap. We chose spinners in three dimensions, because rotations are the elementary building block of all bulk flows, including turbulence, which has a very special relationship to rotation.
What’s next?
We have a three-dimensional chiral active phase [a system of self-spinning particles that breaks symmetry and generates flows], but we don’t yet fully understand the collective behaviors we’ve observed. What are the effective equations for this active medium? If you put a spherical “fish” into the system, for instance, how does it respond to the fluctuating environment? What about the background—is there turbulence? If so, then we can look at the background flow instead of the motion of the spinners.
There are different lenses through which we can look at the system—the active, dense, chiral, many-body system—and we will pursue everything we see.
Chen, P., Weady, S., Atis, S. et al. Self-propulsion, flocking and chiral active phases from particles spinning at intermediate Reynolds numbers. Nat. Phys. (2024)