At first glance, the images look like something from a Fourth of July celebration: luminous bursts radiating outward, their tendrils twisting in hypnotic spirals. But these aren’t fireworks in the night sky. They’re simulations, created by scientists, of a centuries-old physics problem: how fluids move when they can’t mix.
In a new study, a team of researchers in Taiwan led by Chi-Chian Chou and Ching-Yao Chen mapped out what happens when two immiscible fluids like oil and water compete in tight spaces. The result is a dazzling display of “viscous fingering,” a phenomenon that may one day be leveraged against a pressing global challenge: how to permanently trap carbon dioxide underground.
A Battle Between Fluids
The study focused on a type of instability whose name sounds like it belongs on a mystery novel: the Saffman-Taylor instability. When a thinner, more agile fluid invades a thicker, sluggish one, the boundary between them buckles and fragments. Long, branching fingers erupt outward from the point of contact, forming complex, often beautiful patterns.
“This particular interfacial phenomenon has been thoroughly studied for many decades,” the authors note, “because of its intricate pattern formation and potential applications,” including oil recovery and climate change mitigation.
To explore this further, the team used highly accurate simulations based on a physics model called Cahn-Hilliard-Hele-Shaw. This allowed them to reproduce and manipulate the delicate dance between the fluids. In these simulations, a viscous black fluid was first injected into a cell. Then a less viscous transparent fluid was alternated in, back and forth, in carefully timed cycles. Each swap created a new ring of instability.
The result was layer upon layer of fingering explosions — concentric, branching ridges of liquid that looked like the bloom of fireworks. The images earned a spot in the 2023 Gallery of Fluid Motion by the American Physical Society.
Why These Patterns Matter
Carbon dioxide, the dominant greenhouse gas warming the planet, can be captured from the atmosphere or industrial sources. But capturing it is only half the battle. “Removing large amounts of carbon dioxide from the atmosphere is possible,” explained a recent Live Science article. “But it still has to go somewhere.”
That “somewhere” is often underground. One method of carbon sequestration involves injecting CO₂ gas into porous rock formations filled with briny water. This process isn’t as simple as it sounds. The two fluids — gas and water — don’t mix well. And their viscosity contrast can trigger the same kind of fingering instability observed in the lab.
In fact, “the ‘fireworks’ from the simulation show that the number and extent of the fingers can be changed depending on when and how the fluid is injected,” according to Live Science. Controlling this pattern could help engineers keep carbon from seeping back to the surface.
The authors observed a surprising behavior in their simulations. When the fluid alternation was timed precisely, fingers from one cycle would trace the paths laid down in previous cycles. This channeling effect created nested, multi-layered patterns.
In cases with more extreme viscosity differences, the fluid fingers ruptured, forming islands and droplets. These ruptures have not been seen in conventional, continuous injection. “It suggests an additional mechanism is required to rupture the fingers,” the researchers write, “either the thermodynamic phase separation or hydrodynamic injection alternation”.
The team’s work builds on earlier findings showing that changing the injection rate over time — speeding it up or slowing it down — can influence the shape and reach of the fingers. But their new study adds something more: alternating the types of fluids creates a richer palette of behaviors.
To simulate this, the team used a series of advanced mathematical tools. They calculated how the fluid’s concentration changed over time using third-order Runge-Kutta methods and compact finite difference schemes — all designed to track the razor-thin boundaries between fluids. They validated their model against earlier experimental results, ensuring that their virtual fireworks matched what could be seen in the lab.
A Tool for Climate and Beyond
Carbon capture and storage is growing fast. As of 2024, 50 facilities were already operating, with hundreds more in development worldwide. Understanding how fluids behave in these environments is essential for the long-term viability of these projects.
That’s where studies like this one come in. Sometimes, solving the planet’s biggest problems starts with understanding the smallest patterns.
The findings were recently published in Physical Review Fluids.
