May 11, 2026
Maureen Searcy
How UChicago physicists delayed the formation of viscous fingers between fluids
At a glance: Viscous fingering occurs when a thin fluid pushes against a thick fluid in a confined space and pierces through, forming branching, finger-like protrusions. A recent study reveals that changing the shape of the interface where the fluids touch can delay onset and slow the growth of the branches, promising improved efficiency for industrial and environmental processes.
A stable solution
When they reach the bottom of a pump-action soap dispenser, frugal handwashers might fill the bottle with water to push out the last bit of soap left in the tube. But usually, the water drills right through the soap and jets out a slightly sudsy splash.
When you push a less viscous fluid like water into a more viscous fluid like soap in a confined space like a narrow tube, the place where the two fluids meet can be unstable, and the runnier liquid might find a path of least resistance.
Before the water forms a single channel through the soap, tiny protuberances form at the initially smooth interface, or the place where the fluids touch, in a phenomenon called viscous fingering. In certain types of confined spaces, the fingers form a branching pattern.
“The viscous fingering instability is one of the most-studied examples of pattern formation, consistently yielding new insights and variations into the formation of branched structures in the natural world, such as rivers splitting into smaller streams,” said Sidney Nagel, Stein-Freiler Distinguished Service Professor of Physics.
In a new study published in Science Advances, Nagel’s team discovered that physically changing the shape of the interface between two fluids of different viscosity increased stability and reduced finger formation.
This breakthrough could have ramifications for industrial processes and environmental applications. For instance, when oil is extracted from the earth, carbon dioxide is often used to push it out of reservoirs, but if the interface becomes unstable and forms fingers, the gas can shoot straight through the oil to the extraction well. Engineers are then pumping up gas, leaving oil in the ground.
Shapeshifting
When one fluid meets another in a confined space, the stability of the interface depends on a few factors: how easily the fluids mix, the difference in their viscosity, and how fast the fluids are moving. If the interface becomes unstable, it gets wavy and fingers form.
For fluids that don’t readily mix, such as oil and water, surface tension serves as a sort of skin, helping to stabilize the edge between them. For miscible fluids—which can dissolve together into a uniform solution like water and honey, or in the case of the study, water and glycerol—there is little to no surface tension. This would suggest greater instability, with finger formation an inevitability, yet sometimes they never develop.
For fingers to form, the interface between runny and thick has to be sharp and abrupt, like a cliff. But if the fluids are too similar in viscosity, the interface won’t be sharp enough. If the runnier fluid is injected slowly enough, it has time to seep into the thicker fluid, and the interface won’t be abrupt enough. But what if you change the nature of the interface without changing those factors?
“We wanted to know if we could physically change the shape of the interface without altering the viscosity ratio, and whether there’s a direct correlation between its shape and the stability,” said Zhaoning Liu, a graduate student in the Nagel lab and first author on the paper.
Cliff vs. slope
Viscous fingering instability is often studied using a Hele-Shaw cell, an apparatus consisting of two flat, parallel plates separated by an extremely thin gap. The team filled the gap with a high viscosity solution. Then they injected a low viscosity solution through a small hole in the top plate. As the thinner liquid spread out from the center, pushing the thicker liquid outward, the advancing edge between them formed a blunt curve, with a fairly flat face. Fingers eventually formed.
Then they repeated the technique, sliding the bottom plate side to side, a process called shearing, varying how fast and how far, to see how the interface changed. “When we applied shear, the interface bulged out,” said Liu, forming a pointier curve. The motion altered its structure: the sliding stretched the cliff face into a gentle slope. “So the transition from the inner to outer fluid smoothed out.”
The team found that the farther and the faster they slid the plates, the longer it took for fingers to start forming, and once they did, they grew more slowly—indicating that there is a direct correlation between the interface shape and its stability.
| [This video includes flashing imagery that may affect photosensitive viewers.] A low viscosity fluid displaces a high viscosity fluid under stationary conditions (left). The application of shear (right) delays the onset and slows the growth of fingers. (Adapted from video by Zhaoning Liu.) |
In the circular experimental setup, fingers grew in all directions. Yet because the motion was side to side, the fingers didn’t all react the same way. Those growing parallel to the sliding motion were suppressed, while those growing perpendicularly reacted differently. This paper focused on the parallel fingers, while a future publication will explore the perpendicular finger development. Liu would also like to investigate exactly how much the interface shape and how much the viscosity ratio contribute to the instability.
“This study demonstrates a new way to control and delay the instability onset,” said Nagel, “which plays a role in so many industrial processes involving fluids, from oil extraction from the earth to carbon sequestration.” One climate change mitigation effort has been to lock carbon dioxide inside saltwater aquifers, and the ability to control viscous fingering could be the key to trapping more of the greenhouse gas deep underground. “There is a long road ahead to take this research and apply it to such problems, but this is a start.”
Citation: Zhaoning Liu et al., Effect of translational shear on interfacial structure in the viscous fingering instability. Sci. Adv. 12, eaeb2907 (2026).
Funding: National Science Foundation