Updated March 26, 2026
- Resting-state loss tangent predicts how yield stress fluids transition from solid to liquid
- The relationship held across four structurally different material classes
- The KDR model links calm-state properties to nonlinear yielding behavior
Squeeze a bottle of ketchup and nothing happens. Squeeze harder and everything happens at once. That abrupt snap from solid to liquid has a name in physics: yield stress. And for more than a century, no one could predict when it would happen.
The problem was not a lack of trying. Since Eugene Bingham first described plastic flow in 1916, generation after generation of materials scientists attacked the question the same way. They broke things. They applied force, watched structures collapse, and recorded what happened at the moment of failure. The approach was logical, thorough, and consistently insufficient.
Then a team led by Daniel Keane, a chemical engineering PhD student at the University of Rhode Island, found the answer by looking away from the chaos entirely.
What is a yield stress fluid?
A yield stress fluid behaves as a solid under gentle force but flows like a liquid once a critical threshold is crossed. Ketchup, toothpaste, concrete, and bioinks are all yield stress fluids, held together by internal structures that collapse under sufficient stress.
A century spent breaking things
The standard approach to these materials has always been direct. Apply increasing force, watch the structure fail, and record what happens at the breaking point.
The technique is called large amplitude oscillatory shear. It gives researchers a stress-strain curve with a characteristic overshoot, a peak in the loss modulus that signals the moment of yielding.
But this peak varies wildly. Polymer gels, colloidal suspensions, emulsions, and fibrillar networks all yield differently. No single framework could connect them.
"For over a century we have known that many materials undergo this yield transition," said Poling-Skutvik, an assistant professor in chemical engineering and physics at URI. "But we have never been able to predict when the transition occurs."
Key figure
111 years
The duration between the first study of plastic flow and a predictive model for yielding.
One number from the quiet before the storm
Keane, working with Poling-Skutvik and three collaborators, tested four structurally different material classes. What they found was remarkably consistent.
The height of the yielding overshoot appears to depend on a single quantity measurable while the material sits undisturbed. That quantity is the loss tangent: a dimensionless ratio of energy dissipated to energy stored in each deformation cycle.
The correlation held across all four classes. Polymer gels and colloidal gels, materials built from entirely different microstructures, followed the same relationship. So did polymer-linked emulsions and fibrillar networks.
This is a single study, and the pattern awaits independent replication. But within the data, the consistency is genuinely striking.
To explain the relationship, the team turned to the KDR model, an analytical framework developed in 2021 by Krutarth Kamani, Gavin Donley, and Simon Rogers at the University of Illinois Urbana-Champaign. The model describes universal links between resting-state linear viscoelastic properties and nonlinear behavior at yielding. Kamani and Rogers, fittingly, are co-authors on this new paper.
The position of the overshoot, where on the strain axis yielding occurs, depends on both resting properties and flow characteristics. But the height, how dramatically the material yields, seems to be encoded in the calm before the transition.
For over a century we have known that many materials undergo this yield transition, but we have never been able to predict when the transition occurs.
Ryan Poling-Skutvik, University of Rhode Island
Four materials, one pattern
Soft-matter physics is full of models that work beautifully for one class of material and fall apart when applied to another.
Consider the differences. Polymer gels hold themselves together through covalent crosslinks. Colloidal gels rely on particle-particle attraction. Emulsions are droplets jammed against each other. Fibrillar networks are tangled fibers.
These materials have almost nothing in common structurally. Yet they all appear to encode their yielding behavior in the same resting-state measurement. It is the kind of quiet elegance that invites skepticism, which is exactly the right response to a single paper testing four material classes.
"This behavior occurs constantly all around us," Poling-Skutvik noted, "from desserts like custards that smoothly flow onto your spoon to personal care products like toothpaste."
There is something pleasingly ironic about the finding. A century of increasingly sophisticated destruction testing, and the answer was sitting in the material's rest state all along.
Designing materials without destroying them first
The practical implication is direct. Engineers designing new soft materials, from 3D-printable bioinks to industrial coatings, typically need extensive LAOS testing to characterize yielding. That testing is slow and destroys the sample.
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→If resting-state properties reliably predict yielding behavior, the design loop tightens considerably. A simple linear viscoelastic measurement, gentle enough to leave the material intact, could replace the expensive trial-and-error cycle.
"Our results can help to simplify the design of new materials to focus on their properties at rest," Poling-Skutvik said, "rather than having to directly address the more complicated question about the yield transition itself."
The work, published in Physical Review Letters by the five-member team from URI and UIUC, opens a question worth watching. Can the KDR model extend to material classes beyond the four tested? Biological tissues, food systems, and construction materials all exhibit yield stress behavior.
If the loss tangent relationship holds there too, a century-old puzzle may have found its resting place.
Or maybe we could say that the ketchup is out of the bottle? Ka-ching.
Sources
- Primary Research: Solid-Phase Properties Predict the Liquid-Phase Behavior of Yield Stress Fluids (Keane et al., Phys. Rev. Lett. 134, 208202, 2025)
- Additional Context:
- A Solid Hint About When Fluids Will Flow (APS Physics Viewpoint)
- Ketchup: Solid phase properties reveal when yield stress fluids will flow (Phys.org)
Fact Check: Claim-by-Claim Verification Verified
All claims verified against the published paper and supporting sources. Two factual errors were identified and corrected during editorial review.
Sources used for verification
- Universal Relationship between Linear Viscoelasticity and Nonlinear Yielding - journals.aps.org
- Predicting When Ketchup Will Start Flowing - physics.aps.org
- Your ketchup will see you now - phys.org
- KDR Model (2021) - journals.aps.org
