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Pounding on the bottom of a glass bottle of ketchup is one of life's small annoyances. Getting that sweet, red concoction from its solid phase to a liquid takes too long when you're hungry and could even require messy strategies with a butter knife.

Now a team of scientists has shown that determining the point where the solid transitions to a liquid can be predicted from the properties of the solid phase alone. The research has been in ÌÇÐÄÊÓƵical Review Letters.

The new work focuses on yielding, a phenomenon where a solid-like material starts to behave like a liquid. "This behavior occurs constantly all around us, from desserts like custards that smoothly flow onto your spoon to personal care products like toothpaste that are easily squeezed out of tubes but hold their shape on your toothbrush," Ryan Poling-Skutvik of the University of Rhode Island in the United States told ÌÇÐÄÊÓƵ.

Such substances undergo a change when enough stress is induced; the point of change is called the "yield transition," and the substance is called a "yield stress fluid."

"But it also occurs in more complex applications to control how tissues grow by accommodating cell growth and 3D printing, where fluids must be flowed through a nozzle and then solidify when finished," Poling-Skutvik continued.

"Even though we engage with this phenomenon daily, scientists have struggled to relate the yielding phenomenon to material properties for over a century. Our work demonstrates that this transition—at least in part—can be understood by how solid-like the material is at rest."

Yield stress fluids (YSFs) often have a complex, nonlinear response to stress. Below the yield transition they deform in a recoverable way, like a viscoelastic solid, but above it the transition is definite and nonrecoverable.

Although the first study of such "plastic flow" 111 years ago, the precise mechanisms of the physical change have so far been little understood, in part because defining and identifying yielding hasn't been settled, with multiple protocols in place. But one protocol commonly used to identify yielding is "large amplitude oscillatory shear," where sinusoidal stresses and strains are applied to the material at varying amplitudes.

The material has a periodic response in two important ways: the "storage modulus," proportional to the average energy stored per cycle, and the "loss modulus," proportional to the average energy dissipated per cycle due to internal friction.

In many YSFs an overshoot in the loss modulus occurs at large amplitudes, and such nonlinearity marks the yield transition due to nonrecoverable strain. At that point, the loss modulus is at a maximum.

Poling-Skutvik and his team first used a YSF gel made of a polymer distributed in a mixture of water and alcohol decanol. Its density depended on the polymer concentration, which was changed over the course of measurements.

Their experimental apparatus consisted of two parallel plates, and the gel was shaken between them by rotating one of the plates at different frequencies and amplitudes until they induced a yield transition.

By measuring the forces applied to the gel (stress) and its deformations (strain), they were able to calculate the storage and loss moduli. The moduli have units of pressure, force per unit area, but their ratio, called the "loss tangent," is a pure number without dimension; it reflects the degree the substance performs as a solid to how it performs as a liquid.

They also performed the same measurements for other YSFs, such as polymer-linked emulsions (an example is mayonnaise stabilized with a polymer like xanthan gum), colloidal gels such as gelatin, and fibrillar networks, like the extracellular matrix in animal tissues.

Plotting and analyzing the height of loss moduli overshoot versus the loss tangent, they noticed it had a common feature for many YSFs: the overshoot depended on the loss tangent in the same way for the fluid of all compositions of the YSFs tested.

This was surprising, they said, because the loss tangent is determined when the substance is solid-like, whereas the overshoot occurs at the yield transition to a liquid.

With this new knowledge, the group, with lead author Daniel P. Keane, also of the University of Rhode Island, modeled the physics analytically using a model developed just a few years ago, called the KDR model, which is able to accurately model many of the yield transition's features.

They were able to show, both numerically and by solving the model approximately, that the universal transition height as a function of the loss tangent was well accounted for by the KDR model.

Poling-Skutvik said, "Our results can help to simplify the design of new materials to focus on their properties at rest rather than having to directly address the more complicated question about the yield transition itself."

Their work has applications to many substances in food sciences and industrial production, from toothpaste to colloidal slurries used in battery manufacturing.

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