Predicting When Ketchup Will Start Flowing
Complex fluids such as ketchup or toothpaste can switch from a solid-like state to a liquid-like state when subjected to a stress, such as shaking or squeezing. The details of this change can be crucial in areas such as food science and cosmetics. A research team has now shown that the point at which the solid-to-liquid transition occurs can be predicted from the properties of the substance while it is still a solid [1]. This insight could guide the design and control of this industrially important class of fluids.
Materials that undergo such a stress-induced change in flow properties are called yield stress fluids (YSFs), and they include foods like custard and consumer products like face creams, says Ryan Poling-Skutvik of the University of Rhode Island in Kingston. The so-called yielding transition “controls how much force you need to apply to squeeze toothpaste out of the tube,” he says. It also determines the processing conditions for many polymeric substances used in manufacturing.
YSFs are viscoelastic materials, which exhibit behaviors partway between solids and liquids. These materials are often characterized by two properties: The storage modulus G' represents the amount of energy stored in the material as a result of deformation (as in a compressed spring), while the loss modulus G" represents the amount of energy dissipated through internal friction (viscosity). The value of each parameter measures the degree to which the material is, respectively, more solid-like or more liquid-like.
For the more solid-like case, Poling-Skutvik says, imagine a YSF as having a microstructure “like a network of rubber bands” representing chain-like polymer molecules. With enough applied stress, flow begins, and the bands start to slide past one another, dissipating energy through friction. “For over a century we have known that many materials undergo this yield transition,” Poling-Skutvik says, “but we have never been able to predict when the transition occurs.”
To study the transition, the team made measurements on a model YSF gel comprised of a polymer dispersed in a mixture of water and the alcohol decanol. The mixture has a viscoelastic, gel-like consistency that is adjustable by changing the polymer concentration. Poling-Skutvik and colleagues induced a yielding transition by shaking this fluid between two parallel plates, using a standard technique: One of the plates executes rotational oscillations at various frequencies and amplitudes, rather like the shaking of a ketchup bottle. From measurements of the relationship between force and material deformation (stress vs strain) in the fluid, they calculated G' and G".
Many YSFs are known to have an “overshoot” of G" at the yield transition, where the value of this quantity reaches a maximum as the amplitude of the shaking increases, only to decrease at still higher amplitudes [2]. The researchers identified a universal feature of this overshoot for many YSFs: The dependence of the overshoot on the ratio G"/G' in the fluid at rest was the same for all the compositions tested. This ratio, called the loss tangent, is a measure of how much the material behaves like a liquid compared to how much it behaves like a solid.
What’s more, the researchers found similar behavior for other types of YSFs measured previously, such as hydrogels and colloidal suspensions (where microscopic particles dispersed in a solvent clump together in chains and networks). All fit onto the same curve of G" overshoot plotted against the loss tangent.
The researchers say that this result is surprising because the loss tangent is evaluated when the material is solid-like, whereas the G" overshoot occurs during the yielding transition. Thus, says Poling-Skutvik, the results imply that “the same physics that controls how polymers fluctuate under small deformations [when the material is a solid] also plays a role in how they flow under large deformations.” And he says the same applies to other, nonpolymeric YSFs.
The findings are new and counterintuitive, says soft-matter physicist Thibaut Divoux of the Ecole Normale Supérieure in Lyon, France. They raise many questions, he adds, especially because the relationship holds for materials with very different microstructures. In fact, Divoux found the same behavior when he applied the researchers’ analysis to published results on materials like gelatin gels that are not YSFs because the yielding is not reversed when the stress is removed.
Yielding of YSFs occurs in many industrial processes, says Poling-Skutvik, such as colloidal slurries used in battery manufacture and plastics used for 3D printing. He believes the findings will help in the design of such materials, for example, plastics that flow through the printing nozzle but hold their shape once delivered. Divoux agrees that the relationship “can serve as a guideline to make materials such as those used in food and cosmetics.”
–Philip Ball
Philip Ball is a freelance science writer in London. His latest book is How Life Works (Picador, 2024).
References
- D. P. Keane et al., “Universal relationship between linear viscoelasticity and nonlinear yielding in soft materials,” Phys. Rev. Lett. 134, 208202 (2025).
- G. J. Donley et al., “Elucidating the G″ overshoot in soft materials with a yield transition via a time-resolved experimental strain decomposition,” Proc. Natl. Acad. Sci. U.S.A. 117 (2020).