Modeling how gels squish and flow

Cells, toothpastes, and shower gels: Each is a network of particles suspended in fluid. The particles associate with each other, forming a structure that allows the gel to exhibit an elastic response.

Colloidal gels have been described using continuum models, which view gels as continuous materials, and discrete particle models, complex systems that show fine structural changes. Zelai Xu and James J. Feng amended previous models with an elastic strain, representing the material’s ability to bounce back; and a structural parameter, which represents the degree to which particles bond with each other. Their new model bridges previous approaches — a compact continuum model that reflects, to some degree, the structural evolution of a gel under stress.

The pair tested their model with three commonly used flow protocols, comparing their results to experimental conclusions. Their model captured three regimes — nonyielding, yielding, and degelation — as the gel evolved from a solid-like state toward a fluidized state under imposed shear stress or strain rate.

The duo observed hysteresis at the transition between each pair of neighboring regimes and a delay between stress application and yielding — a phenomenon seen in experimental data. When moving through a circular tube, the model gel exhibits all three regimes at different radial positions.

“The model could be linked to applications that are very tangible,” said Feng, “One of those is bioprinting. This process has to be facilitated by the yielding of the gel: it has to be soft enough to flow easily and re-solidify on the substrate.”

Source: “A structural model for yielding and degelation of colloidal gels,” by Zelai Xu and James J. Feng, Journal of Rheology (2025). The article can be accessed at https://doi.org/10.1122/8.0000978 .