A critical relationship between gravitational instability and physical gels and granular media is discovered in research

_{When destabilised sand beds (a) and gels (b), comparable “fingering” instabilities are seen to emerge over time (left to right). Credit: Tokyo Metropolitan University}

The behaviour of granular materials and melting gels is strikingly similar, according to researchers at Tokyo Metropolitan University. They discovered that falling sand beds behave similarly to melting gelatin when heated from below, notably in terms of how crucial parameters scale with the thickness of the fluidized zone. Their results, which were published in Scientific Reports, provide significant contributions to our knowledge of gravity-induced instability, as observed in avalanches, landslides, and industrial transport systems.

While sand and jelly may appear dissimilar, they have several physical qualities. Sand is composed of billions of grains of solid material that may flow as a liquid or clog pipes as a solid. When chilled, materials such as gelatin solutions behave like a solid. When examined in detail, it is clear that the solidity of gels is supported by networks of polymer or protein that crisscross the material; this is similar to how “force chains,” networks of grains pushing against one another, give sand its apparent solidity. This interesting nexus of solid and liquid-like behaviour is at the heart of a variety of natural events, including avalanches and landslides, but remains little understood.

These parallels prompted Dr. Kazuya Kobayashi and Professor Rei Kurita of Tokyo Metropolitan University to directly analyse the fluidization of physical gels and sand beds. They used high-speed cameras to monitor the fluidization of thin layers of sand and gelatin solutions. In the case of sand, pre-formed beds of grains in either air or water were inverted and the base was seen to fall out. For the gelatin, two layers were prepared, one on top of the other, with varying concentrations of gelatin. Concentrations were set to ensure that the bottom layer fluidized entirely first. When the material is heated from below, it destabilises and begins to collapse.

The scientists discovered fingering instabilities in both systems, where thin material fingers fall into the material (or air/water) below, simulating rain droplets pouring down a window. New fingers would grow in between existing ones over time, and the interface between the liquid and solid-like sections would erode. Additionally, the team was able to identify a “fluidized” interface zone above the point at where the fingers begin using a novel imaging approach. The thickness of this area was shown to be highly associated with critical factors such as front receding velocity and finger distance. This type of interaction is referred to as a “scaling” relationship, and it is critical in physics for connecting events that appear dissimilar at first glance but are related at a deeper level by their processes. This is significant evidence in this case for the fact that the commonalities between the materials, namely the connectedness of a force-bearing network, underpin their macroscopic physical behaviour.

The team’s comprehensive studies shed light on how granular materials and gels collapse under gravity, having implications for both natural fluidization events and the design of granular material transport systems on industrial scales.

Further information: Kazuya U. Kobayashi et al, Key connection between gravitational instability in physical gels and granular media, Scientific Reports (2022). DOI: 10.1038/s41598-022-10045-x

Journal information: Scientific Reports

Source: Tokyo Metropolitan University