Tikalon Blog by Dev Gualtieri

Gel and Granular Flow

June 20, 2022

As a Baby Boomer, I remember the ttelevision commercials that insisted that "There's always room for Jell-O," the trademark of a popular gelatin dessert.[1] Aside from an occasional beer on a summer's night, I'm not much of a drinker, so I've never had a jello shot. The popular Middle East confection, Turkish delight is made from corn starch, not gelatin, but my wife makes a version using unflavored gelatin and orange juice, and it's very good. Recipes for gelatin-based Turkish delight can be found on the Internet.

"Turkish Delight," xkcd comic 1980, by Randall Munroe (b. 1984). My children enjoyed The Chronicles of Narnia: The Lion, the Witch and the Wardrobe, the film adaptation of the C.S. Lewis novel, the The Lion, the Witch and the Wardrobe. (Licensed under a Creative Commons Attribution-NonCommercial 2.5 License. View on the xkcd website.)

While doing research on capacitance touch sensors, I made an artificial finger from a water gel of gelatin. A gelatin gel seemed to be a good simulation of a finger both mechanically and electrically. The human body is mostly water,[2] as is a gelatin gel, which is usually mixed to a ratio of 0.125 ounce to 1 cup of water. I wanted a rigid finger, so I increased this to 0.25 ounce, which is the contents of a typical consumer gelatin packet. I used a finger of an acetonitrile glove as a casting mold.

Since I had this artificial finger and one of those cardboard sleeves that insulate your hand from the hot exterior of a thin paper cup, I decided to try an experiment on how well such sleeves protect your fingers from heat. That's when I discovered that my water gel finger melted at temperatures not far above room temperature, about 30-35 °C. Two Japanese scientists from the Tokyo University of Agriculture and Technology and Tokyo Metropolitan University have recently published a study demonstrating that melting gelatin, when heated from below, shows mechanical properties similar to falling beds of granular materials such as sand.[3-4] Their study is published as an open access paper in Scientific Reports.[3]

Granular materials flow under gravitational force while maintaining some rigidity, as landslides and avalanches demonstrate, and their gravitational instability is unpredictable and not well understood.[3] The complex properties of granular materials depend on the friction between grains, the size dispersion of the grains, and the shape of grains.[3] External force propagate in localized paths known as a force chains, and it's been found that jamming in granular systems is similar to the glass transition.[3] Gels are like granular materials at microscopic scale, since their polymer or protein chains are similar to the granular force chains that underpin the solidity of granular materials.[4]

Experimental setups for gel and sand flow experiments

Left, the experimental setup for water gels. The glass sample chamber had dimensions of 30 mm x 126 mm x 2.4 mm. Right, the experimental setup for granular systems. There were two different sample chambers with dimensions 150 mm x 75 mm x 1.2 mm, and 90 mm x 65 mm x 2.4 mm with a manually set sedimentation angle. (Diagrams from ref. 3,[3] licensed under a Creative Commons Attribution 4.0 International License. Click for larger image.)

In their experiments on the gravitational instability of gels, the Japanese scientists used high speed cameras to examine the fluidization of thin beds of sand and gelatin solutions.[4] In the sand experiments, beds of sand grains were formed in either air or water, inverted, and then observed as the base began to fall out.[4] For gelatin, they prepared two layers of different concentration, one on top of the other with the lower layer prepared to completely fluidize first.[4] When heated from below, the upper layer would eventually destabilize and fall.[4] The gelatin solutions were prepared with 3-14 wt% using pure water as a solvent.[4] As an aid to visualization, tracer particles with a density close to that of the gelatin were added at 0.05 wt%.[3] images were recorded with a digital camera at one second intervals.[3]

In the experiments, a finger pattern was observed that is much like the Rayleigh–Taylor instability in fluids when a lighter fluid is pushing a heavier fluid.[3-4] In both the sand and gelatin systems, fingering instabilities were seen in which thin fingers of material fall into the lower material (or air/water), and these resemble raindrops falling down a window.[4] New fingers would appear in between existing ones over time, and the interface between the liquid and solid-like parts would recede.[4] One difference is that in granular materials, new fingers form between existing fingers, something that's not observed in fluid systems.[3]

The researchers found that falling sand and melting gelatin heated from below exhibit the same destabilization mechanism, and their destabilization parameters scale with the flowing, fluidized region thickness.[3-4] The thickness of this region depends on key parameters such as the velocity of the receding front, and the distance between the fingers, a relationship known as a scaling law. Scaling laws connect physical phenomena which seem completely different, but their mechanisms are related at a deeper level.[4] In these materials, the existence of force-bearing networks connect their physical behavior.[4] It also appears that the temporal evolution of the height of the fluidized layer is determined by the strength of the network.[3] This research will enhance our understanding of avalanches, landslides, and industrial flow processes, all of which can be destabilization under the force of gravity.[4]

Dependence of the sol-gel transition temperature on gelatin concentration.

(Graph from ref. 3,[3] licensed under a Creative Commons Attribution 4.0 International License. Click for larger image.)

Gel and Granular Flow

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