Tokyo, Japan – Researchers from Tokyo Metropolitan University have solved a long-standing mystery behind the drainage of liquid from foams. Standard physics models wildly overestimate the height of foams required for liquid to drain out the bottom. Through careful observation, the team found that the limits are set by the pressure required to rearrange bubbles, not simply push liquid through a static set of obstacles. Their approach highlights the importance of dynamics to understanding soft materials.
When you spray a foam on a wall, you will often see droplets of liquid trailing out the bottom. That is because foams are a dense collection of bubbles connected by walls of liquid, forming a complex labyrinth of interconnected paths. It is possible for liquid to travel along these paths, either leaving the foam or sucking in liquid which is brought into contact with the foam. This "absorptive limit" is determined by a quantity known as "osmotic pressure", which reflects the energy change when bubbles are squished together, changing the contact area between liquid and gas.
Or so people thought. Throughout the years, scientists have been perplexed by simple calculations which show how much height a certain foam needs to be for this limit to be met. While the osmotic pressure alone, determined from bubble sizes and surface tension, might show that you need a meter or so of foam height before this limit is met, researchers could see that a foam tens of centimeters high will easily allow leakage of liquid. From cleaning products to pharmaceuticals, foams are a part of everyday life; to design products optimized for specific applications e.g. foams which resist drainage, it is vital that we understand the physical mechanisms at work.
A team led by Professor Rei Kurita of Tokyo Metropolitan University has been looking at drainage in simple foams. The team used various surfactants to create a library of different foams with different properties, sandwich them between transparent plates and stand them upright to reveal what is going on inside while they drain, if at all. Firstly, they discovered a universal behavior where the height at which drainage starts is inversely proportional to the liquid fraction of the foam, independent of surfactant type or bubble size. Their analysis of the limit yields an "effective osmotic pressure" at which the absorptive limit is met significantly lower than what is expected from bubble sizes and surface tension.
Going back to the drawing board, the team looked directly inside the foam with a video camera. For foams which have just made it to the drainage point, they discovered that liquid wasn't simply pushing through the maze of connections but causing the bubbles themselves to rearrange. They found that the limit where drainage occurs is determined not by surface tension but "yield stress," the amount of pressure required to rearrange bubbles. Importantly, this model gives heights for draining foams which match up with reality.
This result upends the fundamental picture of how we look at foam drainage, from a static picture of liquid moving through gaps, to a dynamic one where the gaps themselves can move. The team hopes their findings inspire new insights into the behavior of soft materials, as well as approaches to designing better foam products.
This work was supported by JSPS KAKENHI Grant Number 20H01874.
