Explaining foam in the absence of soap: It’s a tension gradient
November 10, 2020
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by admin

Image of a glass of beer.

Foaming is nature’s way of making beer even more delicious. Yet not all foams are understood because they don’t seem to obey the model that explains most of the rest. Understanding these atypical foams is important, because they often apply in the food-processing and petrochemical industries. So having a new paper that tells us what allows these foams to survive may be of more than academic interest.

Foaming with cause

Foams and froths form when two different liquids are mixed with a gas such as air. But not all liquid combinations will allow a foam to form, no matter how much hard you beat it—I’m looking at you, experimental dark chocolate meringues. While a foam is actually a rather complex beast, the basic physics is not too difficult.

A foam is basically a set of air bubbles, enclosed by thin films that form a self-supporting network. The thin films are subject to two competing forces. The liquid trapped in the interface slowly drains away due to gravity. This causes the layer enclosing the air to thin, which will lead to the eventual collapse of the foam. But the loss of fluid is often slowed (or even entirely prevented) by two factors.

Let’s look at a simple example. A mixture of soap and water will support a foam. Soap is a surfactant with a low surface tension, while water is a liquid with quite a high surface tension. As the film around the air bubble that contains them thins, it can cause surfactant molecules (the soap) to repel each other, expanding the width of the film. This sets up a capillary force that draws liquid (water, in this case) back up into the film.

In some cases, the thinning of the interface also generates a gradient in surface tension. Essentially, the water drains out, leaving a higher soap concentration. But soap has a lower surface tension, so there is a difference in surface tension between the areas of high and low soap concentration. This drags the water back into the film. That keeps the bubble it encases stable.

These explanations rely on surfactants, and the main point about surfactants is that they don’t really like to mix with the fluid that they are put in. The surfactant molecules line the surfaces of thin films, creating a kind of sandwich structure that is key to the forces that keep the foam stable.

Foaming without cause

This has made the foam observed in mixtures of alcohols a bit of a mystery, since those will mix thoroughly. Even more baffling, mixtures of alkanes (oils of different weights) will not foam at all. But, mix an alkane like decane with a ringed molecule like toluene and the mixture will foam. None of these liquids act as surfactants, so how do they support a foam?

A group of French researchers has discovered that it still comes down to how the liquid surface behaves. Picture it like this: imagine a 50/50 mixture of two light oils. The question you should ask is, “What is the composition of the surface?” The immediate and intuitive answer is that it should be almost the same at 50/50. If this is truly the case, then the surface tension of the mixture should be exactly the average of the surface tension of the two oils.

For oils, that is indeed the case. But for other mixtures (like alcohols, or toluene and decane), the ratio of the two liquids is different on the surface compared to the bulk. Initially, this doesn’t matter. But when bubbles form, the liquids start to drain from the films. However, as the thickness of the film changes, the composition of the surface also changes. Essentially, one liquid leaves the surface faster than the other (this is due to the change in surface area to volume ratio). That creates a gradient in surface tension, which pulls liquid back into the the film, stabilizing the foam. However, this gradient can only form if the surface tension changes nonlinearly with the bulk ratio of the two liquids.

Remarkably, this also means that, for thin films of these mixtures, the surface tension (normally a constant for any given mixture) depends on the thickness of the film. That is something I would not have expected—or at least I might have expected it for nanometer-thick films. But these films are micrometers thick.

A cause to foam for?

I know I get carried away because I just like the nice physics. Why does foaming matter? Well, agitation and foaming are things that have to be taken into account in industrial processes. An engineer may have to build in a settling time or change the rate of a flow to account for foam formation (consider the difference between pulling a beer and pouring a coke). With a better understanding of why and how a foam is formed and stabilized, these processes can be better optimized.

Physical Review Letters, 2020, DOI: 10.1103/PhysRevLett.125.178002 (About DOIs)

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