Explain the lather in the absence of soap: it’s a tension gradient



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Image of a glass of beer.

Foam is the natural way to make beer even more delicious. Yet not all foams are understood because they seem not to obey the pattern that explains most of the rest. Understanding these atypical foams is important, as they often apply in the food and petrochemical industries. So having a new paper telling us what allows these foams to survive may be of more academic interest.

Foaming with cause

When two different liquids are mixed with a gas such as air, foams and foams are formed. But not all liquid combinations will allow foam to form, no matter how hard you beat it – I’m looking at you, experimental dark chocolate meringues. Although a foam is actually a rather complex beast, the basic physics aren’t too difficult.

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

Let’s take a look at a simple example. A mixture of soap and water will support a lather. Soap is a surfactant with a low surface tension, while water is a liquid with a rather high surface tension. As the film around the containing air bubble thins, the surfactant molecules (soap) can repel each other, expanding the width of the film. This creates a capillary force that draws liquid (water, in this case) into the film.

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

These explanations are based on surfactants and the main point of surfactants is that they don’t really like to mix with the fluid they are put into. The surfactant molecules coat the surfaces of the thin films, creating a sort of sandwich structure that is critical to the forces that keep the foam stable.

Foam for no reason

This made the foam seen in alcohol mixtures a bit mysterious, as they will mix thoroughly. Even more disconcerting, mixtures of alkanes (oils of different weights) will not foam at all. But mix an alkane like decane with a ring 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 found that it still depends on how the liquid’s surface behaves. Think of it like this: imagine a 50/50 blend 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 indeed the case, the surface tension of the mixture should be exactly the average of the surface tension of the two oils.

For oils, this is actually the case. But for other mixtures (such as alcohols, or toluene and decane), the ratio of the two liquids is different in surface than in mass. Initially, this doesn’t matter. But when bubbles form, liquids begin to drain from the films. However, as the film thickness changes, the composition of the surface also changes. Basically, one liquid leaves the surface faster than the other (this is due to the variation in the ratio of surface to volume). This creates a surface tension gradient, which draws the liquid into the film, stabilizing the foam. However, this gradient can only form if the surface tension changes non-linearly with the mass ratio of the two liquids.

Remarkably, this also means that, for thin films of these blends, the surface tension (normally a constant for a given blend) depends on the thickness of the film. This is something I would not have expected, or at least I would have expected for nano-thickness films. But these films are micrometers thick.

A cause to foam for?

I know I get carried away because I like beautiful physics. Why is foam important? Well, agitation and foaming are things that need to be taken into consideration in industrial processes. An engineer may have to build a stabilization time or change the speed of a flow to account for foaming (consider the difference between throwing a beer and pouring a coke). With a better understanding of why and how a foam forms and stabilizes, these processes can be better optimized.

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

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