## Foam Basics

Everyone finds foams difficult to understand. This is for two broad reasons. The first is that the there are many different processes going on during the life and death of a foam so no single simple theory can describe everything. The second is that those different processes are often presented in different ways by different people so it is hard to see how they all fit together in the area of foam which happens to be of interest at the time. There's nothing we can do about the first reason. This guide is an attempt to address the second reason. Not only do you get the basic theory, you can also explore it live by adjusting parameters and seeing what happens to the properties of interest.

So just start exploring the bits which are of interest to you, playing with parameters till you understand what's going on, then move to the next area. Gradually your grasp of the big picture will improve dramatically.

There are two things people know about their surfactant: its surface tension γ and its critical micelle concentration, cmc. These have a dramatic effect on foaming properties, along with two other key properties, Γ, the excess surface concentration and A the head area. Γ can be found from the slope of the simple measurement of γ v surfactant concentration. That slope tends to be a constant, Γm once γ has decreased by 20mN/m from the starting value of pure water. This allows us to produce our first simple view of how the four properties inter-relate using the sliders for the two given properties.

### Foam Basics

γ mN/m
cmc (µM)
Γm mol/m²
a Å²

The curve is a simplified Langmuir-Szyszkowski plot. In reality Γm is obtained by fitting the data from a real experiment measuring surface tension v. surfactant concentration.

I considered adding a "mixed Γ" option which produces curves for mixtures of primary and secondary surfactants. But I decided against it because outside the academic lab it's probably more work to get the key parameters for the model than it is to measure the curve of your mixtures directly. Mixed surfactants are hugely important, but the formulae for describing them don't usually, as far as I can tell, lead to great practical enlightenment.

What may seem surprising is that Γm does not depend on cmc but, in this model, only on γ. This is indeed a simplification but Γm does not change strongly between surfactants. What is crucial is how quickly a high Γ value is reached which is governed by the cmc (for a single surfactant) and by partition effects (e.g. when lauric acid is added to SLES/CAPB foam, as discussed in Making).

The surface tension affects foam in two obvious ways, though in fact they are the same thing:

• The energy need to increase the surface area A is γδA/δt, so a low γ means more foam for less energy.
• The pressure inside a foam of radius R that contributes to its self-destruction is 2γ/R

So a surfactant which reaches the lowest surface tension for the least amount of surfactant is, in general, going to give an easier, longer-lasting foam. For example, foams with smaller radii tend to last longer because they drain more slowly and are desirable because they feel "richer" - but to halve the radius requires halving γ for the same pressure inside the bubble. Only surfactant at the interface lowers γ so a low cmc is required for good foaming.

Of course if it were that simple there would be no mysteries about foam. In practice many other effects are important, as discussed in the following.