26 May 2015 Roll up! The science of detergency.

Everyone knows that detergents clean by lowering surface tension, wetting the surface+oil and causing the oil to "roll-up" into a ball and come away from the surface.

It is rather obvious that this picture is wrong. Just about any surfactant can lower surface tension enough to get wetting and the basic equations of roll-up show that although oil on cotton (a hydrophilic substrate) might have a chance to fall off, we know that it takes a highly specialised blend of surfactants to get great detergency. When we pay extra for a premium detergent we are (on average) getting more detergency through a superior (and presumably more expensive) blend of surfactants. This superior blend will not be lowering the surface tension of the water by an amount that makes any difference to the basic, erroneous, theory. So it must be achieving greater detergency by other means

Now there is more to a detergent than the surfactants. There are many other things such as "builders" that soften the water and help remove inorganic soil, there are enzymes to attack biological stains, there are bleaches and there are clever systems to avoid redeposition of any oil that has been removed.

But we still need a great detergent to remove oil and the explanation is best found in a powerful theory called HLD-NAC. This is explained at length in my Practical Surfactants website, but the key is that when the surfactant is tuned correctly then the oil/water interfacial tension (IFT) is super-low - a factor 10x or 100x lower than that of just any old surfactant. Many experiments have shown that this super-low IFT is necessary for good detergency. But it has been hard to know why, and how to integrate the theory it into the popular idea of roll-up.

I was trying to understand what was going on when I came across the beautiful work of Dr Jaideep Chatterjee which allows us to explore the effect of IFT on roll-up and its close relative snap-off (where some of the oil snaps off as a drop, leaving some of the oil behind which might in turn roll up or snap off). So I wrote theRoll-up and Eötvös app to bring the theory alive.

The key insight is that for most drops most of the time there is no good reason for the oil to do anything, especially for drops on hydrophobic surfaces which give a low contact angle with the oil. If the IFT is lower (with a slightly better surfactant) then almost nothing changes, though, of course, for drops that started with a high contact angle (oil on cotton) this might help. Only when the IFT is very low do drops with relatively low contact angles start to deform strongly from their original shape as a spherical cap. At a critical level the drops are unstable which means that roll-up (or snap-off) is highly likely, especially when there is some agitation in addition to the modest forces of gravity in standard roll-up.

Dr Chatterjee's insight is that there is a critical value of E, the Eötvös number which is the ratio of gravitational to surface energy effects. (Eötvös is pronounced Urtvursh, with the ur sound like the ur in "hurt", though without the r sound). A high value of E means a high chance of roll-up because gravity is larger than surface tension. E increases with the volume of the drop (bigger drops are easier to remove than smaller ones) and a lower IFT also means higher E. A typical surfactant might give an oil/water IFT of 4mN/m but it needs something like 0.1mN/m (a 40x reduction) to get a high E value that will give good detergency.

The theory involves all sorts of complex numerics (4th order Runge-Kutta algorithms are involved) and was a major challenge to write. At the time of writing there are some glitches in the region of 85 to 110° contact angle, but on the whole it gives a good feel of why a given drop might be stable (won't clean) or unstable (will clean) and how the detergent system should be (re)formulated to get great cleaning.

Detergency is far more complicated than a single app. But my view is that the insights from Chatterjee's Eötvös ideas are crucial for understanding what is going on. They even throw light on the vexed question of whether the best surfactant works at the lowest possible IFT (the so-called optimum surfactant where HLD=0) or at a value slightly away from that minimum. The answer, as has been pointed out by the Oklahoma surfactants group, is that when the IFT is super-low snap-off is super fast, but this can leave a residue which is too small to show further snap-off and flows along the fabric. The key is that during the rinse cycle, the IFT for this surfactant is shifted to a slightly higher value and the remaining oil is readily emulsified or rolled up.