## Friday, April 27, 2012

### A head covered with foam

kw: observations, products, analysis

I am sure you've seen the ads for shampoo, where someone squeezes out an ounce or two of shampoo and lathers up. You see lather flying everywhere. I use one of those advertised shampoos, and I use a drop about the size of a nickel. I began to wonder, just how much does it take to clean my hair?

For most of us, we're really trying to remove oils that our scalps produce, and the amount is really quite small, even for someone with "oily hair". The surfactants in shampoo bind to an amount of oil roughly equal to their own volume. I haven't found any record of some number of milligrams or micrograms of oil that is "normal", so we'll have to make a reasonable estimate.

I have found by observation that if I get my hair very clean, it is pretty flyaway (even if it is no more than two inches long). Within a few hours, it gets more manageable when I brush or comb it, from the first coating of oil. So I estimate that enough oil is produced in about two hours to form a monolayer on all the hair, and production probably continues at this rate all day. By day's end, the hair is not noticeably oily, because a dozen monolayers is still not much oil. Let's calculate how much.

When I had a full head of hair, I kept it about as long as I do now, some 5 cm (2 inches). My hair was brown (getting gray these days), so the number of hair strands was about 50,000. That comes to 250,000 cm or 2,500 m of hair (8,200 ft). Brown hair averages about 60 µm in diameter, so its circumference is about 190 µm, or 0.00019 m. Multiply by 2,500 to get 0.475 m². These are rough calculations, so we'll round it to half a square meter. Just by the way, only about half my scalp has hair now, but the bald portion gets oily, so oil production hasn't slackened off.

To get the volume of one monolayer, now we just need the thickness. Skin oils are hydrocarbon based, so they'll have a sausage shape, with a diameter in the range of half a nanometer, or about 5Å (5 angstroms). 0.5m²×0.5nm = 2.5E-10 cubic meters, or 0.00025 cc, or 0.25 cubic mm. Twelve such volumes amount to 3 cubic mm.

So, the amount of oil you need to remove, if you wish to remove it all, is about 3 cubic mm. That is a dot the size of a pin head. Can we really get away with using a similar amount of shampoo? Would it really work? I have yet to make the experiment. My nickel-sized dollop of shampoo is about half a cc, or 500 cubic mm. I'll try smaller and smaller amounts to see how much does an effective job. I suspect there is a lot more at work here than just oil removal.