paint dry.
© 2002 David Drysdale

In around 1994 I went to an hour long seminar on paint drying.

It was rather interesting.

No, really.

You see, it turns out that making paint is actually a delicate balance between three different processes; good paint has its chemical composition finely tuned so that the speed of all three matches up.

Firstly and most importantly, the paint dries. Once it dries, you're done—nothing is going to change from that point, so you need to tweak the time that it takes to dry by adjusting the solvent content.

Nextly, there's the effect of gravity. If it stayed liquid, sooner or later all of the paint would end up in a big gloopy puddle at the bottom of the wall. That wouldn't be good, so you need to make sure that the paint dries faster than it slides down the wall. You can adjust how fast it slides down the wall by altering the viscosity of the paint.

Finally, there are the brushstrokes. When paint is applied with a brush or a roller, the surface of the paint initially reflects the patterns of the implement—for a brush, if you looked at the wall side-on the surface of the paint would look a bit like a sine wave. For a nice smooth appearance, you want the drying of the paint to take long enough for the surface tension of the liquid paint to flatten out the surface and erase the brushmarks.

So there you have it: three conflicting factors to producing the perfect paint, all of which can be mathematically modelled with normal Navier-Stokes fluid dynamics equations. Who'd a thunk there was so much science in a tin of paint?

(If you want more detail, you could try S.D. Howison, J.D. Morgan, J.A. Ockendon, E.L. Terrill and S.K. Wilson [1997] "A Mathematical Model for Drying Paint Layers" Journal of Engineering Mathematics 32 p377-394).