# Why did equidistant streaks of oil form on this hot pan?

Yesterday, my father-in-law sent me this photo of his greased pan:

After burning olive oil on the pan and pouring out the oil, he noticed that the remaining oil formed equidistant streaks. Why did this happen? What other thin films of fluid behave like this?

The physics here is a competition between gravity and surface tension. Gravity favors a flat configuration, while surface tension favors clumps.

If you pour a bit of oil into a cold pan, it forms a clump because of the surface tension. If you pour a lot of oil in, it'll form a uniform film on the bottom of the pan, because gravity is now more important: forming one large clump would cost a lot of gravitational potential energy. (Specifically for a volume $V$ of oil, the surface tension energy scales as $V^{2/3}$ and the gravitational potential energy scales as $V$.)

As oil heats up, the surface tension drops, as measured in this paper in the International Journal of Food Properties, so it stops clumping up as strongly. So I propose the following explanation. We begin with a lot of oil forming a film on the bottom of the pan. When most of the oil was poured out, the film became too thin to be stable, so it started to clump up. Since the oil was hot, the surface tension was low enough that lines of oil could be produced, rather than circular clumps.

Given that lines are forming, it's not surprising they're uniformly spaced. That's just because the original thickness of the oil film was uniform. What's remarkable to me is that we get organized lines all pointing the same way, rather than a web. My guess is that it's because the oil was poured out relatively slowly and uniformly. If you imagine slowly tilting a pan to the right, you'll get a small initial region on the left where the oil film becomes thin enough to separate into clumps, which are naturally uniformly spaced. If the angle increases a bit, you get another region to the right of that region which clumps up, merging onto the existing clumps on the initial region. So the lines are just "seeded" initially and from there on follow the tilting motion.

• I think this phenomenon is called the Marangone effect, is it not? – niels nielsen Jun 21 '18 at 4:59
• @nielsnielsen - it sure is; it is also responsible for a similar looking phenomena when you swirl wine out of wineglass known as tears of wine – nluigi Jun 21 '18 at 7:49
• @nielsnielsen This is an interesting video regarding the effect youtube.com/watch?v=s6w0tSg-msk – Francesco Bertolaccini Jun 21 '18 at 8:42
• There is a drop at the bottom of the picture, I think the pan is slanted, so the lines are formed by the downwards flow of the oil. – Davidmh Jun 21 '18 at 15:07
• @Davidmh That also sounds reasonable! This is certainly the part I'm the least sure about. Hopefully somebody can do an experiment. – knzhou Jun 21 '18 at 15:33