From: "Yuri Popov"
Date: August 9, 2004 3:41:15 PM CDT

This is Sidney's original letter:

> I read with interest your recent eprint on evaporative patterns.
While I don't work in this area, I wanted to share with you some pictures that I took last winter of the drying of a drop of dirty water that came from my bicycle. The amusing point to me is the formation of radial patterns. Do you have an opinion whether this phenomenon can be treated theoretically?
The 3 figures I attach are in jpg format. I also showed them to Sid Nagel some time ago.
> If you have any reaction, I would be interested.

And here is my reply:

I think the drops you pictured have somewhat different mechanism of pattern formation. In the mechanism I described in the preprint (and in my recent dissertation) the patterns are formed as a result of flows induced by the drop evaporation. On the pictures you provided, it is clear that the pattern exists long before the drop has dried. Actually, there is a lot of remaining water on the first two pictures, while the deposit well _inside_ the contact line is already there. So, one thing is almost sure that the pattern is likely of NOT the purely evaporative origin. My first guess would be that the sand is redistributed in this peculiar way as a result of the initial dynamical processes when the drop hits the surface (it is like a splash). Moreover, apparently there were more than one drop hitting the same location right under some pointed part of your bicycle. So, as for the multiple ring-like patterns, I would guess this is entirely due to this two effects: initial dynamical redistribution during the collision and multiple drops hitting the same spot.

Now, if you ask about the radial (inward-outward) deposit patterns, it seems hard to explain them by using either purely evaporative or purely collision description. If the radial pattern appeared only after the drop dried, this might have been similar to the cracking problems studied not too far from you in Harvard (in David Wietz lab; Eric Dufresne is one person I know was doing this). However, as is again apparent from the photos, the pattern is present long before any substantial amount of water evaporated, and purely "cracking" description does not seem to apply. Generally, many factors can cause this characteristic "angular scale" between the adjacent radial "spikes", and even a slight inhomogenuity can be enhanced many times because of the multiple drops hitting the surface. I find it hard to come up with some simple explanation for the radial (inward-outward) structures.