Nagel’s befuddlement, which he shared with his colleagues, could be stated this way: Why does all the material suspended in a drop of coffee end up at the edge when the drop evaporates, considering that it started out dispersed across the whole drop? The effect was common to all droplets of dispersed colloidal objects, including milk, blood, ink, and paint, evaporating on a wide variety of surfaces, suggesting there should be a general explanation.
The physical picture that emerged was beautiful and simple: As the droplet dries, the liquid evaporating from the thinning outer edge, where the contact angle θ is shrinking to zero, must be replenished by liquid from the drop’s interior. This sets up a strong outward flow in the solvent, which carries most of the solute to the contact line. Pre-existing surface roughness can provide the force to pin the contact line, but the contact line further pins itself through a feedback loop between flow and patterning: the outward flow increases the deposition of solute, which serves to anchor the fluid and reinforce the outward flow.
The simplicity of this picture carries some caveats—the suppression of counterflows that are due to gradients in surface tension (Marangoni flows) is one example. However, in the years since Nagel’s observation, the coffee ring has taken on a life of its own.
The curious case of the coffee ring