Despite making repeated resolutions to give up bad habits, I’m still a daily coffee drinker. (I got a single-cup coffee brewer and I was a goner.) Worse yet, I’m apparently a messy coffee drinker, as I repeatedly find rings where I keep my daily cup of Joe. Now, if I could only turn that small corner of my desk into an effective scientific laboratory, I could even claim to be performing genuine scientific research into evaporation every morning.

Physicists at the University of Pennsylvania have beaten me to the punch, first by conquering the “coffee ring effect” in 2012, and now discovering the math behind those very coffee rings. And it turns out, something so every day as a coffee stain can demonstrate principles useful to creating industrial coatings, printing and paint curing.

The earlier research was conducted by professor Arjun Yodh, director of the Laboratory for Research on the Structure of Matter; then-doctoral candidates Peter Yunker and Matthew Lohr; and postdoctoral fellow Tim Still, all of the department of Physics and Astronomy in the School of Arts and Sciences at the time of their research.

As developers of paints and coatings can attest, formulators go to great lengths to avoid the coffee-ring effect and instead produce paints and coatings that evaporate to an even coating when dried. When a droplet of water is pinned to a surface, as occurs with the wet bottom lip of a coffee cup, the water droplet cannot shrink in circumference as it evaporates but instead flattens out, according to the research. As the droplet flattens, the water and anything suspended in it are pushed to the edges until it finally evaporates fully. By then, most of the particles have reached the edge, and the deposits remain as a ring.

What can change this phenomena is changing the shape of the particles, as Yodh and his team showed in their research in 2012. “Different particle geometries change the nature of the membrane at the air-water interface,” Yodh says. The researchers found that ellipsoidal-shaped particles greatly reduced the coffee-ring effect, a promising development. In the group’s latest research, published in the journal Physical Review Letters, the team shows how sphere shape influences where and how particles are deposited and the relative surface roughness of the deposits. These findings have the potential to influence finished coatings as well.