If you look at the differences between the stains left behind by droplets from coffee versus those from whiskey, you'll notice that while coffee stains usually form a ring around the cup, whiskey stains usually dry more uniformly. Brought to light by highly observant photographer Ernie Button, a unique study was conducted by Princeton scientists to understand what chemical differences there were between the two beverages.
They quickly ruled out the obvious difference as a solution for why the two beverages dry differently; it is not the alcohol content that makes whisky dry differently from coffee. It's the surfactants and polymers from plants like corn, wheat, and barley that are used to make whiskey.
The Princeton scientists created a "whiskey mimic" with surfactants, polymers, and fluorescent beads to test their theory, and they saw a three-step process taking place as whiskey droplets dried.
First, since ethanol in whiskey dries faster than water, a gradient is created that stirs droplets as they dry - a gradient that is nonexistent in coffee. Next, the surfactants pull particles away from the droplet edge as the ethanol evaporates, and polymers anchor particles - both processes that don't happen in coffee droplets.
This process is similar to technology paint companies use to ensure even drying of their product. Check out the video for more details.