A coffee stain. What could be more mundane than a brown ring left behind by a hot cup of Joe? Well, from the scientific perspective, there is so much more to the deposition, diffusion, and evaporation that occur when a droplet is deposited and begins to evaporate from a surface. Indeed, scientists have tried for decades to model and understand this seemingly simple and everyday phenomenon because the physical modeling of how colloidal droplets evaporate is important to everything from painting and printing to DNA sequencing and even nanoscale manufacturing.

Now, mechanical engineer Hassan Masoud of the University of Nevada, Reno, and colleagues there and at the University at Buffalo, New York, have demonstrated that there is a previously overlooked mechanism involved in the so-called "coffee ring" effect and can now more accurately model the dynamics of particle deposition in evaporating sessile droplets. They believe their new calculations will have ramifications across several technological fields.

We now understand particle deposition during evaporation of colloidal droplets much better than before, says Masoud. "Our discovery builds on a large body of work but we took an extra step, modeling the interaction of suspended particles with the free surface of the drop. We believe our findings are going to fundamentally change the common perception on the mechanism responsible for the so-called 'coffee-ring' phenomenon."

At its simplest, when a droplet dries on a surface, the particles suspended in it usually deposit in a ring-like pattern, leaving a stain or residue, called the "coffee-ring" effect; so this isn't really about the mess you leave if your skinny latte sloshes over the edge of your cup before you put it on your desk. Until now, the stain was thought to form as a result of the fluid flow within the drop. Masoud and his team have found that it is the exposed, free, surface of the droplet, the top layer, which is in contact with the air that plays the most important part in the deposition of the particles.

"When the drop evaporates, the free surface collapses and traps the suspended particles," Masoud explains. "Our theory shows that eventually all the particles are captured by the free surface and stay there for the rest of their trip towards the edge of the drop." This effect was demonstrated using the Toroidal Coordinate System, which allowed the team to collapse complicated 3D equations into a 1D form. "Our innovative approach - and using some ugly-long equations - distinguishes our work from previous research," Masoud adds. "No one else has used this coordinate system for this problem, and this allows us to track the motion of particles in the drop in a natural way."

The finding opens up the possibility of manipulating the movements of solute particles by altering the surface tension of the liquid-gas interface rather than trying to control the bulk flow within a droplet, which will have important implications for cleaning solar panels, for instance. [Masoud et al., Phys Rev E. (2017); DOI: 10.1103/PhysRevE.94.063104]

"The next step in this work is to develop a comprehensive computational framework, based on our theory, that accurately accounts for the shape of the suspended particles and their interactions with each other at high concentrations," Masoud told Materials Today.

David Bradley blogs at Sciencebase Science Blog and tweets @sciencebase, he is author of the popular science book "Deceived Wisdom".