Interfacial transport alone accounts for coffee-ring deposition

When a colloidal sessile droplet dries on a substrate, the suspended particles usually deposit on the surface in a ring-like pattern. The phenomenon is commonly known as the ``coffee-ring'' effect and it is widely believed to stem from the transport of solutes towards the pinned contact line by the evaporation-induced flow inside the drop. It is, therefore, assumed that the liquid-gas interface does not play an active role in shaping the deposition pattern. Here, we propose an alternative mechanism for the coffee-ring deposition, in which the particles first intersect the receding free surface and then are transported along the interface until they deposit at the edge. That the interface ``captures'' the solutes as the evaporation proceeds is supported by a Lagrangian tracking of particles advected by the flow field within the droplet. We model the interfacial adsorption and transport of particles by a one-dimensional advection-generation equation in a toroidal coordinate system and show that the theory adequately accounts for the coffee-ring effect. Using this model, we study the final deposition pattern on hydrophilic and hydrophobic surfaces under diffusive and uniform evaporation fluxes.