On the origin and evolution of the depletion zone in coffee stains

The variation in the concentration of surfactant molecules along the air-water interface of a drying sessile drop containing colloidal particle-surfactant mixtures is known to inhibit the formation of coffee stains. This also leads to the formation of particulate deposits with a region almost deprived of the particles, often called the depletion zone. The molecular size of the surface-active species used in such experiments poses limitations on the direct visualization of the build-up of surfactant molecules at the interface and how it correlates with the nucleation and growth kinetics of the depletion zone. We report a quantitative analysis of the origin and evolution of the depletion zone that forms in a drying sessile drop. By evaporating an aqueous sessile droplet containing a mixture of surface-active poly(N-isopropylacrylamide) (pNIPAM) microgels and polystyrene (PS) colloids, we establish that the concentration fluctuations of the PS particles along the air-water interface trigger a surface tension driven Marangoni flow along the interface. As a result of this, a depletion zone forms within the particulate deposit, which is analogous to the depletion zones observed for dried drops of particle- surfactant mixtures. The critical time at which the depletion zone forms correlates to the time at which surface tension-driven stress along the interface is maximum. Moreover, we show that the increase in the initial concentration of PS particles results in a decrease in the critical time. By using in situ video microscopy, we established that the rate at which the depletion zone grows is non-linear in time. The growth rate of the depletion zones for drops containing different concentrations of PS particles collapses into a master curve upon scaling with concentration and radius of the drop.