Linear growth of colloidal rings at the edge of drying droplets

The ring-like deposit along the perimeter of drying droplets is commonly observed, and its formation process is crucial to the applications attempting to promote or attenuate this phenomenon. In this paper, the growth of colloidal rings formed at the edge of drying droplets has been measured by utilizing fluorescent colloidal particles. The experimental observations indicate a nearly linear growth in the ring mass with time, which is quite different from the power-law growth predicted by Deegan et al. The observed linear growth of the colloidal ring is then explained by a model considering the thermal Marangoni effect in the drying droplets. The analysis shows that, when the Marangoni effect is remarkable, both the capillary outward flow and the convective Marangoni flow appear inside the drying droplet. In such case, not all the particles dispersed in the droplet, but only the particles in the outward flow region can be brought to the contact line to form the colloidal ring, and as a result, the ring will grow linearly with time. The present work may provide a better understanding for the formation of the colloidal ring in the presence of Marangoni effect.