Evaporation induced flow inside circular wells

Wide used technique of patterning surfaces with solid particles utilizes the evaporation of colloidal droplets from a substrate. In particular, evaporation of liquid samples is a key problem in the development of microarray technology (including labs-on-a chip), especially in the case of open reactors [1]. A plenty of works are devoted to the evaporation of the sessile droplets [2–5]. One assumes that a droplet has a shape like a spherical cap. Nevertheless, investigation of the drops with more complex geometry is of interest. Thus when a high concentrated colloidal droplet evaporates from a substrate, the solute particles in solution will form a ring like deposit wall near the edge of the drop (Fig. 1). One can consider this case as evaporation of a liquid drop inside open circular well with vertical walls formed by gel. In the paper [1] the flow field inside a liquid sample in very thin circular wells was measured. The confidence between measured velocity [1] and the estimations obtained with theory of ring formation [2] is reasonable. In this paper, the relationship between hydrodynamical flow inside a liquid sample evaporating in open circular well and the mode of evaporation is examined. We found analytical expressions of height averaged radial velocity for different modes of evaporation. Velocity field inside the circular well was found for the particular case of flat air–liquid interface.