In this paper, we demonstrate the dynamics of bidispersed oil droplets in an evaporating water sessile drop. This phenomenon is therefore equivalent to a unique liquid droplet based “coffee stain” effect, with the depositing colloidal particles (of a classical “coffee stain” problem) being replaced by the oil droplets partially wetting the substrate. The important difference with respect to the classical “coffee stain” problem, as revealed by our experiments, is that the oil droplets, unlike the colloidal particles, cannot reach the contact line; rather the aversion of the oil droplets to the air ensures that the oil droplets always remain at a finite distance from the contact line. We call this effect an “enclosure” effect, characterized by this distance. We provide a theoretical model to explain this phenomenon, and our theoretical results match well with the experimental observations. The “enclosure” effect depends on the droplet size, thereby allowing an automatic size-based separation of the oil droplets. Additionally, this effect depends on the wettability of the oil droplets and the sessile drop, as well as the relative velocity of the oil droplets with respect to the rate of decrease of the sessile drop contact angle. Our identification of this new phenomenon in a liquid-droplet based “coffee stain” problem will have a huge impact on microscale control and manipulation of liquid droplets in a two phase system.