Passive Droplet Control in Two-Dimensional Microfluidic Networks

Microfluidic networks for droplet-based microfluidics have been recently introduced with the aim of realizing flexible Lab-on-Chip devices. In this paper, we investigate, for the first time, a two-dimensional network topology, in which biological samples, embodied in so-called payload droplets, are delivered to a specific destination. Two-dimensional networks can be useful in many applications, such as the automation of laboratory experiments on microwell plates. The path of the payload droplet is determined by the network geometry and the distance to so-called control droplets (i.e., passive droplet control). In order to route single or multiple payload droplets to a specific destination, we introduce droplet frames that include single or multiple payload droplets and several control droplets for their path control. We derive closed-form expressions for the droplet distances within the frame to realize the desired droplet routing. These expressions are solely based on the network geometry and fluid properties. Computer simulations based on the analogy between microfluidic networks and electrical circuits verified the proposed routing scheme.