Quantifying transport within a two-cell microdroplet induced by circular and sharp channel bends

A passive method for obtaining good mixing within microdroplets is to introduce curves in the boundaries of the microchannels in which they flow. This article develops a method which quantifies the role of piecewise circular or straight channel boundaries on the transport within a two-cell microdroplet. Transport between the two cells is quantified as an easily computable time-varying flux, which quantifies how lobes intrude from one cell to the other as the droplet traverses the channel. The computation requires neither numerically solving unsteady boundary value problems nor performing trajectory integration, thereby providing an efficient new method for investigating the role of channel geometry on intra-droplet transport.