Drop mixing in a microchannel for lab-on-a-chip platforms.

We present theory, simulations, and experiments for discrete drop mixing in microchannels. The drops are placed sequentially in a channel and then moved at a set velocity to achieve mixing. The mixing occurs in three different regimes (diffusion-dominated, dispersion-dominated, and convection-dominated) depending on the Péclet number (Pe) and the drop dimensions. Introducing the modified Péclet number (Pe*), we show asymptotic curves that can be used to predict the mixing time and the required distance for mixing for any of the three regimes. Simulations of the mixing experiments using COMSOL agree with the theoretical limits. In our experimental work, we used a polydimethylsiloxane (PDMS) microchannel with a membrane air bypass valve to remove the air between drops. This approach enables precise control of the mixing and merging site. Experimental, simulation, and theoretical results all agree and show that mixing can occur in fractions of a second to hours, depending on the parameters used.