Experimental test of scaling of mixing by chaotic advection in droplets moving through microfluidic channels

Abstract

This letter describes an experimental test of a simple argument that predicts the scaling of chaotic mixing in a droplet moving through a winding microfluidic channel. Previously, scaling arguments for chaotic mixing have been described for a flow that reduces striation length by stretching, folding, and reorienting the fluid in a manner similar to that of the baker’s transformation. The experimentally observed flow patterns within droplets (or plugs) resembled the baker’s transformation. Therefore, the ideas described in the literature could be applied to mixing in droplets to obtain the scaling argument for the dependence of the mixing time, $\mathrm{t\sim (aw/U)}\log \mathrm{(Pe),}$ where w [m] is the cross-sectional dimension of the microchannel, a is the dimensionless length of the plug measured relative to w, U [m s⁻¹] is the flow velocity, Pe is the Péclet number $\mathrm{(Pe=wU/D),}$ and D [m² s⁻¹] is the diffusion coefficient of the reagent being mixed. Experiments were performed to confirm the scaling argument by varying the parameters w, U, and D. Under favorable conditions, submillisecond mixing has been demonstrated in this system.