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 plugs͒ 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, tϳ(aw/U)log(Pe), where w ͓m͔ is the cross-sectional dimension of the microchannel, a is the dimensionless length of the plug measured relative to w, U This letter describes an experimental test of a simple argument that predicts the scaling of mixing of solutions by chaotic advection inside droplets moving through winding microfluidic channels.1 In microfluidic systems 2,3 operating at low values of the Reynolds number Re, streams of reagents flow laminarly. Diffusive mixing across laminar streams is slow because the mixing time t diff ͓s͔ is proportional to the square of the initial striation length stl(0) ͓m͔, the distance over which the mixing occurs by diffusion with a diffusion coefficient D ͓m 2 s Ϫ1 ͔:Mixing that occurs purely by diffusion is too slow for many applications of microfluidic systems, including highthroughput analysis and kinetic measurements. Methods designed to accelerate mixing aim to reduce the striation length, and several attractive approaches have been developed and reviewed. 2 Chaotic advection 4,5 enhances mixing by stretching and folding the fluid to give rise to an exponential decrease in the striation length stl. 4 In principle, presence of chaos does not guarantee widespread rapid mixing because poorly mixed islands can coexist with well-mixed chaotic regions.

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