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, t ∼ (aw/U)log(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 (Pe = wU/D), and D [m^2 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.
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机译：这封信描述了一个简单论据的实验测试，该论证预测了通过缠绕微流体通道的液滴中混沌混合的比例。以前，已经描述了用于混沌混合的缩放参数，用于通过拉伸，折叠和重新定向流体以类似于面包师变换方式的方式来减小条纹长度的流。实验观察到的液滴（或塞子）中的流动模式类似于面包师的转变。因此，文献中描述的思想可以应用于液滴的混合以获得与混合时间t〜（aw / U）log（Pe）相关的缩放比例参数，其中w [m]是横截面微通道的尺寸，a是相对于w测得的塞子的无量纲长度，U [m s ^ -1]是流速，Pe是佩克利数（Pe = wU / D），D [m ^ 2 s ^ -1]是被混合的试剂的扩散系数。通过改变参数w，U和D来进行实验以确认缩放参数。在有利条件下，已在该系统中演示了亚毫秒级混合。
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