The appropriate conditions for thin-domain calculations as well as high-efficiency method for solution of the model equations were derived. The diffusion-based mixers were a valuable component in lab-on-a-chip designs, because of the significance of diffusion on the microfluidic length scale. It was found that the resulting mass transport equation could be solved in a streamfunction-pressure coordinate system. The results from the model equations show that if the flow rate is unchanged, the improvement in mixing can be expressed in terms of an upper bound based on the increase in pressure drop.
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