# Interdisciplinary Applied Mathematics

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 Solute D (x10 9 m2/s) Solute D(x10-9 m Nitrogen 1.88 Oxygen 2.10 Hydrogen 4.50 Propane 0.97 Acetone 1.16 Hemoglobin 0.069 Ovalbumin 0.078 Fibrinogen 0.020

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TABLE 9.1. Diffusivity D of different substances in water at 25°.

The objective is therefore to achieve rapid mixing using the minimum amount of space. More specifically, the objective of mixing is to maximize the interfacial area in two coflowing fluids using the minimum amount of space, time, or energy. As we will see in the next section, this implies stretching of the interfacial area as much as possible. Mathematically, this is expressed simply in terms of the Peclet number Pe. Relying on clasical diffusion only, the mixing length L is proportional to h Pe, where h is the microchannel height. Achieving complete mixing using the concepts of Lagrangian chaos or chaotic advection, as we will discuss in the next section, leads to L ж    h lnPe.    For    solutions    based    on    large    molecules,    the    Peclet

number achieves high values, and hence the logarithmic scaling becomes very important.

Micromixers are devices that have been proposed and tested in microfluidics research to enhance mixing rates. In the literature, both the mixing process and the mixing microdevices are characterized as either passive or active. In particular, passive mixing refers to a process whereby the interface follows the flow without any back effect on the flow (noninteracting case), whereas active mixing involves interfaces interacting with the flow. On the other hand, micromixers are also broadly classified as passive and active or static and dynamic, respectively. Most of the active mixers involve moving parts, and they expend additional energy resources, unlike the passive mixers. In terms of robustness, passive mixers are superior, but they are topologically very complex and hence difficult to fabricate. In addition, once they are incorporated in a microfluidic design they cannot be used for any other function. Active micromixers are reconfigurable and simpler to fabricate, although perhaps more complicated to operate.

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