4.7 Summary [flow patterning/microfluidic mixing top]

In this chapter, we present the passive scalar transport equation:

which can be nondimensionalized to the following form:

This nondimensional form highlights the Peclet number Pe = Uℓ∕D, which indicates the relative magnitude of the convective fluxes as compared to the diffusive fluxes in the system.

Mixing is driven by diffusion processes, which proceed over a characteristic length proportional to . Flow processes can facilitate mixing by changing the characteristic length over which this diffusive mixing must occur. Microfluidic devices use flows with low Re and high Pe, leading to slow mixing. The net effect is that scalars in microfluidic systems are often unmixed over time scales relevant to experiments. This attribute facilitates laminar flow patterning but interferes with processes that require mixing. Chaotic advection facilitates mixing by shortening the required diffusion length scales, but this sort of advection occurs only if specifically designed for with carefully crafted microfluidic geometries.

When scalars are transported axially along microchannels, Taylor-Aris dispersion controls the effective axial diffusivity, leading to an effective diffusivity given by

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