# Interdisciplinary Applied Mathematics

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For applications, it was argued in (Stroock et al., 2002), that the mixing of a stream of proteins in an aqueous buffer (D = 10~10 m2/s) with U = 1 cm/s and h = 100 /am would require a channel of length L = 100 cm for regular advection compared to L =1 cm for chaotic advection achieved using a V-grooved microchannel. This improvement simply reflects the difference in the linear versus logarithmic dependence on the Peclet number for regular and chaotic advection, respectively.

The first active micromixer designed to exploit the good mixing of chaotic advection was    presented    in    (Evans    et    al.,    1997).    It    attempted to    establish

chaotic advection using a sink/source system, the so-called blinking vortex, first presented in (Aref, 1984). Unmixed fluid is drawn into a mixing chamber, and subsequently two sink/source systems are alternately pulsed. Here we present a somewhat different concept and design, which was also developed by the same research group at UC Berkeley. It is a pulsatile micromixer based on a bubble micropump developed in (Deshmukh et al., 2000). The use of pulsatile flow creates a greatly lengthened interface that leads to faster mixing. A schematic of the bubble micromixer is shown in Figure 9.5. Two pulsatile pumps are operated out of phase to mix two streams of fluid in a mixing channel. Fluid 1 is pushed into the mixing channel while fluid 2 is drawn from the inlet for half of the cycle, and the process is reversed    for    the other half    of    the    cycle.    The    pumps    consist    of    a

bubble chamber and two check valves. When a bubble is created, it acts as a piston and drives the fluid out. The check valves control the direction of the fluid. When the bubble collapses, fluid is drawn in only from the

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