Figure 1
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The most important feature in terms of local mixing is the dynamic behavior of the droplet (or bubble) wake, which has been
extensively studied (24–25). Studies of wake phenomena and fluid flow past solid obstacles date as far back as Leonardo da
Vinci (26). Subsequent studies focused on the development of highly accurate pendulum clocks for the determination of a ship's
location at high sea. The construction of these clocks required a detailed understanding of the airflow and drag around a
swinging pendulum (The Longitude Act was passed in England in 1714, in which Parliament promised a prize of 20,000 pounds
for the solution of the "longitude problem." To win the prize, the inventor had to construct an accurate and reliable pendulum
clock, requiring a precise understanding of the wake behind the pendulum) (27).
Notations
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The wake behind droplets and bubbles consists of a primary wake moving in close association with the droplet and a secondary
wake extending far downstream (28). Typically three different wake types are observed: a steady-wake without circulation (see
Figure 1a), a steady wake with a well-developed circulation zone that can grow significantly (see Figure 1b), and an unsteady
wake with vortical structures and vortex shedding (see Figure 1c) (22, 25, 28–33).
Clearly the mixing in these wakes is very different. For example, Figure 2 shows the contour plots of dissolving gas from
a bubble rising with the three different wake types. It can be seen that in the case of the steady wake, the gas is concentrated
in a small region behind the bubble (see Figures 2a and 2b). In the case of vortex shedding, the gas is rapidly dispersed
into the liquid phase (see Figure 2c). It is obvious that in the case of fast, mixing-sensitive reactions, these different
types of wakes will result in different product distributions. In an article published in 2000, the authors addressed this
problem by analyzing computationally this phenomenon for a fast parallel-consecutive reaction network:
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