# Interdisciplinary Applied Mathematics

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FIGURE 9.5. Schematic of the bubble micromixer. (Courtesy of D. Liepmann.)

the half-channel height is 50 ym to 150 ym.

The flow from the side-channels is set to oscillate out of phase at phases (0,^,0), while both amplitudes and frequencies are different for the three pairs. Both simulations and experiments were performed to evaluate the performance of this mixer (Bottausci et al., 2004). In the experiment, velocity profiles were measured using PIV, and also the mixing variance coefficient (MVC) was computed from photographs of the concentration field (side views (x-y) only). Typical results for MVC are shown in Figure 9.7(a) for the case in which only one side-channel is activated at 28 Hz. On the horizontal axis, S denotes the base-2 logarithm of the number of small boxes used to compute the mixing variance coefficient. The mixing variance coefficient, or MVC, is normalized such that a value of zero corresponds to complete mixing, whereas a value of 0.25 corresponds to no mixing. The experimental results are in agreement with the numerical predictions, but at small scales the experiments show better MVC value; see Figure 9.7(a). The quality of mixing decreases with the scale size. Figure 9.7(b) shows numerical results for the MVC, with all three pairs of side-channels activated at    oscillation    frequencies    of    26.025    Hz    for    the    first,    59.34 Hz    for the

second, and    92.925    Hz    for    the    last    side-channel.    We    see that    overall,    the

MVC values decreased compared to the actuation of the single side-channel in Figure 9.7(a). This indicates significantly improved mixing and validates the theory that the oscillation frequency should be increasing downstream. Proper optimization techniques can be incorporated to select the set of frequencies automatically for a given application.

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