Interdisciplinary Applied Mathematics

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Transport of microbubbles can be achieved either by pressure-driven or electrokinetically driven flows. It may be more efficient to build up back

pressure on the bubbles using the latter. However, it has been found in experiments in (Takhistov et al., 2002), that air bubbles were stationary even though the electrokinetic velocity was 1 mm/s. Therefore, it is important to understand the physical mechanisms that are in place so that we can modify them to induce bubble motion. Here, we follow the work of (Takhistov et al., 2002), who developed the theory of asymmetric double layers. The reason that the bubble may stay stationary despite the fast surrounding flow can be explained by simple scalings. Specifically, the electrokinetic velocity ue is proportional to E, where E is the electric field, which scales in inverse proportion to the cross-sectional area; hence, the flowrate is independent of the cross-sectional area. This, in turn, implies that the flowrate in the annular region (between the bubble and the capillary) is the same as that behind the bubble, and thus there is no extra pressure buildup due to the lack of liquid accumulation, so the liquid simply flows around it.

There are many possibilities of circumventing this difficulty, e.g., by disturbing the gap flow and thus reducing the flowrate in the annular region. This can be achieved    by    changing    the    conductivity    of    the    film,    i.e.,    by

adding appropriate ionic surfactants, which will cause the development of an electric double layer (EDL) at the liquid-air interface in addition to the EDL on the capillary wall. The relative size of these two EDLs is a major factor in determining the motion of the bubble.

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