Interdisciplinary Applied Mathematics

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In the experiments of (Takhistov et al., 2002), air bubbles were created in solutions of KCl/H2SO4 in a micropipe of diameter d = 2R = 0.55 mm and length 3 cm. The glass walls were treated properly so that a positive zeta potential Zc was produced, although typical glass surfaces are negatively charged. A small amount (2 x 10~5 mol/l) of an anionic surfactant SDS (sodium dodecyl sulfate) was used to create the interface EDL. Voltages in the range of 10 to 120 volts were applied, and the concetration of KCl varied from 10~6 to 10~2 l/m. The main finding of these experiments was that there exists a window of operation parameters within which bubble motion occurs, and it can reach even 3 mm/s for short bubbles. Specifically, this window is defined by the voltage range (20 to 80 volts) and the KCl concentration C0 (between 10~5 to 10~3 mol/l).

A summary of the results is shown in Figure 8.15, taken from (Takhistov et al., 2002). The measured bubble velocity also depends on the aspect ratio of the    bubble    lb/d, as    shown    in    Figure    8.16,    also    taken    from    (Takhistov

et    al.,    2002). Overall,    a    strong    dependence    of    the    bubble    velocity    u0    is

obtained in terms of the applied voltage V, the electrolyte concentration Co, and    the    bubble    length    lb.    Below    the    critical    value    of    C0 and above    the

critical value of voltage, the electric current stops completely. In addition to the experiment with the anionic surfactant, Takhistov et al. also conducted experiments with a cationic surfactant, but no bubble motion was observed.

It is important to understand the reasons for this behavior, which produces a mobile versus a stationary bubble. Takhistov et al. argued that the most dominant mechanism is the enhancement of the film conductivity

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