Figure 3

The field dependence of dc electric voltages induced by the steady motion of arrays of identical bubbles.

Three different configurations are examined, which are indicated in the top panel. The dynamics of each bubble is described by Eqs. (1), (2) and (5) with S = 1 [see the caption of Fig. 2 for the other parameters assumed here]. (a) obtained by Eq. (14) and by numerically solving the Poisson equation (11) correspond to solid lines and open symbols, respectively and (b) similarly for . The electric voltages are proportional to the field gradient and depends on the number of bubbles and the sample geometry. See also Discussion in the main text.