Soap-film flow induced by electric fields in asymmetric frames

Net fluid flow of soap films induced by (ac or dc) electric fields in asymmetric frames is presented. Previous experiments of controllable soap film flow required the simultaneous use of an electrical current passing through the film and an external electric field or the use of nonuniform ac electric fields. Here a single voltage difference generates both the electrical current going through the film and the electric field that actuates on the charge induced on the film. The film is set into global motion due to the broken symmetry that appears by the use of asymmetric frames. If symmetric frames are used, the film flow is not steady but time dependent and irregular. Finally, we study numerically these film flows by employing the model of charge induction in ohmic liquids.

Figure 1

Schematic of experiments for symmetric [circular (a) and rectangular (b)] and asymmetric [right-angled trapezoidal (c) and isosceles trapezoidal (d)] apertures.

Figure 2

PIV of soap film flow in a circular aperture in two instants of time, with an interval of 1.5 s. The frequency and root mean square of voltage are 6.5 Hz and 250 V, respectively.

Figure 3

PIV of soap film flow in a rectangular aperture in two instants of time, with an interval of 2 s. The frequency and root mean square of voltage are 6.5 Hz and 250 V, respectively.

Figure 4

Applied voltage in a right-angled-trapezoid aperture is dc and the voltage is 500 V. For an isosceles trapezoid, the frequency and root mean square of applied voltage are 6.5 Hz and 100 V, respectively.

Figure 5

PIV of a soap film flow in right-angled-trapezoidal (left) and isosceles-trapezoidal (right) apertures. In a right-angled-trapezoid aperture, the frequency and root mean square of applied voltage are 100 Hz and 250 V, respectively, and in an isosceles-trapezoid aperture, the frequency and root mean square of applied voltage are 6.5 Hz and 100 V, respectively.

Figure 6

(a) Average angular velocity vs the applied voltage frequency. The root mean square of applied voltage is 250 V. (b) Average angular velocity vs root mean square of applied voltage. The frequency of applied voltage is 6.5 Hz.

Figure 7

(a) and (b) Surface charge distribution in $\mathrm{C}/{\mathrm{m}}^2$ of right-angled and isosceles trapezoidal frames. $V_0=100\mathrm{V}$ and $f=6.5\mathrm{Hz},$ and physical parameters of the film can be seen in Table 1.

Figure 8

Velocity magnitude in $\mathrm{m}/\mathrm{s}$ and vector field. (a) Case of a right-angled trapezoid, $V_0=100\mathrm{V}$ and $f=6.5\mathrm{Hz}.$ (b) Case of an isosceles trapezoid, $V_0=200\mathrm{V}$ and $f=6.5\mathrm{Hz}$. Physical parameters of the film can be seen in Table 1.

Figure 9

Simulated average angular velocity (solid line) and experimental angular velocity as a function of voltage (points) for the right-angled trapezoid and for an applied signal of $f=6.5\mathrm{Hz}$. Physical parameters of the film are shown in Table 1.