New Electrohydrodynamic Flow Caused by the Onsager Effect

We report a new type of electrohydrodynamic (EHD) flow generated around a circular cylinder and a spherical particle in a dielectric liquid under dc and ac electric fields. The EHD flow is observed for various combinations of dielectric liquids and polar additives. We suggest that the EHD flow is caused by a gradient of electrical conductivity produced by a nonuniform electric field and subsequent generation of free charge in the bulk liquid. Analytical and numerical analyses which are based on the leaky-dielectric model show good agreement with experimental results.

Figure 1

Streamlines around circular cylinders ($h=5\mathrm{mm}$, $E_0=5\mathrm{kV}/\mathrm{cm}$, $f=30\mathrm{Hz}$) and spherical particles ($h=2.5\mathrm{mm}$, $E_0=5\mathrm{kV}/\mathrm{cm}$, $f=40\mathrm{Hz}$) immersed in dodecane solution mixed with 5 wt % of Span 85. (a) Tungsten cylinder, $d=500\mu \mathrm{m}$, (b) Teflon cylinder, $d=770\mu \mathrm{m}$, (c) glass sphere, $d=750\mu \mathrm{m}$, and (d) polymethyl methacrylate sphere, $d=750\mu \mathrm{m}$. $E_0=\Delta V/h$ in which $\Delta V$ is the root-mean-square voltage applied between the two electrodes. All the photos are in the same scale. Scale bar is $500\mu \mathrm{m}$.

Figure 2

Mechanism of the NUF EHD flow for conducting cylinder (a),(b) and dielectric cylinder (c),(d). Panels (a) and (c) show the electric-field lines (vertical lines), conductivity contours (circular arcs), and sign of free charges; panels (b) and (d) show the streamlines. The figures are based on the analytical solution for dc case, where $\overline{\sigma }=6.15\times {10}^{-9}$, and the dielectric constant of fluid ${ϵ}_r=2.01$.

Figure 3

Comparison of numerical simulation (right) with experimental results (left): (a) tungsten cylinder and (b) spherical glass particle. The numerical simulation was executed under the same conditions as those of Figs. 1a, 1c.

Figure 4

The dependency of average flow velocity on (a) electric-field strength ($f=30\mathrm{Hz}$) and (b) frequency ($E_0=5\times {10}^3\mathrm{V}/\mathrm{cm}$) for the case of tungsten cylinder. All the data are plotted to logarithmic scale. In (a), circles and triangles are for $d=500\mu \mathrm{m}$ and $d=250\mu \mathrm{m}$, respectively, and solid lines represent $E^3$ curves. In (b), solid lines represent theoretical values. In the inset of (b), the two lines $\overline{AB}$ and $\overline{AC}$ connect the center of the vortices.