Induced-charge electro-osmosis around metal and Janus spheres in water: Patterns of flow and breaking symmetries

We establish experimentally the flow patterns of induced-charge electro-osmosis around immobilized metallic spheres in aqueous electrolyte. The ac field modifies local electrolyte concentration and causes quadrupolar flows with inward velocities being smaller than the outward ones. At high fields, the flow becomes irregular, with vortices smaller than the size of the sphere. Janus metallodielectric spheres create dipolar flows and pump the fluid from the dielectric toward the metallic part. The experimentally determined far-field flows decay with distance as $r^{-3}$.

Figure 1

(a)–(f) The ac electric-field ($E=10\mathrm{mV}/\mu \mathrm{m}$, $f=1\mathrm{kHz}$) -induced ICEO around the Au sphere ($2a=50\mu \mathrm{m}$) in an $h=60\mu \mathrm{m}$ chamber filled with water. (a) ICEO trajectories. (b) Map of experimental velocities. (c) Numerically reconstructed velocity map with Fourier harmonics $n=2$ and 4 [Eq. (2)]. (d) and (e) Radial dependence of Fourier coefficients in (d) linear and (e) log-log representations. (f) Volumetric flow through the cross sections of the cell. (g) Maximum inward $|u_{\mathrm{in}}|$ and outward $|u_{\mathrm{out}}|$ velocities as a function of $E^2$. Dashed lines in (e) show a $1/r^3$ slope.

Figure 2

Experimental map of the fluorescence intensity caused by positively charged dye rhodamine 6G at (a) zero electric field and (b) electric field $E=15\mathrm{mV}/\mu \mathrm{m}$ and 1 kHz.

Figure 3

(a) Experimental ICEO trajectories and (b)–(e) velocity patterns measured over randomly selected 40-ms time intervals, around a homogeneous Au sphere, with $E=40\mathrm{mV}/\mu \mathrm{m}$, $f=8\mathrm{kHz}$, and $2a=50\mu \mathrm{m}$.

Figure 4

The ICEO flows around Janus particles with (a)–(e) $\mathbf{E}\perp \mathbf{P}$ and (f)–(h) $\mathbf{E}\left|\right|\mathbf{P}$. (a) and (f) The ICEO trajectories. (b) and (g) Experimental ICEO velocities maps. (c) and (h) Numerically reconstructed velocity maps with (c) two Fourier harmonics $n=1,2$ in and (h) four harmonics $n=1,2,3$, and 4. (d) Radial dependence of coefficients for the case in (b) and (c). (e) Volumetric flows.