New Electric-Field-Driven Mesoscale Phase Transitions in Polarized Suspensions

We report the discovery of a new class of an electric field-driven bulk phase transition due solely to dipolar interactions in a suspension under the action of a uniform ac field where the effects of other competing forces are suppressed. This transition appears after the well-known chain-column formation and causes the uniform suspension of columns to rearrange into a cellular pattern consisting of particle-free domains surrounded by particle-rich walls. Interestingly, the characteristic size of these domains scales linearly with the interelectrode spacing and remains insensitive to the size of the particles.

Figure 1

Formation of a cellular pattern in the plane perpendicular to the field direction. The particles are seen as white spots and the particle-free domains as black; $87\mu \mathrm{m}$ particles, cavity diameter 1.5 in., gap 1.8 mm, $3\mathrm{kV}\mathrm{rms}/0.1\mathrm{kHz}$. (a) Experimental setup. (b) View from an angle $\sim 30°$ to the electrodes; $2(\mathrm{v}/\mathrm{v})\%$ suspension. (c) Particle rearrangement following the field application; $3(\mathrm{v}/\mathrm{v})\%$ suspension.

Figure 2

Characteristics of phase transitions. (a) Cellular patterns formed in hexagonal (side 0.87 in., gap 2.0 mm), square ($2\mathrm{in}.\times 2\mathrm{in}.$, gap 1.8 mm), and circular (diameter 2 in., gap 1.8 mm) cavities. The particles are seen as white spots and the particle-free domains as black; $45\mu \mathrm{m}$ particles, $5(\mathrm{v}/\mathrm{v})\%$ suspension, 30 min exposure to $3\mathrm{kV}\mathrm{rms}/0.1\mathrm{kHz}$. (b) Variation of GL with exposure time; $87\mu \mathrm{m}$ particles, $1(\mathrm{v}/\mathrm{v})\%$ suspension, cavity diameter 1.5 in., gap 3.5 mm, $6\mathrm{kV}\mathrm{rms}/0.1\mathrm{kHz}$. The nuclei appeared about 16 min following the field application.

Figure 3

Mesoscale nature of the structural transition. The plots show the dependence of the final average radius of the cells, $R_c$, and the particle-free domains, $R_f$, as a function of the interelectrode spacing, $L=0.61–3.53\mathrm{mm}$, and initial particle concentration, $c=0.5–10(\mathrm{v}/\mathrm{v})\%$. All the experiments presented in the plots were conducted at the field strength $(E_{\mathrm{rms}}\sim 1.7\mathrm{kV}/\mathrm{mm})$ and frequency (0.1 kHz) of the applied ac field within a circular cavity of diameter, $D=2\mathrm{in}.$ Various symbols refer to different initial particle concentrations, $c$ $(\mathrm{v}/\mathrm{v})\%$. The filled and hollow symbols refer to experiments conducted with 87 and $45\mu \mathrm{m}$-sized particles, respectively. The inset in the right plot shows a sketch of the various structural parameters.

Figure 4

Dynamics of the pattern evolution. (a) The particle rearrangement following the application of $3\mathrm{kV}\mathrm{rms}/0.1\mathrm{kHz}$. The particles are seen as white spots and the particle-free domains as black; $87\mu \mathrm{m}$ particles, $2(\mathrm{v}/\mathrm{v})\%$ suspension, cavity diameter 1.5 in., gap 1.8 mm. (b) The straight lines show the initial growth of the particle-free domains, $R/R_f$. (c) Experimental data (symbols) on the growth of the particle-free domains and as predicted by Eq. (1) (solid line). The experimental conditions are listed in the supplementary information [24].