Electrohydrodynamic aggregation with vertically inverted systems

Flow patterns surrounding particles suspended near electrodes within an electrolyte solution can be induced with an electric field due to an electrohydrodynamic (EHD) force. Depending on electrolyte, particle, and field properties, a variety of particle packing and stability states have been observed in EHD flow. In this work, we report evidence of EHD flow-induced aggregation of 2-μm sulfonated latex beads in NaCl and NaOH electrolyte solutions, in inverted particle-electrode orientations. Experimental conditions were chosen to match previous work where aggregation was observed at a bottom electrode. Particles remain stable at the top electrode for times greater than 1 h, and aggregation behavior is quantified in terms of growth rate and particle packing density and order. Similar aggregation behavior is seen at both top and bottom electrodes, with aggregate growth occurring more quickly within NaCl solutions than NaOH solutions at both the bottom and top electrode. In addition, an observed secondary location of stability for the vertical position of particles in NaOH electrolyte at the bottom electrode is not seen at the top electrode. Comparing these metrics to predictions made by a scaling model for EHD flow, particle aggregation behavior is successfully predicted at both top and bottom electrodes, but some of the observed differences in aggregate packing are not. Thus we suggest that modifications to existing models or their interpretation may be needed to improve predictions of the behavior of such systems.

Figure 1

Microscopy images of aggregation of 2 μm particles in NaCl and NaOH solutions at 6.67 kV/m and 100 or 25 Hz, respectively. Images captured using phase contrast microscopy and a 20× objective. Particles are allowed to settle near the electrode, then are imaged for 80 s with the field applied at 10 s.

Figure 2

Schematic of particle stability location at top electrode with a $1\mathrm{m}M$ NaOH electrolyte and 25 Hz, 6.67 kV/m field magnitude. Some particles are held in place by EHD forces, while particles further from the electrode (either due to incomplete settling prior to inversion or bifurcation) are unstable and settle to the bottom electrode, in contrast with behavior at the bottom electrode for this system, where two planes of stability are observed.

Figure 3

Aggregates of 2 μm particles observed near electrode for inverted (a,b) and normal (c,d) orientations, within 1 mM NaOH (a,c) and NaCl (b,d) electrolyte aqueous solutions and an applied field of 10 V p.p., 100 Hz (NaCl), and 25 Hz (NaOH) with electrode separation of $750\mu \mathrm{m}$. Aggregate packing is quantified with particle spacing and order parameters, where a lower order parameter and higher spacing corresponds to a randomly packed aggregate (rcp), and higher order parameter and smaller mean separation corresponds to hexatic close packed (hcp) aggregates. Data represents an average of spacing and order calculations for at least 15 aggregates at each condition, measured over 4360 frames taken at 4000 fps after aggregates had formed.

Figure 4

Potential distribution plots for particles in NaOH (a,b) and NaCl (c,d) electrolytes at bottom (a,c) and top (b,d) electrodes. Potential is calculated for electrohydrodynamic (solid line, ehd), double-layer (dotted circles, dl), van der Waals (dotted squares, vdw), and gravitational forces (dash-dot, g). The total potential represents the sum of all forces (dash, total). Electrohydrodynamic potential is calculated based on the model by Ristenpart et al. [9] Separation represents the distance of the particle from the electrode. Model parameters are detailed in Table 1. All potentials are scaled by thermal potential $k_{B}T$.