Initial Electrospreading of Aqueous Electrolyte Drops

The early spreading of a liquid drop on a solid surface driven by inertial, capillary, and electrostatic forces is of fundamental interest, since most commonly used surfaces are (naturally) charged. We studied the effect of applying an electric potential between a drop and a surface on the early spreading of aqueous electrolyte drops. We found that spreading dynamics not only depended on the potential, but also on the electrolyte concentration. Based on molecular dynamics simulations of the ion distribution in spreading nanodrops under an applied potential, we propose a simple model to explain the relation between applied potential, electrolyte concentration, and early spreading dynamics.

Figure 1

(a) Sketch of the setup: a drop of initial radius $R$ hangs from a needle with inner radius $r_n=400\mu \mathrm{m}$. The needle is at a distance $d=2\mathrm{mm}$ from the surface. Between the needle and surface a potential $U$ is applied. (b) Log-log plots of drop spreading radii $r$ vs spreading times $t$ on completely wetting nongrounded glass (circles) and grounded $\mathrm{Si}/{\mathrm{SiO}}_2$ (squares) surfaces recorded at 200 000 fps. The images show four high-speed video snapshots at $t=0$ and 0.5 ms. The scale bar is 1 mm. A higher magnification image shows $\beta$ as the angle formed between the conical lower end of the drop and the glass surface.

Figure 2

Spreading exponent ${\alpha }^{\prime }$ vs. applied potential $U$ for a hydrophilic (closed symbols) and a hydrophobic (open symbols) surface, and for pure water (squares) and four different electrolyte concentrations (symbols). Inset: $\alpha$ vs. ${\theta }_{\mathrm{eq}}$ for pure water and four electrolyte concentrations with $U=0$.

Figure 3

Molecular dynamics simulations snapshots of water nanodrops with $R\approx 4.5\mathrm{nm}$ and $c\approx 0.5\mathrm{mol}/\mathrm{kg}$ NaF before contact and at equilibrium. Blue (dark) particles are ${\mathrm{Na}}^{+}$ ions and green (light) particles are ${\mathrm{F}}^{-}$ ions. Spreading radii $r$ vs time $t$: (a) without electric field and (c) with electric field of $0.1\mathrm{V}/\mathrm{nm}$. The two dashed black lines separate the regions of inertial spreading (I), viscous spreading (II), and equilibrium (III). The other lines are power law fits of the spreading radii. Only each 4th data point is shown for clarity. (c) Number density distribution of ${\mathrm{Na}}^{+}$ (black) and ${\mathrm{F}}^{-}$ (red) in a water nanodrop with respect to the distance $D$ to the silicon surface at equilibrium, with (dashed lines) and without (solid lines) an applied electric field of $0.1\mathrm{V}/\mathrm{nm}$.

Figure 4

(a) Sketch of the equivalent electric circuit: ${\epsilon }_l$ is the permittivity of the drop; $c_a$ is the capacitance and ${\epsilon }_a$ the permittivity of air; $c_{\mathrm{EDL}}$ is the capacitance and $d_{\mathrm{EDL}}$ is the thickness of the EDL; $c_{\mathrm{ox}}\approx$ is the capacitance and $d_{\mathrm{ox}}\approx 5\mathrm{nm}$ is the thickness of the native silicon oxide layer. Since the distance needle substrate is large compared to $d_{\mathrm{ox}}$ and $d_{\mathrm{EDL}}$ the capacity of air is negligible. (b) ${\alpha }^{\prime 2}-{\alpha }^2$ vs. $U^2$, replotted from Fig. 2 with corresponding symbols. For clarity of presentation, differently colored data sets are offset vertically by the value of 0.1.