Effect of axial electric field on the Rayleigh instability at small length scales

The effect of an electric field along the longitudinal axis of a nanoscale liquid thread is studied to understand the mechanism of breakup. The Rayleigh instability (commonly known as the Plateau–Rayleigh instability) of a nanosized liquid water thread is investigated by using molecular dynamics simulations. The breakup mechanism of the liquid nanothread is studied by analyzing the temporal evolution of the thread radius. The influence of the temperature of the liquid nanothread and the electric-field strength on the stability and breakup is the major focus of the study. The results show that the axial electric field has a stabilizing effect even at nanoscale. The results from the simulations are in good agreement with the solutions obtained from the dispersion relation developed by Hohman et al. for the liquid thread. The critical electric-field strength necessary to avoid the breakup of the liquid thread is calculated and other effects such as the splaying and whipping instability are also discussed.

Figure 1

Schematic of the simulation box elucidating the general configuration of water molecules with length ($L$) and diameter ($D$) in the presence of an axial electric field ($E$). The figure is not to scale.

Figure 2

Equilibration curves for a nanothread of length 90 nm and radius 1 nm at 300 K (Case 10; see Table 3).

Figure 3

Dispersion relation for a zero-viscosity fluid as a function of $E$ for $\beta =77$.

Figure 4

Effect of electric field on the dynamic viscosity of liquid water.

Figure 5

Effect of electric field on the surface tension of liquid water.

Figure 6

Temporal evolution of the minimum thread radius with the initial thread radius as 1 nm at 300 K.

Figure 7

First breakup time for the three temperatures studied for various thread radii.

Figure 8

Number of drops formed for the three temperatures studied for various thread radii.

Figure 9

Dispersion curves for Case 10 ($L=90$ nm and $r=1$ nm at 300 K) for various electric-field strength, $E$, and $\beta =77$.

Figure 10

Snapshots of MD trajectory from Case 8 to Case 13 (Table 3) (left column indicates the cases without electric field and the corresponding cases with critical electric-field strength predicted from the solution of the dispersion relation is on the right column).

Figure 11

The snapshots of MD trajectory from Case 10 (length is 90 nm and radius is 1 nm) with $E=2900$ kV/cm at various time intervals.

Figure 12

Critical electric-field strength predicted from the solution of the dispersion relation and MD simulations for various thread radii.

Figure 13

The snapshots of MD trajectory for the liquid thread for the Case 10, at different time intervals. (a) 0 ps, (b) 15 ps, (c) 27.5 ps, and (d) 87.25 ps.

Figure 14

The spatiotemporal evolution of thread radius without electric field for Case 10.

Figure 15

The spatiotemporal evolution of thread radius with electric field, $E=10000$ kV/cm (1.0 V/nm) for Case 10.

Figure 16

Temporal variation of minimum radius for Case 10 ($L=90$ nm and $r=1$ nm at 300 K) with $E=10000$ kV/cm.

Figure 17

Effect of electric field on thermal fluctuations.

Figure 18

Variation of Laplace pressure difference across the thread surface with surface tension as a function of $E$.

Figure 19

Temporal evolution of a liquid thread for (left column) Case 10 and (right column) Case 8, at different time intervals with electric-field strength of 70 000 and 10 000 kV/cm. (a) 25 ps, (b) 50 ps, (c) 75 ps, (d) 77.5 ps, (e) 80 ps, and (f) 82.5 ps.