Dynamics of liquid nanothreads: Fluctuation-driven instability and rupture

The instability and rupture of nanoscale liquid threads is shown to strongly depend on thermal fluctuations. These fluctuations are naturally occurring within molecular dynamics (MD) simulations and can be incorporated via fluctuating hydrodynamics into a stochastic lubrication equation (SLE). A simple and robust numerical scheme is developed for the SLE that is validated against MD for both the initial (linear) instability and the nonlinear rupture process. Particular attention is paid to the rupture process and its statistics, where the “double-cone” profile reported by Moseler and Landmann [Science 289, 1165 (2000)] is observed, as well as other distinct profile forms depending on the flow conditions. Comparison to the Eggers' similarity solution [Phys. Rev. Lett. 89, 084502 (2002)], a power law of the minimum thread radius against time to rupture, shows agreement only at low surface tension; indicating that surface tension cannot generally be neglected when considering rupture dynamics.

Figure 1

MD simulations using the different molecular models for water. Left panel: rupture dynamics of a short thread predicted by the TIP4P/2005; right panel: perturbation instabilities of a long thread modelled by the coarse grained mW model. The details of these models are introduced in Appendix pp1.

Figure 2

Schematic of a liquid thread with a perturbed interface.

Figure 3

(a) The auto-correlation function (ACF) for shear stress, obtained from an MD simulation of a periodic cube of liquid; (b) an illustration of the linear interpolation used in evaluating the temporal stochastic term $N^t$.

Figure 4

Ensemble-averaged interface profiles at two time instances ($t_1=4.66\times {10}^{-2}$ and $t_2=1.69$) for (a) decreasing grid-size with fixed time step ($▵t=4.66\times {10}^{-7}$) and (b) decreasing time step with fixed grid size ($▵z=0.05$).

Figure 5

Convergence characteristics for decreasing (a) grid size and (b) time step. Average (over $z$) deviation of ensemble-averaged interface profiles to the finest resolution profile in Figs. 4 and 4, respectively.

Figure 6

The root mean square (rms) of nondimensional disturbance amplitude versus nondimensional wave number; a comparison of ensemble-averaged MD simulations (dotted lines), ensemble-averaged SLE simulations (dashed lines), the SLE-RP analytical result (solid lines), and thermal capillary wave (TCW) theory (dashed-and-dotted lines). Comparisons are for (a) Thread 3 at three (nondimensional) time instances, $t=5.9$, 11.8, and 17.6; (b) Threads 1 and 2 (equal $\text{Th}$) for $t=9.3$; and (c) Threads 2 ($t=9.3$) and 3 ($t=9.3$, 14.7) with the equal $\text{Oh}$. The inset in (a) shows selected MD and SLE realizations.

Figure 7

Minimum thread radius against time to rupture ($t_{\mathrm{b}}-t$). Comparison of MD and nonlinear SLE for (a) Thread 4 and (b) Thread 5.

Figure 8

The temporal evolution of the minimum thread radius for different values of surface tension: comparison between similarity solutions [25] and an ensemble-average of nonlinear SLE calculations. Here, the choice of the maximum value of the surface tension ($\gamma =14.0\mathrm{mN}{\mathrm{m}}^{-1}$) used in the SLE comes from liquid argon at $84.0\mathrm{K}$.

Figure 9

Ensemble-averaged interface profiles at three time instances leading to rupture: a comparison of the nonlinear SLE solver (solid lines) and MD data (dashed lines); (a) Thread 4: $t_{\mathrm{b}}-t_1=0.13$ (black), $t_{\mathrm{b}}-t_2=1.04$ (red), $t_{\mathrm{b}}-t_3=2.73$ (blue); (b) Thread 5: $t_{\mathrm{b}}-t_1=0.09$ (black), $t_{\mathrm{b}}-t_2=1.44$ (red), $t_{\mathrm{b}}-t_3=3.50$ (blue).

Figure 10

Thread 5 rupture profiles from different models: (a) an MD simulation (b) a selected realization from the SLE (c) a solution to the LE (conventional lubrication equations).

Figure 11

Comparison of rupture profiles in experiments (a), (b) and MD (c), (d) with numerical selected solutions to the SLE: (a) $\text{Oh}=2.60\times {10}^{-3},\text{Th}=1.17\times {10}^{-7}$, experimental image reproduced from [51]; (b) $\text{Oh}=1.00,\text{Th}=4.50\times {10}^{-2}$, experimental image reproduced from [19]; (c) $\text{Oh}=0.71,\text{Th}=4.96\times {10}^{-2}$, Cylinder 1 from Ref. [24]; and (d) $\text{Oh}=1.41$, $\text{Th}=1.98\times {10}^{-1}$, Cylinder 3 from Ref. [24].

Figure 12

Rupture profiles for different combinations of $\text{Oh}$ and $\text{Th}$. Solid lines represent the ensemble average (the expected profile), dashed lines an estimate of the most-probable profile, and the region bounded by the 10th and 90th percentile value of $h\left(z\right)$ is shaded gray.

Figure 13

Time evolution of minimum thread radius, $h_{\text{min}}$; a comparison between the LE (dashed and dotted lines) and SLE (solid lines) for $\text{Th}=0.02$ and $\text{Oh}=$ (a) 0.01, (b) 1, and (c) 100. Note, $t_{\mathrm{b}}$ is the breakup time predicted by the SLE. Dashed lines represent similarity solutions in different dynamic regimes. Linear solutions in the VI-regime and V-regime come from Refs. [12] and [10], respectively. The power-law solution in the F-regime for (c) is obtained from Ref. [25].

Figure 14

The temporal evolution of minimum thread radius for different $\text{Oh}$, with $\text{Th}=0.02$. The similarity solution comes from the Ref. [11].