Simulations of liquid nanocylinder breakup with dissipative particle dynamics

In this work, we use a dissipative-particle-dynamics-based model for two-phase flows to simulate the breakup of liquid nanocylinders. Rayleigh’s criterion for capillary breakup of inviscid liquid cylinders is shown to apply for the cases considered, in agreement with prior molecular dynamics (MD) simulations. Also, as shown previously through MD simulations, satellite drops are not observed, because of the dominant role played by thermal fluctuations which lead to a symmetric breakup of the neck joining the two main drops. The parameters varied in this study are the domain size, cylinder radius, thermal length scale, viscosity, and surface tension. The breakup time does not show the same scaling dependence as in capillary breakup of liquid cylinders at the macroscale. The time variation of the radius at the point of breakup agrees with prior theoretical predictions from expressions derived with the assumption that thermal fluctuations lead to breakup.

Figure 1

Computational setup.

Figure 2

(Color online) Snapshots of a liquid nanocylinder along the $z\text{−}y$ plane at DPD times of (a) 50, (b) 100, (c) 150, (d) 200, (e) 250, (f) 300, (g) 350, (h) 400, and (i) 450; $k=0.22$ in Eq. (17).

Figure 3

(Color online) Snapshots of a liquid nanocylinder along the $z\text{−}y$ plane at DPD times of (a) 50, (b) 100, (c) 150, (d) 200, (e) 250, (f) 300, (g) 350, (h) 400, and (i) 450; effect of random number seed.

Figure 4

(Color online) Snapshots of a liquid nanocylinder along the $z\text{−}y$ plane at DPD times of (a) 50, (b) 100, (c) 150, (d) 200, (e) 250, (f) 300, (g) 350, (h) 400, and (i) 450; effect of domain size.

Figure 5

(Color online) Snapshots of breakup of a liquid nanocylinder along the $z\text{−}y$ plane at DPD times of (a) 1, (b) 30, (c) 60, (d) 90, (e) 120, (f) 150, (g) 180, (h) 210, (i) 240, and (j) 270; simulation with the cylinder length four times larger than in simulation in Fig. 2.

Figure 6

(Color online) Snapshots of a nanocylinder with $k=1.26$ at DPD times of (a) 1, (b) 250, (c) 500, (d) 750, and (e) 1000.

Figure 7

(Color online) Snapshots of a liquid nanocylinder in periodic domain at DPD times of (a) 600, (b) 700, (c) 800, (d) 830 (e) 840, and (f) 850; $k_{B}T=0.01$.

Figure 8

(Color online) Snapshots of a liquid nanocylinder in periodic domain at DPD times of (a) 400, (b) 450, (c) 500, (d) 520, (e) 530, and (f) 540; $k_{B}T=0.013$.

Figure 9

(Color online) Snapshots of a liquid nanocylinder in periodic domain at DPD times of (a) 200, (b) 300, (c) 400, (d) 450, (e) 460, and (f) 470; $k_{B}T=0.016$.

Figure 10

(Color online) Snapshots of a liquid nanocylinder in periodic domain at DPD times of (a) 150, (b) 200, (c) 250, (d) 280, (e) 290, and (f) 300; $k_{B}T=0.019$.

Figure 11

(Color online) Variation of breakup time with system temperature $k_{B}T$.

Figure 12

(Color online) Variation of breakup time with cylinder radius.

Figure 13

(Color online) Snapshots of breakup of liquid nanocylinder along the $z\text{−}x$ plane at DPD times of (a) 50, (b) 100, (c) 200, (d) 230, (e) 300, (f) 400, (g) 500, (h) 600, (i) 700, and (j) 800. Viscous length scale is about 25 times the value for simulation in Fig. 5.

Figure 14

(Color online) Minimum cylinder radius $r_{\text{min}}$ as a function of time $\left(T_b-t\right)$. Note that $T_b$ is the breakup time.