Self-pinning of a nanosuspension droplet: Molecular dynamics simulations

Results are presented from molecular dynamics simulations of Pb(l) nanodroplets containing dispersed Cu nanoparticles (NPs) and spreading on solid surfaces. Three-dimensional simulations are employed throughout, but droplet spreading and pinning are reduced to two-dimensional processes by modeling cylindrical NPs in cylindrical droplets; NPs have radius $R_{\mathrm{NP}}\cong 3\mathrm{nm}$ while droplets have initial $R_0\cong 42\mathrm{nm}$. At low particle loading explored here, NPs in sufficient proximity to the initial solid-droplet interface are drawn into advancing contact lines; entrained NPs eventually bind with the underlying substrate. For relatively low advancing contact angle ${\theta }_{\mathrm{adv}}$, self-pinning on entrained NPs occurs; for higher ${\theta }_{\mathrm{adv}}$, depinning is observed. Self-pinning and depinning cases are compared and forces on NPs at the contact line are computed during a depinning event. Though significant flow in the droplet occurs in close proximity to the particle during depinning, resultant forces are relatively low. Instead, forces due to liquid atoms confined between the particles and substrate dominate the forces on NPs; that is, for the NP size studied here, forces are interface dominated. For pinning cases, a precursor wetting film advances ahead of the pinned contact line but at a significantly slower rate than for a pure droplet. This is because the precursor film is a bilayer of liquid atoms on the substrate surface but it is instead a monolayer film as it crosses over pinning particles; thus, mass delivery to the bilayer structure is impeded.

Figure 1

Two orthographic projection views of a simulation configuration at time $t=0$ (Pb atoms are light gray; Cu atoms are dark gray). The image is for a $R_0=42\mathrm{nm}$ drop with 20 Cu particles in contact with the (001) surface of Cu. The spreading direction is $x$, the free surface normal direction is $z$, and the droplet's (and particles’) cylindrical axes are along $y$. The periodic repeat lengths of the simulation cells are $L_x=300$ nm and $L_y=5\mathrm{nm}$; graphics are rendered using atomeye [34].

Figure 2

Comparison between simulations of (left) a pure Pb(l) drop ($\varphi =0$) and (right) a Pb(l) drop containing 20 particles ($\varphi =8\%$) wetting Cu(001) substrates: (a) $t=0$; (b) $t=1\mathrm{ns}$; (c) $t=4\mathrm{ns}$. In all simulation renderings, light (dark) atoms are Pb (Cu) and only a portion of the substrate is shown.

Figure 3

Comparison between simulations of (left) a pure Pb(l) drop ($\varphi =0$) and (right) a Pb(l) drop containing 20 particles ($\varphi =8\%$) wetting Cu(111) substrates: (a) $t=0$; (b) $t=1\mathrm{ns}$;(c) $t=4\mathrm{ns}$. In all simulation renderings, light (dark) atoms are Pb (Cu) and only a portion of the substrate is shown.

Figure 4

Extent of droplet spread in $x$ versus time $t$. Data are presented for Pb droplets wetting Cu (001) and Cu(111) for varying particle loading: $\varphi =0,0.8\%,4\%,\mathrm{and}8\%$.

Figure 5

Simulation snapshots of systems at later times: (a) $\varphi =8\%$ droplet wetting Cu(111) ($t=7\mathrm{ns}$); (b) $\varphi =0$ droplet wetting Cu(111) ($t=7\mathrm{ns}$); (c) $\varphi =8\%$ droplet wetting Cu(001) ($t=10\mathrm{ns}$).

Figure 6

Contact line region images and fluid flow behavior for a pinning case on Cu(111). Data are shown at (a) $t=1.5\mathrm{ns}$ (early time of spreading), (b) $t=2.5\mathrm{ns}$ (right before pinning), and (c) $t=3.2\mathrm{ns}$ (when self-pinning is complete). All vector magnitudes adopt the scale depicted in the legend.

Figure 7

A plan view image of a magnified contact line region at late time ($t=7\mathrm{ns}$) for the $\varphi =8\%$ pinning case on Cu(111). The inset shows a log-log presentation for precursor film kinetic data where both a starting time $t_0=3\mathrm{ns}$ and starting position $x_0$ for the precursor spreading regime have been used (see text). Data are presented for the two layers of Pb atoms in the film for $\varphi =0$ and $\varphi =8\%$. The dotted line segment shown at the late time illustrates a slope of $\frac{1}{2}$.

Figure 8

Contact line region images and fluid flow behavior for a depinning case on Cu(001). Images show the advancing liquid front as it starts detaching from the particle: (a) $t=1.6\mathrm{ns}$, (b) $t=1.7\mathrm{ns}$, (c) $t=1.8\mathrm{ns}$, (d) $t=1.9\mathrm{ns}$, (e) $t=2.0\mathrm{ns}$, (f) $t=2.1\mathrm{ns}$. All vector magnitudes adopt the scale depicted in the legend.

Figure 9

Data are continued from Fig. 8 with images here showing when the advancing liquid front has detached from the particle and continued to spread forward: (a) $t=2.2\mathrm{ns}$, (b) $t=2.3\mathrm{ns}$, (c) $t=2.4\mathrm{ns}$, (d) $t=2.5\mathrm{ns}$, (e) $t=2.6\mathrm{ns}$, (f) $t=2.7\mathrm{ns}$. All vector magnitudes adopt the scale depicted in the legend.

Figure 10

Force on a particle versus time for three zero force cases: (a) a Cu particle on a Cu substrate, (b) a Cu particle immersed in Pb(l) at zero flow, and (c) a Cu particle at a Cu(001)/Pb(l) interface for zero flow condition. Top images show simulation configurations at $t=1\mathrm{ns}$; bottom images show force computed using 100 time sample averages (see text). In legends, P-S is particle-substrate and P-L is particle-liquid.

Figure 11

Force on the particle shown in Figs. 8 and 9. Force components in $x$ (triangles) and $z$ (no symbol) are shown and force exerted on the particle by the liquid (solid curves) is distinguished from force exerted by the substrate (broken curves).

Figure 12

Force due to liquid atoms on the particle shown in Fig. 8 (also for data in Fig. 11). Force contributions are distinguished based on where in the system liquid atoms are located (as shown by horizontal and vertical dividing lines). The largest vector shown corresponds to 8.3 nN and all vectors are scaled the same. Times shown are the same as in Fig. 8.

Figure 13

Force due to liquid atoms on the particle shown in Fig. 9 (also for data in Fig. 11). These images show a continuation from Fig. 12; times shown are the same as in Fig. 9.