Dynamic wetting at the nanoscale

Although the capillary spreading of a drop on a dry substrate is well studied, understanding and describing the physical mechanisms that govern the dynamics remain challenging. Here we study the dynamics of spreading of partially wetting nanodroplets by combining molecular dynamics simulations and continuum phase field simulations. The phase field simulations account for all the relevant hydrodynamics, i.e., capillarity, inertia, and viscous stresses. By coordinated continuum and molecular dynamics simulations, the macroscopic model parameters are extracted. For a Lennard-Jones fluid spreading on a planar surface, the liquid slip at the solid substrate is found to be significant, in fact crucial for the motion of the contact line. Evaluation of the different contributions to the energy transfer shows that the liquid slip generates dissipation of the same order as the bulk viscous dissipation or the energy transfer to kinetic energy. We also study the dynamics of spreading on a substrate with a periodic nanostructure. Here it is found that a nanostructure with a length scale commensurate with molecular size completely inhibits the liquid slip. The dynamic spreading is thus about 30% slower on a nanostructured surface compared to one that is atomically smooth.

Figure 1

Snapshots of typical droplet simulations: (a) quasi-2D system with droplet radius $R=24.4$ nm and (b) 3D system with droplet radius $R=10.2$ nm.

Figure 2

Time histories of contact-line position $r$ of complete wetting (${\theta }_{\mathrm{eq}}=0^{\circ }$) and partial wetting (${\theta }_{\mathrm{eq}}={90}^{\circ }$) for droplets with different sizes $R=6.1$, $12.2$, and $24.4$ nm, presented with (a) dimensional units, (b) viscous scaling, and (c) inertial scaling.

Figure 3

Snapshots of droplets at nondimensional time $t{(\gamma /\rho R^3)}^{1/2}=1$. The top row depicts the cases with $R=24.4$ nm for (a) ${\theta }_{\mathrm{eq}}={90}^{\circ }$ and (b) ${\theta }_{\mathrm{eq}}=0^{\circ }$. The bottom row depicts the cases with $R=6.1$ nm for (c) ${\theta }_{\mathrm{eq}}={90}^{\circ }$ and (d) ${\theta }_{\mathrm{eq}}=0^{\circ }$.

Figure 4

Contact line position evolution of droplets ($R=12.2$ nm) with different equilibrium contact angles ${\theta }_{\mathrm{eq}}=0^{\circ }\text{,}{45}^{\circ }\text{,}{90}^{\circ }\text{,}\text{and}{135}^{\circ }$, with the inertial scaling.

Figure 5

Dependence of (a) the exponent $\alpha$ and (b) the prefactor $C$ on the equilibrium contact angle ${\theta }_{\mathrm{eq}}$ for droplets with various radii and dimensions.

Figure 6

Identification of macroscopic parameters from comparison between MD and continuum simulations, for a droplet of radius $12.2$ nm, showing nondimensional spreading distance $r/R$ vs $\tau =t/{(\rho R^3/\gamma )}^{1/2}$. Solid lines represent MD simulations, symbols continuum simulations with a particular slip length: squares, $\lambda =0$ (no slip); diamonds, $\lambda =0.125$; left-pointing triangles, $\lambda =0.25$; up-pointing triangles, $\lambda =0.5$. (a) ${\theta }_{\mathrm{eq}}=3^{\circ }$, (b) ${\theta }_{\mathrm{eq}}={45}^{\circ }$, (c) ${\theta }_{\mathrm{eq}}={90}^{\circ }$, and (d) ${\theta }_{\mathrm{eq}}={135}^{\circ }$.

Figure 7

Contact line evolution on a nanostructured surface $r/R$ as a function of $t/{(\rho R^3/\gamma )}^{1/2}$ for substrate potentials corresponding to equilibrium contact angles (a) ${\theta }_{\mathrm{eq}}=0^{\circ }$, (b) ${\theta }_{\mathrm{eq}}={45}^{\circ }$, and (c) ${\theta }_{\mathrm{eq}}={90}^{\circ }$. In each panel the black diamonds represent the MD simulation on a smooth surface, the black small dots the MD simulations on the rough surface, and the red (gray) solid curves the continuum model simulations with zero slip.

Figure 8

Evolution of the different energy transfer rates, where ${\Gamma }_{\rho }$ is the rate of change of kinetic energy, ${\Gamma }_{\mu }$ the viscous dissipation, and ${\Gamma }_{\lambda }$ the viscous friction due to liquid slip at the wall, as functions of $\tau =t/{(\rho R^3/\gamma )}^{1/2}$.