Large effect of lateral box size in molecular dynamics simulations of liquid-solid friction

Molecular dynamics simulations are a powerful tool to characterize liquid-solid friction. A slab configuration with periodic boundary conditions in the lateral dimensions is commonly used, where the measured friction coefficient could be affected by the finite lateral size of the simulation box. Here we show that for a very wetting liquid close to its melting temperature, strong finite size effects can persist up to large box sizes along the flow direction, typically $\sim 30$ particle diameters. We relate the observed decrease of friction in small boxes to changes in the structure of the first adsorbed layer, which becomes less commensurable with the wall structure. Although these effects disappear for lower wetting cases or at higher temperatures, we suggest that the possible effect of the finite lateral box size on the friction coefficient should not be automatically set aside when exploring unknown systems.

Figure 1

(a) Density (black line) and velocity (red dots) profiles for three lateral box sizes, $l_x=3.13,6.27$ and $18.8\mathrm{nm}$; the red dotted line is a linear fit of the velocity profile in the bulk region. As illustrated in the three panels, the slip velocity $v_{\mathrm{s}}$ is measured as the liquid velocity at the position of the first density peak. (b) Snapshots of the systems, from left to right: perspective view of the small system and side views of three systems with increasing lateral size $l_x$.

Figure 2

Evolution of the friction coefficient $\lambda$ (averaged over the two confining walls) as a function of the box size $l_x$ along the flow direction. The main curve (solid black points) was obtained for $T=85\mathrm{K}$ and $\alpha =0.774$ (highly wetting case). For comparison, a second curve (open red squares) was obtained for $T=90\mathrm{K}$, and a third (open blue diamonds) was obtained for a wetting coefficient $\alpha =0.387$.

Figure 3

Probability distribution of the surface density of the contact layer (the first adsorption layer) for three lateral box sizes. The surface density can take only discrete values, corresponding to an integer number of particles in the contact layer (see text for details).

Figure 4

(a) Evolution of the friction coefficient with the instantaneous surface density of the contact layer (see text for details on how this is calculated) for the smallest system ($l_x=3.13\mathrm{nm}$); left and right snapshots illustrate the organization of particles in the contact layer for a surface density of 7.33 and $7.64{\mathrm{nm}}^{-2}$, respectively. (b) Probability distribution of the surface density in the same system.

Figure 5

Comparison of the structures of the contact layer at the two most probable surface densities, 7.33 and $7.64{\mathrm{nm}}^{-2}$, for a system size $l_x=3.13\mathrm{nm}$. (a) Snapshots of the contact layer. (b) Average two-dimensional Fourier transform of the contact layer structure. (c) Average of the instantaneous Fourier transforms after a rotation procedure to orient them along the same principal axis.

Figure 6

Cosine of the contact angle, estimated by sessile droplet simulations, as a function of the wetting coefficient $\alpha$. Three density distributions of the droplet for $\text{cos}\theta <0$, $\approx 0$, and $>0$ are also shown.

Figure 7

Density profiles along $z$ in the contact layer for the two most probable surface densities in the smallest system, with $l_x=3.13\mathrm{nm}$. The cartoon on the left illustrates that the contact layer can approach closer to the wall when it is more commensurate.

Figure 8

Probability distribution of surface density for the smallest system ($l_x=3.13\mathrm{nm}$) and for two different wetting coefficients $\alpha$.