Near-surface viscosity effects on capillary rise of water in nanotubes

In this paper, we present an approach for predicting nanoscale capillary imbibitions using the Lucas-Washburn (LW) theory. Molecular dynamics (MD) simulations were employed to investigate the effects of surface forces on the viscosity of liquid water. This provides an update to the modified LW equation that considered only a nanoscale slip length. An initial water nanodroplet study was performed to properly elucidate the wetting behavior of copper and gold surfaces. Intermolecular interaction strengths between water and corresponding solid surfaces were determined by matching the contact angle values obtained by experimental measurements. The migration of liquid water into copper and gold capillaries was measured by MD simulations and was found to differ from the modified LW equation. We found that the liquid layering in the vicinity of the solid surface induces a higher density and viscosity, leading to a slower MD uptake of fluid into the capillaries than was theoretically predicted. The near-surface viscosity for the nanoscale-confined water was defined and calculated for the thin film of water that was sheared between the two solid surfaces, as the ratio of water shear stress to the applied shear rate. Considering the effects of both the interface viscosity and slip length of the fluid, we successfully predicted the MD-measured fluid rise in the nanotubes.

Figure 1

(a) Schematic simulation domains of liquid water uptake into a nanoscale capillary tube. (b) Water droplet on a solid substrate. (c) Liquid water molecules in a periodic cubic box. (d) Thin film of liquid water sheared between two solid walls.

Figure 2

Contact angle variation as a function of wall-fluid interaction strength.

Figure 3

(a) Variation in velocity profiles according to the surface wettability in the vicinity of a solid wall; (b) slip length as a function of wall-fluid interaction strength ratio.

Figure 4

(a) Height of fluid meniscus inside nanoscale capillaries made of copper and gold at 0.7 ns. (b) The uptake of liquid water into capillary for the cases ${\varepsilon }_{\mathrm{r}}^{\text{Cu-water}}=1.7$ and ${\varepsilon }_{\mathrm{r}}^{\text{Au-water}}=1.3$ compared to the prediction of modified LW equation (2) at 0.7 ns.

Figure 5

Shear stress $\left(S_{XZ}\right)$ and density distributions of liquid water sheared between solid walls presented together for the cases (a) ${\varepsilon }_{\mathrm{r}}^{\text{Cu-water}}=1.7$ and (b) ${\varepsilon }_{\mathrm{r}}^{\text{Au-water}}=1.3$. (c) The local viscosity profiles plotted for the corresponding cases of ${\varepsilon }_{\mathrm{r}}$. (d) The influence of wall-fluid interaction strength on the near-surface and bulk viscosity.

Figure 6

The ratio of the height of the fluid meniscus derived from the theoretical predictions (2) and (8) to the MD-measured fluid rise at 0.7 ns for several cases of surface wettability. The dashed red line denotes the height ratio for theory and MD meniscus results, in which the MD fluid rise and prediction are entirely matched.