Anomalous capillary filling and wettability reversal in nanochannels

This work revisits capillary filling dynamics in the regime of nanometric to subnanometric channels. Using molecular dynamics simulations of water in carbon nanotubes, we show that for tube radii below one nanometer, both the filling velocity and the Jurin rise vary nonmonotonically with the tube radius. Strikingly, with fixed chemical surface properties, this leads to confinement-induced reversal of the tube wettability from hydrophilic to hydrophobic for specific values of the radius. By comparing with a model liquid metal, we show that these effects are not specific to water. Using complementary data from slit channels, we then show that they can be described using the disjoining pressure associated with the liquid structuring in confinement. This breakdown of the standard continuum framework is of main importance in the context of capillary effects in nanoporous media, with potential interests ranging from membrane selectivity to mechanical energy storage.

Figure 1

Top: Schematic of the system. Bottom: Snapshot of a system used for the MD simulations (tube radius $a_c=3.9\AA$), made using the VMD (Visual Molecular Dynamics) software [28]. The empty right reservoir is not shown.

Figure 2

Example of data acquisition (tube radius $a_c=5.1$ Å). Top: number of molecules inside the tube $N$ as a function of time. Bottom: measured meniscus pressure jump $p_0-p_L$. MD results are in blue, linear fits in orange, and equilibration phases are gray areas.

Figure 3

Left: Capillary velocity $v_c$ as a function of the tube radius $a_c$, measured from MD simulations (violet squares). The brown line corresponds to the continuum prediction $v_c=4\mathrm{\Delta }\gamma /\left\{\pi C\left(a_c\right)\eta \right\}$, with $C\left(a_c\right)$ computed using the finite element method (see text for details), $\mathrm{\Delta }\gamma =14$ mN/m, and $\eta =0.855$ mPa s. Right: Normalized capillary velocity $v_c\pi C\left(a_c\right)\eta /\left(4\mathrm{\Delta }\gamma \right)$ (full violet squares) and meniscus pressure jump $\mathrm{\Delta }{p}^{\text{men}}a/\left(2\mathrm{\Delta }\gamma \right)$ (open green circles), with $a$ the effective radius of the tube (see text).

Figure 4

Top: Ascension under a gravity field (Jurin-like numerical experiment) inside subnanometric nanotubes. Tube radii from left to right: 3.9, 4.3, 5.5, and 8.2 Å. Bottom: Snapshot of water molecules inside CNTs of various radii, $a_c=3.9$, 4.3, 4.7, 5.1, 5.5, 5.9, 6.2, 7.0, and 8.2 Å.

Figure 5

Left: capillary velocity of the model liquid metal $v_c$ as a function of the CNT radius $a_c$. Right: meniscus pressure jump $p_0-p_L$ estimated from static measurements. Green symbols represent MD results, and brown lines correspond to standard continuum predictions (see text).

Figure 6

Capillary filling of slit graphitic channels. Symbols: total pressure drop $\mathrm{\Delta }{p}^{\text{men}}$ measured in static simulations (left) and capillary velocity (right) as a function of the interplate distance $h_c$. Brown line: continuum prediction (without structuring effects), using $\mathrm{\Delta }\gamma =25$ mN/m. Violet line: extended prediction with structuring effects (see text for details).

Figure 7

Left: Geometry used for the finite element calculations. Two reservoirs are separated by a membrane containing a channel of radius $a$ and length $L$. The black dashed line corresponds to an axisymmetric condition. The full line represents the effective liquid-solid interface, where a perfect slip boundary condition applies. Note that the atomic chamfering of the entrance due to the spherical shape of carbon atoms is accounted for in the geometry used for the finite element calculations. Right: value of the $C$ coefficient calculated from the normalized hydrodynamic resistance; data extracted from Ref. [34]. Circles represent MD results with armchair tubes, squares represent MD results with zigzag tubes, and the line is the hydrodynamic prediction computed with finite element calculations.