Molecular transportation phenomena of simple liquids through a nanoporous graphene membrane

The mechanism of pressure-driven transport of simple liquid through a nanoporous graphene membrane has been analyzed using nonequilibrium molecular dynamics simulation. In this study, we investigate liquid dynamics properties such as local density, pressure variation, and local viscosity depending on the flow region. With movement of the specular reflection wall at the end of the front and back reservoirs, a pressure difference occurs mainly due to the change in the relative distance between the liquid molecules in the corresponding reservoir. The interfacial pressure difference strongly depends on the intermolecular force of the graphene membrane governed by the layered structure of the simple liquid and the applied flow velocity. The local viscosity was calculated for a nanochannel of simple liquid sheared by graphene walls. The liquid velocity adjacent to the pore edge was considered as the slip velocity, which provides updates in the Sampson flow equation. We observed that the entrance interfacial pressure and higher local viscosity in the vicinity of the graphene membrane, which are associated with the optimized definition of the wall-liquid boundary near the pore edge, play a critical role in the permeation of simple liquids through the nanoporous graphene membrane.

Figure 1

(a) Schematics of the flow of liquid argon through a nanoporous graphene membrane, (b) physical description of the specular reflection wall, and (c) inset of the graphene pore with the three probable pore boundaries.

Figure 2

The density distribution of argon along with the axial direction of flow within the $a_{\mathrm{cc}}=1.10925\mathrm{nm}$ pore radius

Figure 3

(a) The pressure distribution of argon along the axial direction of flow within the $a_{\mathrm{cc}}=1.10925\mathrm{nm}$ pore radius at $U_w=1.5\mathrm{m}{\mathrm{s}}^{-1}$, and (b) variation of the pressure difference between the front and back reservoirs in the bulk and interface region, respectively, with the increase of $U_w$.

Figure 4

(a) Schematics of the MD simulation of liquid argon sheared by graphene walls, (b) the velocity distribution of liquid argon along the $z$ direction of the channel, and (c) shear stress component ($S_{xz}$) of liquid argon compared with density distribution from the nanopore flow simulation.

Figure 5

The distribution of (a) the shear rate $\left(\dot{\gamma }=\frac{d{v}_x}{dz}\right),$ and (b) local viscosity of liquid argon as a result of the shear-driven flow by the graphene walls.

Figure 6

The 3D averaged argon velocity profile in the radial direction ($xy$ plane) within an $a_{\mathrm{cc}}=1.10925\mathrm{nm}$ pore radius at $U_w=3.5\mathrm{m}{\mathrm{s}}^{-1}$.

Figure 7

A comparison of the velocity profile from the NEMD simulations and modified Sampson flow equation within an $a_{\mathrm{cc}}=1.10925\mathrm{nm}$ nm pore radius by varying the pressure difference in the bulk and interface regions (a,b) with the bulk viscosity, and (c), (d) with the interface viscosity at $U_w=1.5$ and 3.5 $\mathrm{m}{\mathrm{s}}^{-1}$.

Figure 8

Comparison of the velocity profile from NEMD simulations and the modified Sampson flow equation for three probable pore boundaries with $\mathrm{\Delta }{P}_{\mathrm{peak}}$ and ${\mu }_{\mathrm{int}}$ at $U_w=1.5\mathrm{m}{\mathrm{s}}^{-1}$. The data were obtained for an $a_{\mathrm{cc}}=1.10925\mathrm{nm}$ pore radius.

Figure 9

A comparison of velocity profiles from the NEMD simulations and modified Sampson flow equation for the pore boundary at $L^{\prime \prime }$ with $\mathrm{\Delta }{P}_{\mathrm{peak}}$ and ${\mu }_{\mathrm{int}}$. Each line and circle symbol profile with the same color (from bottom) represents the data for $U_w=1.0,1.5,2.0$, and $2.5\mathrm{m}{\mathrm{s}}^{-1}$, respectively. Data ware obtained for an $a_{\mathrm{cc}}=1.10925\mathrm{nm}$ pore radius.