We present an investigation of molecular permeation of gases through nanoporous graphene membranes via molecular dynamics simulations; four different gases are investigated, namely helium, hydrogen, nitrogen, and methane. We show that in addition to the direct (gas-kinetic) flux of molecules crossing from the bulk phase on one side of the graphene to the bulk phase on the other side, for gases that adsorb onto the graphene, significant contribution to the flux across the membrane comes from a surface mechanism by which molecules cross after being adsorbed onto the graphene surface. Our results quantify the relative contribution of the bulk and surface mechanisms and show that the direct flux can be described reasonably accurately using kinetic theory, provided the latter is appropriately modified assuming steric molecule-pore interactions, with gas molecules behaving as hard spheres of known kinetic diameters. The surface flux is negligible for gases that do not adsorb onto graphene (e.g., He and H2), while for gases that adsorb (e.g., CH4 and N2) it can be on the order of the direct flux or larger. Our results identify a nanopore geometry that is permeable to hydrogen and helium, is significantly less permeable to nitrogen, and is essentially impermeable to methane, thus validating previous suggestions that nanoporous graphene membranes can be used for gas separation. We also show that molecular permeation is strongly affected by pore functionalization; this observation may be sufficient to explain the large discrepancy between simulated and experimentally measured transport rates through nanoporous graphene membranes.

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A droplet placed in a liquid-liquid solution is expected to grow, or shrink, in time as $t 1=2 . In this Letter, we report experimental evidence that when the composition in the interface is far from thermodynamic equilibrium due to the nonideality of the mixture, a droplet shrinks as $t. This scaling is due to the coupling between mass and momentum transfer known as Korteweg forces as a result of which the droplet self-propels around. The consequent hydrodynamic convection greatly enhances the mass transfer between the droplet and the bulk phase. Thus, the combined effect of nonideality and nonequilibrium modifies the dynamical behavior of the dissolving droplet. DOI: 10.1103/PhysRevLett.103.064501 PACS numbers: 47.51.+a, 64.75.Bc, 68.05.Àn The formation and dissolution of gas bubbles and liquid droplets in liquid-gas and liquid-liquid systems are major concerns in many industrial processes as they occur in mixing and separation, in dispersion of food products, and in pharmaceutically controlled drug delivery, for instance. When a gas bubble or a liquid droplet is placed in a gas-liquid or liquid-liquid mixture, it is expected to grow (or to shrink) by diffusion; this process is described by the well-known diffusion equation, as @ 1 =@t ¼ Àr Á j 1 in terms of the local concentration 1 ðr; tÞ and mass flux j 1 of component A in the mixture. If one assumes a binary, ideal mixture, the net mass flux can be calculated by Fick's law, j 1 ¼ ÀD 0 r 1 , where D 0 is the experimentally determined diffusion coefficient. Based on this model, the seminal work by Epstein and Plesset [1], which describes successfully the t 1=2 shrinkage dynamics of a spherical air bubble in an air-water solution, has been recently extended and the t 1=2 scaling experimentally validated also for a liquid droplet (aniline or water) dissolving in a liquidliquid (water-aniline or aniline-water) solution [2].Fickian diffusion, however, is strictly limited to ideal mixtures and cannot hold for multiphase systems, even at thermodynamic equilibrium. A more general formulation for the mass flux can be found by means of nonequilibrium2 are the chemical potentials of the two components, and 1 , 2 , are the mobility (or Onsager) coefficients. While the diffusivity D 0 can be a constant for a binary system, the mobility coefficients are composition dependent [4]. For an ideal mixture or in the dilute limit, this formulation reduces to Fick's law. Following Cahn and Hillard [5], for a heterogeneous system, the local molar Gibbs free-energy g can be written as the sum of a local and a nonlocal contribution: g ¼ g loc þ 1 2 a 2 RTðr Þ 2 , where a is the characteristic length scale of inhomogeneity [6] (different formulations for the free energy have also been developed [9]). Using a mobility coefficient of the form ¼ ð1 À ÞD 0 and assuming the Flory-Huggins local free energy, Mauri et al. [7] proposed the net mass flux j ¼ À ð1 À ÞD 0 r~, with~¼ 0 þ log 1À þ Éð1 À 2 Þ À a 2 r 2 where É is the Margules parameter. As a result, we can write j ¼ ÀD 0 r þ ð1...

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