Continuum/Nano-Scale Simulation of Surface Diffusion Process in Flow
Authors: Yang Xiaofan , Zheng Z. Charlie 
Published: August 2012

Fluid transport with diffusion through micro-/nano-channels is found in many natural phenomena and industrial processes, including fluid transport or diffusion through nano-materials, molecular/atomistic transfer across nuclear pores or in the MEMS devices among other applications. Those nano-pores can be treated as nano-channels in the thin layers of the membranes. The transport phenomena of fluid in such small confined channels, usually in the size of ten molecular diameters or less, differs significantly from its bulk behaviors and cannot be described with continuum theory. In this case, molecular dynamics (MD) simulation, rather than continuum methods, is better suited to study the phenomena. The surface diffusion, related to both the fluid and solid material properties and the flow rate, can be used as a parameter for estimating the adsorbing capacity of a porous nano-material. The transport of fluids through porous materials occurs mainly by diffusion. In this study, a molecular-continuum hybrid scheme is used for the study of the diffusion in a representative Couette flow problem. By varying the velocity of the moving-solid wall, we investigated the effect of the shearing condition on the mass flux going through the pores. The relationship of the physical mechanisms and the transport phenomena (e.g. Fick’s law) were then linked among the different length scales. Activated carbon with its high surface area has been emerging as a promising candidate for an adsorbent due to not only its stable thermodynamic and mechanical properties but also its homogenous and isotropic porous distribution and relatively even pore size. In this study, we focus on the characteristics of the permeation and the adsorption process between different gases and the carbon substrate under various shearing conditions. The investigation of the diffusion process of fluids through the pores of the nano-materials has become an interesting topic in recent decades. This investigation has been divided into two major areas: 1) the diffusivity estimation and 2) the transient diffusion rate. We apply a continuum/MD hybrid scheme to a model problem of various gases transport through a carbon substrate with several pores in a channel flow under different shear rates. Instead of inserting and deleting particles from the control volumes used in the DCV-GCMD method, we keep the number of particles in the simulation system constant. The interactions between fluid/fluid, fluid/solid and solid/solid are all assumed to be under Lennard-Jones potentials. In the modeled Couette flow, the two solid walls are constructed with nano-pores that allow fluids to go through the substrate to study the transient diffusion rate (flux). Before simulating the fluid transport through the nano-pores, we need to validate the natural diffusion properties of the bulk fluid. To do this, a system (as a cube) consisting of pure liquid argon molecules is used to perform the pure MD simulation. The radial distribution function (RDF) is used as the parameter to verify the natural diffusion of the liquid argon fluid in the bulk flow, which is a structural correlation. It describes the spherically averaged local organization around any given molecule. Figure 1 shows a good comparison of the radial distribution functions between the MD prediction and the experimental measurement of Eisenstein and Gingrich (1942). By comparing our calculation to Wu et al. (2008) under similar circumstances, we found that the average (from 8 pores) and corrected mass flux J · (RTh) is linearly proportional to the average pressure gradient along the pore. And the slope of this relationship is the transport diffusivity, which is 4.6 × 10−7m2/s under 273K and 4.9 × 10−7m2/s under 300K. This indicates that the current simulation follows the Fick’s law exactly. Similarly, for other gases, the same linear relationships can also be obtained. These calculations are listed in Table 1 that shows the transport diffusivity increases with temperature. The mass fluxes of three gases at various pore widths are calculated as shown in Fig. 2. Generally, with larger pores, the mass fluxes increase. However, among three gases, the increase of H2 is much faster than the other two gases because of hydrogen’s smaller molecular size. In another word, smaller molecules as H2 have faster diffusion rates during the adsorption process.