Numerical Modeling of Diffusion in Complex Media with Surface Interaction Effects (original) (raw)

Numerical modeling of diffusion within composite media

2013

t. Within biological systems, which contain complex and composite media, diffusion may depend not only on internal geometry, but also on the chemical interactions between solid phase and transported particles. New hierarchical multiscale microstructural model for diffusion within complex media is presented. Hierarchical modeling approach is then employed to construct a continuum diffusion model based on a novel numerical homogenization procedure, using which we evaluate constitutive material parameters.

On diffusion in nanospace

Diffusion in nanospace does not strictly obey to Fick's law generally used in macroenvironment. Deviation from this law is due to surface effects, i.e. due to interaction between transported molecules and bounding surfaces. A hierarchical modeling approach which accounts for interface effects on the diffusion coefficient was introduced in Ziemys et al. (2011). The model employs molecular dynamics (MD) for calculation scaling functions to reduce the diffusion coefficient corresponding to "bulk" values. With this reduced diffusion coefficient, modeling is performed using the finite element method (FE) within an incremental iterative scheme. In this paper we summarize this hierarchical (multiscale) model and present its generalization to include adsorption at the walls. Also, we briefly discuss further possible applications of the multiscale modeling of diffusion through complex media with distributed solid constituents, as in case of polymers or biological fluids.

Multiscale Modelling of Transport, Reaction and Phase Change in Heterogeneous Media

JOURNAL OF CHEMICAL ENGINEERING OF JAPAN, 2007

Methodology for the modelling of transport (convection, diffusion, heat conduction), reaction, and phase transformation processes in spatially complex heterogeneous media is reviewed and demonstrated on several application examples, including computer simulations of polymer particle growth and fragmentation, modelling of reaction and diffusion in a catalyst washcoat, and drying of solvent from a static granular bed. The commonalities and differences between each application are discussed, and perspectives on future research directions in multi-scale modelling are provided.ˇǏ

Hierarchical modeling of diffusive transport through nanochannels by coupling molecular dynamics with finite element method

Journal of Computational Physics, 2011

We present a successful hierarchical modeling approach which accounts for interface effects on diffusivity, ignored in classical continuum theories. A molecular dynamics derived diffusivity scaling scheme is incorporated into a finite element method to model transport through a nanochannel. In a 5 nm nanochannel, the approach predicts 2.2 times slower mass release than predicted by Fick's law by comparing time spent to release 90% of mass. The scheme was validated by predicting experimental glucose diffusion through a nanofluidic membrane with a correlation coefficient of 0.999. Comparison with experiments through a nanofluidic membrane showed interface effects to be crucial. We show robustness of our discrete continuum model in addressing complex diffusion phenomena in biomedical and engineering applications by providing flexible hierarchical coupling of molecular scale effects and preserving computational finite element method speed.

Connecting theory and simulation with experiment for the study of diffusion in nanoporous solids

Adsorption

Nanoporous solids are ubiquitous in chemical, energy, and environmental processes, where controlled transport of molecules through the pores plays a crucial role. They are used as sorbents, chromatographic or membrane materials for separations, and as catalysts and catalyst supports. Defined as materials where confinement effects lead to substantial deviations from bulk diffusion, nanoporous materials include crystalline microporous zeotypes and metal–organic frameworks (MOFs), and a number of semi-crystalline and amorphous mesoporous solids, as well as hierarchically structured materials, containing both nanopores and wider meso- or macropores to facilitate transport over macroscopic distances. The ranges of pore sizes, shapes, and topologies spanned by these materials represent a considerable challenge for predicting molecular diffusivities, but fundamental understanding also provides an opportunity to guide the design of new nanoporous materials to increase the performance of tra...

Monte-Carlo simulations of surface and gas phase diffusion in complex porous structures

Chemical Engineering Science, 2003

A new procedure for estimating surface di usivities and tortuosities within realistic models of complex porous structures is reported. Our approach uses Monte-Carlo tracer methods to monitor mean-square displacements for molecules restricted to wander on pore walls within model random mesoporous solids typical of those used as adsorbents, heterogeneous catalysts, and porous membranes. We consider model porous solids formed from initial packings of spheres with unimodal, Gaussian, or bimodal distributions of size; changes in pellet porosity are achieved by increasing microsphere radii and by randomly removing spheres from highly densiÿed packings in order to simulate densiÿcation and coarsening, respectively. Geometric tortuosities for the surface phase reached large values at void fractions near 0.04 and 0.42 for densiÿed solids; the surface tortuosity gave a minimum value of 1.9 at a void fraction of ∼0.26. These high tortuosities correspond to percolation thresholds for the void and solid phases, which in turn re ect packing densities at which each phase becomes discontinuous. Surface tortuosities for coarsened solids at low void fractions were similar to those in densiÿed solids; however, at void fractions above ∼0.3, surface tortuosities of coarsened solids increased only gradually with void fraction, because coarsening retains signiÿcant overlap among spheres at void fractions above those giving disconnected solids in densiÿed structures. Simulations of bulk di usion within voids were used to compare the transport properties and connectivity of the void space with those of surfaces that deÿne this void space. Surface and void tortuosities were similar, except for void fractions near the solid percolation threshold, because unconnected solid particles interrupt surface connectivity but not gas phase di usion paths. Surface and void tortuosities were also similar for channels within linear chains of overlapping hollow spheres as both tortuosities increased with decreasing extent of sphere overlap. These simulations provide a basis for estimates of surface and void tortuosities, which are essential in the interpretation and extrapolation of di usion rates in complex porous media. Surface and void di usivity estimates di ered signiÿcantly from those obtained from lattice and capillary models of complex porous structures. ?

Multicomponent diffusion in nanosystems

The Journal of Chemical Physics, 2011

We present the detailed analysis of the diffusive transport of spatially inhomogeneous fluid mixtures and the interplay between structural and dynamical properties varying on the atomic scale. The present treatment is based on different areas of liquid state theory, namely kinetic and density functional theory and their implementation as an effective numerical method via the Lattice Boltzmann approach. By combining the first two methods it is possible to obtain a closed set of kinetic equations for the singlet phase space distribution functions of each species. The interactions among particles are considered within a self-consistent approximation and the resulting effective molecular fields are analyzed. We focus on multispecies diffusion in systems with short-range hard-core repulsion between particles of unequal sizes and weak attractive long-range interactions.

Modelling diffusion from simulated porous structures

Chemical Engineering Science, 2008

An algorithm has been developed for the simulation of liquid diffusion from a porous material in the presence of a concentration gradient. A network model, Pore-Cor, was used to create simulated porous networks. These structures comprised cubic pores connected by cylindrical throats each centred on the coordinates of a three-dimensional 10 × 10 × 10 Cartesian matrix of positions. The simulated structure was then saturated with a mixture of benzene and cyclohexane and immersed in static pure cyclohexane. The algorithm then simulated the diffusion of benzene from the porous structure into the surrounding cyclohexane. The effects on the diffusion process of the geometries of the simulated structures were investigated by generating predefined structures and isolating the effect of each geometric parameter. The method presented in this study should lead to a predictive tool for studying the diffusion processes within real samples, as the pore network model can generate void structures which have porosity and percolation properties that closely match experimental mercury intrusion porosimetry data of real porous materials.