Stochastic reconstruction

The mesoscopic modeling approach consists of a stochastic reconstruction method for the generation of the CL and GDL microstructures, and a two-phase lattice Boltzmann method for studying liquid water transport and flooding phenomena in the reconstructed microstructures. 

Detailed description of a porous microstructure is an essential prerequisite for unveiling the influence of pore morphology on the underlying two-phase behavior. This can be achieved either by 3-D volume imaging or by constructing a digital microstructure based on stochastic reconstruction models. Non-invasive techniques, such as X-ray micro-tomography, are the popular methods for 3-D... 

The stochastic reconstruction method is based on the idea that an arbitrarily complex porous structure can be described by a binary phase function which assumes a value 0 in the pore space and 1 in the solid matrix29 The intrinsic randomness of the phase function can be adequately qualified by the low order statistical moments, namely porosity and two-point autocorrelation function.29 The porosity is the probability that a voxel is in the pore space. The two-point autocorrelation function is the probability that two... 

The steady-state flow numerical experiment was primarily designed to evaluate the phasic relative permeability relations. The numerical experiment is devised within the two-phase lattice Boltzmann modeling framework for the reconstructed CL microstructure, generated using the stochastic reconstruction technique described earlier. Briefly, in the steady-state flow experiment two immiscible fluids are allowed to flow simultaneously until equilibrium is attained and the corresponding saturations, fluid flow rates and pressure gradients can be directly measured and correlated using Darcy s law, defined below. 

An alternative to stochastic reconstruction of multiphase media is the reconstruction based on the direct simulation of processes by which the medium is physically formed, e.g., phase separation or agglomeration and sintering of particles to form a porous matrix. An advantage of this approach is that apart from generating a medium for the purpose of further computational experiments, the reconstruction procedure also yields information about the sequence of transformation steps and the processing conditions required in order to form the medium physically. It is thereby ensured that only physically realizable structures are generated, which is not necessarily the case when a stochastic reconstruction method such as simulated annealing is employed. 

Kainourgiakis ME, Kikkinides ES, Stubos AK, Kanellopoulos NK. (1999) Simulation of self-diffusion of point-like and finite-size tracers in stochastically reconstructed Vycor porous glasses. J Chem Phys 111 2735-2743. 

Fig. 1. The computer-generated RES A (left) and its stochastic reconstruction B (right).

Total export of individual PAH compounds was calculated by the weighted export of the individual PAH compounds. As weighting factor, the probability of a specific combination of soil profiles and contamination level was chosen. The weighting factor is thus given by the probability of occurrence as obtained by the stochastic reconstruction of the soil profiles. For all selected PAH the observed export varied by more than 4 orders of magnitude (Fig. 1.7). Export decreases in the order of Phenanthrene > Benzo(k) fluoranthene > Pyrene > Benzo(a)pyrene. Due to the linear relations of the partition coefficients, the export of the individual PAH is proportional to both the... 

Stochastic reconstruction A type of reconstruction in which limited experimental data is used to generate a statistically representative model of a material Strength See bonding-, impact-, tensile strength... 

Recently, a new class of stochastic CL models has been developed (Mukherjee and Wang, 2006). These models simulate species transport in a small 3D domain of the catalyst layer. The domain is subdivided into elementary computational cells representing either a void space or an electrolyte/carbon phase. The structure of this domain is obtained by the stochastic reconstruction of micro-images of real catalyst layers. 

Stochastic reconstruction of the MPL (Source Ref. 32, with permission from Elsevier.)... 

Characterisation of nanostructured materials by combination of neutron scattering and 3D stochastic reconstruction techniques... 

The purpose of the stochastic reconstruction procedure applied in the present work is the generation of a digitised 3-dimensional snapshot of Z(x) with a specified statistical behaviour assumed to be described by the first two moments of Z(x), namely the porosity and the two point correlation function. The algorithm used for the reconstruction was first proposed by Joshi [16] and was extended in three dimensions by Quiblier [17] and Adler et al. [2]. In brief, the space is discretised in cubic elements, the position of which is characterized by the vector x"=(i,J, k) where i,j, k integers with values 1, 2,..., N and a random value Ai x ) is assigned to any element. The values X(x ) are uncorrelated and normally distributed with a... 

The analysis is based on averages of four realizations of reconstructions of two different porous media with c=0.42 and 8=0.355, respectively. Typical cross sections for each medium are shown in Fig. 2. A comparison between the experimental autocorrelation functions (SANS data) and the autocorrelation functions measured on the reconstructed media is presented in Fig. 3a and 3b. It is evident that the stochastic reconstructions exhibit nearly identical autocorrelation functions with the experimentally observed ones. This indicates that the reconstructed materials respect the basic statistical content of the actual porous materials. 

In this annealing technique, the scaling method was applied for two scales. Scales are defined based on different observable structures at different resolutions of SEM and their statistical information. The annealing stochastic reconstruction and the direct simulation of the charge continuity equation are performed in the following subsections. 

Barbosa, R., Andaverde, X, Escobar, B. Cano, U. Stochastic reconstruction and a scaling method to determine effective transport coefficients of a proton exchange membrane fuel cell catalyst layer. J. Power Sources 196 (2011a),pp. 1248-1257. 

Barbosa, R., Escobar, B., Cano, U., Pedicini, R., Ornelas, R. Passalacqua, E. Stochastic reconstruction at two scales and experimental validation to determine the effective electrical resistivity of a PEMFC catalyst layer. Ci Trara. 41 1 (2011b), pp. 2061-2071. 

Capek, R, Hejtminek, V, Brabec, L., Zikanova, A. Kocirik, M. Stochastic reconstruction of particulate media using simulated annealing Improving pore connectivity Transp. Porous Media 76 (2009), pp. 179-198. 

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