Contradictory concepts in tortuosity determination in porous media in electrochemical devices

Abstract

Porous media are a vital component in almost every electrochemical device in the form of electrode, support or gas diffusion layers. Microstructural parameters of porous layers such as tortuosity, porosity and pore size diameter are of high importance and crucial for diffusive mass transport calculations. Among these parameters, the tortuosity remains ill-defined in the field of electrochemistry, resulting in a wide range of different calculation approaches. Here, we present a systematic approach of calculating the tortuosity of different porous samples using image and diffusion cell experimental-based methods. Image-based analyses include a selection of geometric and flux-based tortuosity calculation algorithms. Differences between the image and diffusion cell-based results are encountered and attributed to the small pore diameters and thereby induced Knudsen effects within the samples which govern the diffusion flux. Highlights Microstructural analysis of oxygen transport membrane porous supports.  Correlative tortuosity determinations via X-ray tomography and diffusion cell experiments.  Evaluation of the effect of tortuosity, porosity and sample thickness on diffusion resistance.  Visible differences between different tortuosity calculation approaches are encountered.  Diffusion cell experiments yield the highest and geometric-based image quantification algorithms result in the lowest tortuosity values.

Tortuosity of porous media: Image analysis and physical simulation

“…Basically, the 18-neighborconnectivity criterion is used in the LBM simulation because of the adoption of the D3Q19 lattice arrangement, while the RWM, FDM and FVM simulations follow the 6-neighbor-connectivity criterion which only permits direct exchange of dependent variables occurring between adjacent pore voxels with common faces. However, according to the comparison results in previous studies (Iwai et al, 2010;Cooper et al, 2013;Tariq et al, 2014;Cooper et al, 2016;Tjaden et al, 2017), as well as our computational experiences (as shown in Figure 14, 27 and 30), numerical errors are very tiny and negligible for the high-delity simulations performed on 3D high-resolution images of porous media samples. Therefore, the above analysis results on physical tortuosities are reliable, although dierent numerical simulation methods are used for this comparison study.…”

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

“…As a final note that generalizes the conclusions of Tjaden et al [493,494], over the past century, numerous correlations for the tortuosity as a function of the porosity have been proposed, leading to some form of = ( s ) , based on empirical findings, theoretical calculations and Monte Carlo simulations over packings of spheres and other objects (e.g., to represent fibers), overlapping or not, with mono-or polydisperse distributions of sizes [313]. A popular correlation is = s −a , sometimes called Archie's Law (in petroleum engineering) or related to the Bruggeman's [495] effective medium approximation in its simplest form (often used in electrochemical research [494]), where a = 0.5, while the model of Wakao and Smith [413] would predict a = 1.…”

“…Tjaden et al [493,494] have investigated the calculation of tortuosities in electrochemical devices. They have presented a systematic approach of calculating the tortuosity of different porous samples using image and diffusion cell experimental-based methods.…”

The Effects of Constriction Factor and Geometric Tortuosity on Li‐Ion Transport in Porous Solid‐State Li‐Ion Electrolytes

“…Comparing the 100% volume and the 90% sub‐volume tortuosity values, the X‐, Y‐, and Z‐axes showed differences of 0.12%, 0.06%, and 0.14%, respectively. For reference, Tjaden et al observed differences of 7% between their 100% volume and their 90% sub‐volume tortuosity values and concluded that their 3D image volume was large enough to be representative 57. As such, the Trilayer 1 image region was considered as representative of the overall sample.…”