Mass transfer in fibrous media with varying anisotropy for flow battery electrodes: Direct numerical simulations with 3D X-ray computed tomography

Abstract

A numerical method for calculating the mass transfer coefficient in fibrous media is presented. First, pressure driven flow was modelled using the Lattice Boltzmann Method. The advection-diffusion equation was solved for convective-reacting porous media flow, and the method is contrasted with experimental methods such as the limiting current diffusion technique, for its ability to determine and simulate mass transfer systems that are operating at low Reynolds number flows. A series of simulations were performed on three materials; specifically, commercially available carbon felts, electrospun carbon fibers and electrospun carbon fibers with anisotropy introduced to the microstructure. Simulations were performed in each principal direction (x,y,z) for each material in order to determine the effects of anisotropy on the mass transfer coefficient. In addition, the simulations spanned multiple Reynolds and Péclet numbers, to fully represent highly advective and highly diffusive systems. The resulting mass transfer coefficients were compared with values predicted by common correlations and a good agreement was found at high Reynolds numbers, but less so at lower Reynolds number typical of cell operation, reinforcing the utility of the numerical approach. Dimensionless mass transfer correlations were determined for each material and each direction in terms of the Sherwood number. These correlations were analyzed with respect to each materials' permeability tensor. It was found that as the permeability of the system increases, the expected mass transfer coefficient decreases. Two general mass transfer correlations are presented, one correlation for isotropic fibrous media and the other for through-plane flow in planar fibrous materials such as electrospun media and carbon paper. The correlations are Sh = 0.879 Re 0.402 Sc 0.390 and Sh = 0.906 Re 0.432 Sc 0.432 respectively.

Developments in X-ray tomography characterization for electrochemical devices

“…Image-based modelling can provide a powerful tool in the prediction and optimisation of LIBs [83]; as previously mentioned, models based on X-ray CT data may be employed to generate structures or evaluate local transport properties [70], allowing 3D or 4D distributions of local current or potential to be mapped [97], possibly even across multiple length scales [98], even to the extent of cell failure [95]. Nevertheless, imaged-based modelling such as this is not limited to LIB and has recently seen interest from other battery chemistries [71,99].…”

The effect of non-uniform compression and flow-field arrangements on membrane electrode assemblies - X-ray computed tomography characterisation and effective parameter determination

“…To quantify the change in the membrane thickness, a chord length distribution was employed, as described by Kok et al [65]. Chords refer to the straight lines drawn at each membrane voxel element, and their length represents the membrane thickness at particular coordinates.…”

Redox flow batteries for energy storage: their promise, achievements and challenges

“…Both the local mass transfer at fibre level and the global mass transfer coefficient in utility-scale electrodes experiencing non-homogeneous porous fluid flow can be simulated. For instance, by digitising their geometry from X-ray CT scans, mass transfer coefficients and dimensionless correlations have been calculated for carbon felts using the Lattice Boltzmann method (LBM) [27,28]. This allowed correlations to be established at low Reynolds numbers [27], along global dispersion and reaction rate coefficients [28].…”

“…This approach could be used to validate mechanical stress distribution models [52]. CT is also being employed to study the effect of compression on carbon felt properties [27], and to determine the surface area of porous electrodes (but only after calibration and validation of the methodology) [69]. In relation to materials research, limited attention has been given to the advantages and limitations of composite membranes [70,71] Additive manufacturing to build 3D objects has also been consider to design electrochemical cells with characteristics that would not be possible to realise by CNC and to created rapid prototypes [11].…”