Permeability and flow through a packed bed of beads in a rectangular cross‐section affected by overlapping wall effects. Issue 1 (18th November 2019)

• Record Type: Journal Article
• Authors: Boettcher, Konrad; Neumann, Tim; Ehrhard, Peter
• Other Names: Eberhardsteiner J. guestEditor.; Schöberl M. guestEditor.
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 19:Issue 1(2019)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2019-11-18
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.201900302
• Languages: English
• ISSNs: 1617-7061

Abstract

Abstract: The beads in a packed bed are usually distributed randomly. Therefore, on a macroscopic scale, a fluid flows uniformly through such a porous medium. For thin porous media, deviations are known near the regions of confinement. This so‐called wall effect is extensively investigated in literature for circular confinements. In this work, the wall effect and the flow through porous media in a rectangular domain is studied. This has great importance during the initial filling process of lithium‐ion batteries with the liquid electrolyte. Such batteries consist of collector foils, on which the porous electrodes are attached. Their thickness is only 5 – 10 times a particle diameter d P and may be modeled as a monodisperse bed of spheres. The filling flow is extremely slow and may be in the pre‐Darcy flow region, wherefore the validity of Darcy's law is experimentally checked. Then, the local porosity function depending on the distance to the wall is experimentally determined. For very thin porous media, the wall effect of each wall may overlap each other, which is taken into account by using an overlapping model from the literature. The widely used model of Carman‐Kozeny [1] relates the permeability with the porosity. Its validity in the near‐wall region is checked by comparing experimentally‐obtained mean pore diameters to those related to the model of Carman‐Kozeny. The flow through a porous media is computed and compared to experimental results from literature for circular confinement and preliminary optically‐matched PIV measurements.