Population Balance Models for Particulate Flows in Porous Media: Breakage and Shear-Induced Events

Icardi, Matteo; Pasquale, Nicodemo Di; Crevacore, Eleonora; Marchisio, Daniele; Babler, Matthaus U.

Abstract

Transport and particulate processes are ubiquitous in environmental, industrial and biological applications, often involving complex geometries and porous media. In this work we present a general population balance model for particle transport at the pore-scale, including aggregation, breakage and surface deposition. The various terms in the equations are analysed with a dimensional analysis, including a novel collision-induced breakage mechanism, and split into one- and two-particles processes. While the first are linear processes, they might both depend on local flow properties (e.g. shear). This means that the upscaling (via volume averaging and homogenisation) to a macroscopic (Darcy-scale) description requires closures assumptions. We discuss this problem and derive an effective macroscopic term for the shear-induced events, such as breakage caused by shear forces on the transported particles. We focus on breakage events as prototype for linear shear-induced events and derive upscaled breakage frequencies in periodic geometries, starting from nonlinear power-law dependence on the local fluid shear rate. Results are presented for a two-dimensional channel flow and a three dimensional regular arrangement of spheres, for arbitrarily fast (mixing-limited) events. Implications for linearised shear-induced collisions are also discussed. This work lays the foundations of a new general framework for multiscale modelling of particulate flows.

Citation

Icardi, M., Pasquale, N. D., Crevacore, E., Marchisio, D., & Babler, M. U. (2023). Population Balance Models for Particulate Flows in Porous Media: Breakage and Shear-Induced Events. Transport in Porous Media, 146, 197-222. https://doi.org/10.1007/s11242-022-01793-5

• Journal Article Type: Article
• Acceptance Date: Apr 22, 2022
• Online Publication Date: May 26, 2022
• Publication Date: 2023-01
• Deposit Date: Jun 1, 2022
• Publicly Available Date: Jun 1, 2022
• Journal: Transport in Porous Media
• Print ISSN: 0169-3913
• Electronic ISSN: 1573-1634
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 146
• Pages: 197-222
• DOI: https://doi.org/10.1007/s11242-022-01793-5
• Keywords: General Chemical Engineering; Catalysis
• Public URL: https://nottingham-repository.worktribe.com/output/8226923
• Publisher URL: https://link.springer.com/article/10.1007/s11242-022-01793-5