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Population Balance Models for Particulate Flows in Porous Media: Breakage and Shear-Induced Events
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2023 (English)In: Transport in Porous Media, ISSN 0169-3913, E-ISSN 1573-1634, Vol. 146, no 1-2, p. 197-222Article in journal (Refereed) Published
Abstract [en]

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. 

Place, publisher, year, edition, pages
Springer Nature , 2023. Vol. 146, no 1-2, p. 197-222
Keywords [en]
Mixing, Particulate flows, Population balance equation, Porous Media, Upscaling, Shear flow, Spheres, Flows in porous media, Particulate process, Population balance modelling, Population-balance equations, Porous medium, Shear-induced, Transport process, Porous materials, channel flow, equation, numerical model, particle motion, power law
National Category
Fluid Mechanics
Identifiers
URN: urn:nbn:se:kth:diva-324148DOI: 10.1007/s11242-022-01793-5ISI: 000805541800001Scopus ID: 2-s2.0-85130737131OAI: oai:DiVA.org:kth-324148DiVA, id: diva2:1739557
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QC 20230227

Available from: 2023-02-27 Created: 2023-02-27 Last updated: 2025-02-09Bibliographically approved

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Bäbler, Matthäus

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