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

Population balance models for particulate flows in porous media:breakage and shear-induced events