We develop the flow and the particulate transport models in a wall-flow gasoline particulate filter (GPF). The filter is constituted of inlet channels which are separated from outlet channels by a porous wall. We model the flow inside the channel using incompressible Navier-Stokes equation coupled with the spatially averaged Navier-Stoke equation for the porous wall. For the particulate transport, we use coupled advection and spatially averaged advection-reaction equations, where the reaction term models the particles trapping. The concentration of deposited particulates at the back of the filter downstream the flow increases with Reynolds number. These results are in agreement with the published experimental measurements of the spatial distribution of particles inside the filter.

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