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Wall flow particulate filters have been used as a standard exhaust aftertreatment device for many years. The interaction of particulate matter (PM) regeneration and catalytically supported reactions strongly depends on the given operating conditions. Temperature, species concentration and mass flow cause a change from advective to diffusive-controlled flow conditions and influence the rate controlling dominance of individual reactions. A transient 1D+1D model is presented considering advective and diffusive transport phenomena. The reaction scheme focuses on passive PM conversion and catalytic oxidation of NO. The model is validated with analytical references. The impact of back-diffusion is explored simulating pure advective and combined advective diffusive species transport. Rate approaches from literature are applied to investigate PM conversion at various operating conditions.