# Impact of Particulate Size During Deep Loading on DPF Management
## 3 Results and Discussion
Figure 6 shows how the collected soot mass can be subdivided into the part that is trapped in the porous medium (deep filtration) and the part that is accumulated in the cake (cake filtration). The plot highlights that during the initial phase of filtration, most of the incoming soot particles are collected in deep filtration stage. At 1700 s, the trapped mass in porous media is equal to that one collected in the cake layer. After that time, soot layer keeps growing until it reaches the height of 88 \(\upmu\)m.  
The efficiency of clean material was evaluated by imposing a particle diameter variation in the field 20-1000 nm, which is the typical range of soot sizes of diesel engine exhaust. Figure 7 shows the dependence between the particle dimension and filter performance and highlights the coupling between soot size and filter characteristics. Figure 5: Collected mass versus time. Figure 6: Variation of collected with time during filtration stages. The trend in the upper part of the figure highlights that the worst filtering condition is reached for the 350 nm diameter particle for which the initial collection efficiency of the device is about 0.61. The curve was obtained by assuming that Brownian diffusion and interception are independent each other. In the bottom part of the plot, two curves are shown, one represents the efficiency obtained by accounting only for the diffusion effect; the other was obtained by considering only the interception mechanism. Their effect on soot size is opposite: As particle diameter increases, diffusion coefficient and then Brownian diffusion efficiency decreases. In the meantime, interception efficiency increases. The evolution of material properties was simulated accounting for the variation of porosity and permeability of the porous media with time in correspondence of the progress in accumulation process; in the model, the porous medium was divided into slabs. The mass in every slab volume is computed by the local efficiency. Figure 8 shows the evolution with time of the mass accumulated into each slab (15 slabs were considered). The traces, parametrized with time (its variation is between 0 s and 3600 s, with steps of 600 s), highlight the difference in the behavior of each slab as function of the distance from the interface between the porous media and the channel (the first slab is placed close to the surface, 15 th slab is close to the outlet channel). It is possible to observe that soot mass mainly accumulates in the slabs located close to the interface. The correspondent variation of properties of these slabs inhibits the further mass deposition in the slabs placed close to the outlet channel. Figures 9 and 10 show the evolution of porosity and permeability with time, respectively. The plot of Figure 9 highlights that after 2400 s all curves almost overlap in a single trace. Figure 8: Collected soot mass in each slab versus time. Figure 7: Variation of filter efficiency with particle size. At the initial instant of simulation, all material is characterized by a porosity value of 48%; the first 600 s are characterized by a sharp decrease of porosity in the first slabs. After 1800 s, porosity decrease with time is less evident, and it slowly reaches the saturation limit of 22%, which corresponds to the complete filling of the volume available in the unit cell of the first slab. Permeability curves reproduce the porosity behavior in each slab and show how soot mainly accumulate in the slabs close to the inlet channel; slabs close to the outlet channel keep their properties almost unchanged with time. The influence of particle size on pressure drop evolution was studied aimed at investigating if a proper process of loading could be a possible way to reduce DPF back pressure, thus allowing to increase the time interval between two subsequent regeneration events.