# On the Impact of Particulate Matter Distribution on Pressure Drop of Wall-Flow Particulate Filters
## 4 Discussion of the Results
### Pressure Drop
In this case, the filtration velocity gets reduced in the thin particulate layer region as the onset is moved back. Despite an intermediate region with the highest filtration velocity, it gets the minimum value also in the rear end, where the particulate layer has the maximum thickness. This kind of profile leads progressively  
Figure 8: Particulate layer permeability as a function of the porosity. Figure 4:0 Impact of the onset of the soot mass distribution on the DPF pressure drop as a function of the particulate layer porosity and the soot mass loading (number of injections) in DPF #A.  
to the almost linear pressure drop decrease shown in Figure 7 as the soot mass distribution onset is moved back. Several combinations of values of particulate layer porosity and onset of the soot mass distribution provide the experimental pressure drop, i.e., the white line represented in the plots of Figure 4:1 This is due to the influence of these variables on filtration velocity and particulate layer permeability and thickness. Figure 10 represents a set of filtration velocity profiles determined by combinations of particulate layer porosity and the onset of soot mass distribution that reproduce the experimental pressure drop after every water injection event. In all cases, the compaction of the particulate layer must be accompanied by moving back the soot mass distribution since it leads to lower filtration velocity both in the thin layer region and in the rear end region, reducing the length of the transition from fast to slow velocities. This trend is more apparent as the amount of soot and the number of injections increase, since the soot is progressively dragged towards the rear end of the inlet channels. Figure 4:2 Filtration velocity profiles for different soot mass distribution onsets and particulate layer porosities providing the experimental pressure drop after every modeled injection event in DPF #A.  
Figure 4:3 Filtration velocity profile as a function of the soot mass distribution onset and the particulate layer porosity after the first water injection event in DPF #A. The analysis of the pressure drop after the water injection events provides general trends on the change of the particulate layer properties. In order to describe with higher detail its characteristics after every injection, several pairs of particulate layer porosity and soot mass distribution onset were selected to model the soot loading process following the injection event. Figure 11 represents the cases for the first and the 13 th water injections. As shown in (a), the slope of the pressure drop after the first water injection is very sensitive to the properties of the particulate layer. In fact, the best fitting for the soot loading process is obtained for the case of no effects on the particulate layer porosity, whose reference value before injection is 0.65, just a minimum drag of the particulate layer with an onset of the soot mass distribution in 0.045 m being required. Shorter drag would have minor effects on the pressure drop increasing rate, but requiring higher porosity of the particulate layer than baseline. By contrast, noticeable drag of the particulate layer after the first injection would require great compaction of the particulate layer, leading to small porosity values and to an excessive slope of the pressure drop increase as a function of the soot loading. As the number of injections increases, the slope of the pressure drop loss sensitivity to the particulate layer properties since the onset of the soot mass distribution increases for all possible porosities. As shown in the 13 th water injection, in which the effectiveness of the injection process is limited, the onset of the soot mass distribution is within a small range.