# On the Impact of Particulate Matter Distribution on Pressure Drop of Wall-Flow Particulate Filters
## 4 Discussion of the Results
### Pressure Drop
This means that the worst loading conditions of the DPF are determined by an homogeneous particulate layer along the whole channel, which is the natural profile towards soot loading processes' convergence [28]. These results evidence the interest for soot and ash accumulation in the rear end of the inlet channels. On the other hand, given any onset for the growth of the particulate layer thickness, the pressure drop decreases as the porosity increases. These kinds of conditions would be caused by an engine operating at high mass flow, thus at medium-low temperature, thus resulting in a high Peclet number [35]. In addition, the impact is greater in homogenous soot mass distribution and as soot loading increases. Higher soot loading correlates with the injection number according to Figure 2, i.e., the 13 th water injection takes place at higher soot loading conditions. Keeping as a reference a particulate layer porosity of 0.65, the analysis of the plots in Figure 6 reveals that the experimental pressure drop obtained in DPF #A after the first pre-DPF water injection can be only attained provided that the particulate layer begins its growth several centimeters after the channel inlet (\(\sim\)4.5 cm). This trend is more clear as the number of injections increases, even taking into account that the pressure drop after the thermal transient related to the injection event grows up from 8500 Pa-9200 Pa. In the 13 th water injection, the growth of the particulate layer should begin at 12.5 cm from the monolith inlet, assuming that the particulate layer porosity is kept in 0.65. Therefore, the onset of the soot mass distribution is progressively moved towards the channel end as the amount of soot increases. This fashion in soot mass distribution in the particulate layer explains the need to increase the target pressure drop after the 13 th water injection that was necessary to impose during  
Figure 6: DPF pressure drop as a function of the particulate layer porosity and the soot mass distribution onset after different injection events in DPF #A.  
the soot loading test shown in Figure 2. In order to ensure the effectiveness of the water injection technique [12], it is necessary to allow the particulate layer thickness to grow again along the inlet channels before to perform the next water injection. In addition, it is worth noting how the rear soot accumulation should be more intensive if the porosity of the particulate layer decreases as a result of a water compaction process. According to [PERSON]'s law, this effect indicates that the permeability decrease caused by the porosity reduction has much more negative impact than the benefits brought by a thinner particulate layer. Figure 8 represents the particulate layer permeability as a function of the porosity, according to Equation (7). In contrast, the thickness is a function of the porosity, the soot distribution profile and, consequently, the axial location along the inlet channel, in agreement with Figure 5.  
Based on these magnitudes, the resulting pressure drop is finally defined by the filtration velocity. Figure 9a shows the filtration velocity profile along the inlet channel for a particular onset of the soot mass distribution (\(\delta_{pl}=0.11\) m) as a function of the particulate layer porosity after the first water injection. As the porosity decreases, the filtration velocity gets reduced in the initial inlet channel region. However, the filtration velocity is higher for low porosities in the rear end region. The flow tends to accumulate in the rear end of the inlet channel increasing the gas pressure because of the lower permeability related to low porosity. As a consequence, more mass flow passes across the thicker particulate layer region at higher velocity when the porosity decreases, thus leading to higher pressure drop. Complementarily, the filtration velocity profile for a particular porosity (\(\epsilon_{pl}=0.75\)) is represented in Figure 9b as a function of the soot mass distribution onset.