# On the Impact of Particulate Matter Distribution on Pressure Drop of Wall-Flow Particulate Filters
## 4 Discussion of the Results  
### Pressure Drop  
Figure 2 shows the DPF pressure drop during the soot loading tests up to 30 g in soot mass. According to the experimental analysis presented in [12], the restructuring of the soot deposits in the particulate layer was hypothesized as the main cause to explain the decrease in pressure drop after every injection event and the capability to limit maximum pressure drop regardless of the amount of collected soot. This hypothesis has been analyzed in this work diagnosing the main particulate layer properties. A variety of soot mass distributions in the particulate layer with different effective porosity have been computed applying the wall-flow DPF model. The porous wall has been kept saturated with a soot penetration thickness of 2%. These characteristics are based on the results obtained from the modeling of the soot loading process up to the first water injection event, which are described in [28]. Therefore, the objective has been to identify the main trends in particulate layer properties' variation that provide the pressure drop after a pre-DPF injection event. In particular, the pressure drop at the end of the injections marked with a red circle in Figure 2 has been analyzed. The selected pressure drop value is the one after the end of the thermal transient that follows a pre-DPF water injection. This value determines the benefit in pressure drop reduction [12]. For the sake of simplicity, the properties of all inlet channels have been assumed to be the same, which implies the assumption of a homogeneous water distribution within the monolith cross-section. Therefore, the results of the parametric study must be understood as lumped representative properties of the collected soot. According to the results presented in [28] and as the boundary condition for the modeling work, the particulate layer porosity before the first water injection event is known to be 0.65. This data were obtained assuming that the representative collector unit diameter in the particulate layer is that of the mode of the particle size distribution (69 nm). Nevertheless a range of particulate layer porosity from 0.4-0.97 has been considered in this work. It provides a wide range to analyze the possible effect of particulate layer compaction at the same time that the maximum values of porosity reported in the literature [35] have been covered. Concerning the soot mass distribution, an increase of the particulate layer thickness has been assumed along the inlet channels till the plug end. In every axial location, the thickness of the particulate layer is assumed to be homogenous on all of the channel walls. Linear and parabolic laws to define the rate of thickness increase have been explored. In addition, the particulate layer thickness is assumed to be very thin and constant from the inlet cross-section up the a given distance from which the increasing thickness profile is imposed. This distance, which will be referred to as the onset of the soot mass distribution (\(\delta_{pl}\)) from now on, has been also varied in order to determine its impact on the  
Figure 2: Soot loading test in DPF #A defining the conditions of the parametric studies. pressure drop. This study is based on the conclusions obtained from Scanning Electron Microscope (SEM) analysis [34]. Figure 3 shows SEM pictures corresponding to two different samples of DPF #B, which was loaded with 44.6 g. The pictures show the cross-section of an inlet channel at two different distances from the monolith entrance. One of the samples was subjected to a pre-DPF water injection. Both cases show that the penetration is very small, as concluded from experimental [25] and modeling [23] studies, just affecting the porous wall rugosity. On the one hand, the baseline sample shows a similar thickness of the soot cake both at the inlet and rear end. On the other hand, the case of the sample subjected to water injection shows an irregular thin particulate layer at the inlet region of the channel.