# On the Impact of Particulate Matter Distribution on Pressure Drop of Wall-Flow Particulate Filters
## 4 Discussion of the Results
### Pressure Drop
The soot tends to be accumulated in the end region of the channel close to the plug. This is confirmed by Figure 4, which shows three pictures of the rear end (21.5 cm from monolith inlet) in different inlet channels. A clear random accumulation of soot layer fragments can be observed. Its effect can be assumed equivalent to a fast increase of the particulate layer thickness in this region, thus decreasing the inlet channel effective cross-section area. Figure 4: Pictures of soot agglomerates accumulation in the rear end of three inlet channels (21.5 cm from monolith inlet) after water injection in DPF #B.  
Figure 3: Scanning Electron Microscope (SEM) pictures of the cross-section of DPF #B inlet channels with the same soot loading at different locations in baseline and after water injection conditions: (**a**) baseline at 2.5 cm; (**b**) baseline at 20.5 cm; (**c**) pre-DPF water injection at 2.5 cm; (**d**) pre-DPF water injection at 20.5 cm. The swept-in particulate layer porosity and onset of the soot mass distribution provide an extensive family of particulate layer structures. Figure 5a shows how the particulate layer porosity changes the soot thickness along the inlet channels. The grey dashed series represents the particulate layer thickness just before the first injection event, the particulate layer porosity being 0.65. In all remaining cases, the soot mass distribution is exactly the same, i.e., at a given point, the amount of soot is the same at any particulate layer porosity. In these examples, the onset of the soot mass distribution is at \(\delta_{pl}=0.1\) m from the inlet monolith cross-section imposing a parabolic profile. Therefore, the change in porosity is the responsible of the different cake thickness according to Equation (16):  
\[w_{pl,i}=\frac{\alpha_{in}-\sqrt{\alpha_{in}^{2}-\frac{m_{s,pl,i}}{\Delta x_{ pl}}}}{2} \tag{16}\]  
where subscript \(i\) identifies the node of computation along the channel. The density of the particulate layer (\(\rho_{pl}\)) is a function of the carbon density and the porosity of the particulate layer:  
\[\rho_{pl}=\rho_{C}\left(1-\epsilon_{pl}\right) \tag{17}\]  
Below a porosity of 0.6, the particulate layer thickness is very thin along the whole channel. However, as the porosity increases, the thickness undergoes a faster growth, as clearly observed for 0.95 in porosity. The differences in thickness become evident from the very beginning of the soot mass distribution onset and increase towards the inlet channel rear end. In contrast to porosity, the onset of the soot mass distribution in the particulate layer, whose effect is represented in Figure 5b, gives rise to quite homogeneous cake thickness, most of the differences being concentrated in the rear end region. This is especially evident as the soot mass distribution is moved back, which produces a sharp rate of thickness increase from 0.15 m in the onset length. The DPF pressure drop resulting from the parametric study imposing experimental inlet flow conditions and soot loading after the water injection is shown in Figure 6 for Injections 1, 5, 9 and 13. A parabolic soot mass distribution is considered in these computations. In all plots, the white line represents the solution domain corresponding to the experimental pressure drop value for every injection. Figure 5: Effect of particulate layer porosity and soot mass distribution onset on the particulate layer thickness profile in DPF #A. As observed in all cases, moving back the soot mass distribution onset provides an almost linear decrease of the pressure drop regardless of the particulate layer porosity. This is shown in Figure 7, which presents the pressure drop dependence on the onset of the soot mass distribution for the parabolic profile and different water injections. The maximum pressure drop is always found when the onset of the particulate layer is placed close to the monolith inlet.