# Impact of Particulate Size During Deep Loading on DPF Management
## 3 Results and Discussion
Filter behavior was analyzed by considering six diameters of particles 50 nm, 300 nm, 350 nm, 400 nm, 500 nm, and 1 \(\upmu\)m.  
The filtering efficiency was evaluated by means of the unit collector model for each size, and Figure 11 shows the obtained values. The curve exhibits two zones of high efficiency values (nano/ultrafine particles and large agglomerates) and a region of low efficiency (fine particles), in correspondence of the diameter with maximum penetration. Figure 10: Evolution with the time of permeability in each slab of the porous medium. Figure 9: Evolution with the time of porosity in each slab of the porous medium. Figure 12 highlights the influence of soot particle diameter on pressure drop evolution with time. Particle dimension of 50 nm and 1000 nm let the filter porous medium rapidly reach the maximum packing density. Deep and transient stages are completed in a short time (0.5 h), and particles are then collected in cake filtration mode. Particle diameters of 300, 350, 400 and 500 nm (characterized by lower values of efficiencies), instead, cause a slow loading of the porous medium. The saturation level of the slabs close to the inlet channel is very low for a long temporal interval, thus allowing particles to reach the deeper slab. Higher penetration of particles is allowed, thus resulting in higher values of pressure drop until the transient stage is attained. When cake filtration starts (in the range of 1.25 h and 1.5 h, depending on the soot dimension), it is characterized by a pressure drop behavior whose gradient is the same of those caused by the soot layer growth of 50 and 1000 nm particles. Figure 13 shows the evolution with time of the efficiency for the different particles sizes. Nano particles present value of efficiency of 99.9% for clean filter, and after approximately 30 min, saturation condition is reached. Figure 11: Filter efficiency as function of soot particle diameter. Figure 12: Pressure drop evolution with time during loading stage as function of particle diameter. The same behavior is observed for large agglomerates, whose initial efficiency for the clean filter is 93.4%. Fine particles show a value around 60% for the efficiency value at the beginning of loading process, and a longer amount of time is needed to complete the deep filtration stage. In order to highlight the effect of such behavior on filter loading, the pressure drop trend versus the trapped mass (obtained for 50 nm, curve a, and 350 nm, curve b, as particles diameters) is shown in Figure 4:0  
The transition from deep bed to cake filtration is exhibited at approximately 6 kPa for the 50 nm particles, and 9 kPa for 350 nm particles. If the regeneration process is established to start at a threshold value of 11 kPa (light blue line on the plot), it means that in case of curve b, 46 g of soot was accumulated, while 79 g of soot was trapped for curve a. Looking at the values of time corresponding to such cumulated mass amount, it can be observed that 46 g are collected in approximately 2.6 h, while 79 g of soot is trapped in about 4.2 h.  
These results contribute to add information on the loading/regeneration process, highlighting how the way in which the initial filter loading is performed affects the DPF behavior. This has consequence not only when the subsequent cake filtration stage takes place, but also after the regeneration phase, when the filter is loaded again. If the engine operates in such a way to generate smaller particles in the exhaust gas flow during the initial stage of filter use, a lower pressure drop characterizes the cake filtration phase start. This means that regeneration event may be planned after a longer period, if in the definition of regeneration is mainly affected by the pressure drop or, if the collected mass is the key parameter to set the regeneration event, it means that the engine backpressure is lower, thus enhancing the engine performance.