Modeling nano-particle deposition in diesel engine filters

In this work, we develop a simple, fully analytical one-dimensional model based on lubrication theory to predict nano-particle deposition along the unit channel of a clean diesel particulate filter. Soot deposition along the channel depends on filter design parameters, which can be optimally selected to minimize the uneven distribution of soot. At the initial stage of the filtration process, the porous wall resistance is controlling; at later stages, the local resistance of the deposited soot is controlling. Typically, a hundredfold increase in filter resistance may be observed over time, and the maximum variability in the soot deposition is observed at the initial stages of the process. Therefore, in this work, we focus on the deposition of soot in a clean filter, focusing on the one dimensional variability along the main flow direction. In a clean filter, the porous wall resistance can be considered uniform along the filter length and the flow field and nano-particle transport equations can be solved analytically. Model predictions compare surprisingly well with those obtained from more complex three-dimensional simulations, thereby demonstrating that the essential physics is captured correctly. Based on the very simple framework identified in this paper, more complex models can be developed and used to predict the filter behavior over time (i.e. build-up of the soot cake and back-pressure rise up to the regeneration step) provided that (i) the variation in time of filter permeability due to local soot loading is implemented and (ii) equations are solved numerically.