Mixing Rules for an Exact Determination of the Dielectric Properties of Engine Soot Using the Microwave Cavity Perturbation Method and Its Application in Gasoline Particulate Filters

In recent years, particulate filters have become mandatory in almost all gasoline-powered vehicles to comply with emission standards regarding particulate number. In contrast to diesel applications, monitoring gasoline particulate filters (GPFs) by differential pressure sensors is challenging due to lower soot masses to be deposited in the GPFs. A different approach to determine the soot loading of GPFs is a radio frequency-based sensor (RF sensor). To facilitate sensor development, in previous work, a simulation model was created to determine the RF signal at arbitrary engine operating points. To ensure accuracy, the exact dielectric properties of the soot need to be known. This work has shown how small samples of soot-loaded filter are sufficient to determine the dielectric properties of soot itself using the microwave cavity perturbation method. For this purpose, mixing rules were determined through simulation and measurement, allowing the air and substrate fraction of the sample to be considered. Due to the different geometry of filter substrates compared to crushed soot samples, a different mixing rule had to be derived to calculate the effective filter properties required for the simulation model. The accuracy of the determined mixing rules and the underlying simulation model could be verified by comparative measurements on an engine test bench.