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Cremer impedance, first proposed by Cremer (Acustica 3, 1953) and then improved by Tester (JSV 28, 1973), refers to the locally reacting boundary condition that can maximize the attenuation of a certain acoustic mode in a uniform waveguide. One limitation in Tester’s work is that it simplified the analysis on the effect of flow by only considering high frequencies or the ‘well cut-on’ modes. This approximation is reasonable for large duct applications, e.g., aero-engines, but not for many other cases of interest, with the vehicle intake and exhaust system included. A recent modification done by Kabral et al. (Acta Acustica united with Acustica 102, 2016) has removed this limitation and investigated the ‘exact’ solution of Cremer impedance for circular waveguides, which reveals an appreciable difference between the exact and classic solution in the low frequency range. Consequently, the exact solution can lead to a much higher low-frequency attenuation level.

Air pollution caused by exhaust particulate matter (PM) from vehicular traffic is a major health issue. Increasingly strict regulations of vehicle emission have been introduced and efforts have been put on both the suppression of particulate formation inside the engine cylinders and the development of after-treatment technologies such as filters. With modern direct injected engines that produce a large number of really small sub-micron particles, the focus has increased even further and now also includes a number count. The problem of calculating particle trajectories in flow ducts like vehicle exhaust systems is challenging but important to further improve the technology. The interaction between particles and oscillating flows may lead to the formation of particle groups (regions where the particle concentration is increased), yielding a possibility of realizing particle agglomeration.