Measurement of axial effective diffusivity in oscillatory pipe flow by Laplace transform method

Analysis of gas transport in oscillatory flow though an airway model with complex geometry such as a single bifurcation, relies on the theoretical understanding of gas exchange during High-frequency oscillation; HFO. Our purpose was to develop a method for measuring the mean effective diffusivity in an oscillatory flow between two points, by applying Laplace Transform Method. The measurement time T_max, which is the area of the Laplace integration, and the Laplace parameter s are related to the accuracy of the measured effective diffusivity, D_eff. In this study, numerical analysis was carried out to investigate the Laplace Transform Method. We defined the parameter K required to obtain optimum s, and found that K ≅ 0.1. Then we applied this method to evaluate D_eff in a straight tube and a single symmetrical bifurcation. The theoretical results for a straight tube agreed with the measured D_eff. D_eff for the bifurcating tube was greater than that for the straight tube by a factor of Dn²/α⁴, that proved the effect of the secondary flow.