Abstract
A moment method of a q-th order extended log-normal size distribution (ELND) is established for the Brownian aerosol coagulation in a wide range from the free-molecule to the continuum regimes, in order to readily apply the moment method to not only log-normal distribution (LND) but also zeroth-order logarithmic distribution (ZOLD) . We can easily choose LND or ZOLD in the ELND moment method by merely altering q (q =-1 or 0, respectively) . Since the moment method of ZOLD has not been established in a wide coagulation regime, ZOLD was mainly examined by using the ELND moment method. The results of the ELND moment method are similar to those of the volume-conserving sectional method. For total particle number per unit volume and total surface area per unit volume, the differences between the moment and the sectional methods are within 4 % in the cases of initial standard deviations of 1.5 and 1.75. The results are insensitive to the time step size used in numerical time integration (the fourth-order Runge-Kutta method) , when the time step size is shorter than 4800 s. The simple ELND moment method is expected to be widely used, when the observational and experimental results described by LND and ZOLD are examined in large-scale scientific simulations of environmental and climate changes.
