Evaluation of the accuracy of the three-dimensional size distribution estimated from the Schwartz-Saltykov method

The validity of estimation of the three-dimensional size distribution (3-DSD) using the Schwartz-Saltykov (SS) method has been evaluated by applying the discrete two-dimensional size-distribution (2-DSD) model. The coefficient for the SS method has been generalized, and the verification of this method has been studied by focusing on the measured number of sectioned particles on the cross section of the specimen, the step width of the histogram for the SS method, and the oversight of small sectioned particles. The total number of particles per unit volume (total N_v (T. N_v)) and the number of particles in each size class, estimated by the SS method, are found to be always underestimated compared with the true N_v value, without regard to the oversight of small sections. The T.N_v value can be reasonably estimated by an extrapolation method, in which the step width of the histogram approaches zero. The relative frequency in a distribution function is correctly determined independent of the step width when the oversight involves a sectioned particle size equal to or less than one-tenth of the true mean diameter of the particles. The quantitative 3-DSD can be obtained from the reasonably estimated value of T.N_v and the correctly determined relative frequency.