Indetermination of particle sizing by laser diffraction in the anomalous size ranges

•The anomalous change of the Mie scattering kernel is presented.•The mechanism of the indetermination of particle sizing is interpreted.•The existence of the indetermination is verifed.

The laser diffraction method is widely used to measure particle size distributions. It is generally accepted that the scattering angle becomes smaller and the angles to the location of the main peak of scattered energy distributions in laser diffraction instruments shift to smaller values with increasing particle size. This specific principle forms the foundation of the laser diffraction method. However, this principle is not entirely correct for non-absorbing particles in certain size ranges and these particle size ranges are called anomalous size ranges. Here, we derive the analytical formulae for the bounds of the anomalous size ranges and discuss the influence of the width of the size segments on the signature of the Mie scattering kernel. This anomalous signature of the Mie scattering kernel will result in an indetermination of the particle size distribution when measured by laser diffraction instruments in the anomalous size ranges. By using the singular-value decomposition method we interpret the mechanism of occurrence of this indetermination in detail and then validate its existence by using inversion simulations.