A simple approximate formula for the aspect ratio of oblate particles

A simple approximative formula is derived, which can be used to quantify the shape of oblate particles or an average shape of the corresponding particle system, when the results of sedimentation analysis (Stokes equivalent diameters) are known and results from either microscopic image analysis (assuming stable orientation, i.e., with the plane perpendicular to the direction of observation) or laser diffraction (assuming random orientation) are available for the same sample. In the latter case Cauchy's stereological theorem is applied to account for random orientation. Furthermore, it is shown that for sufficiently large aspect ratios, this formula is very close to the well-known Jennings-Parslow relation and can replace this more complicated expression in many practical cases, e.g., in the routine characterization of ceramic raw materials (kaolins and oxide or non-oxide platelet powders).