The chord length distribution of a two-sphere aggregate

Mono-disperse particle suspensions are widely used in the field of particle technology. However, particles may aggregate. As a consequence, the presence of aggregates changes the properties of the suspension. The monitoring of the ageing suspension can be performed by using light extinction or turbidity measurements (TM). Intensity attenuation is depending on the particle concentration and on their scattering cross section. The latter is related to the chord length distribution (CLD) of particles. At the beginning of the aggregation process, only spherical particles and two-sphere aggregates are present in suspension. Thus, interpretation of turbidity signal needs the knowledge of the chord length distribution of spheres and two-sphere aggregates. This paper presents a calculation of CLD for a two-sphere aggregate available for explaining turbidity measurements (CLD-TM). The corresponding expression is compared to the CLD obtained by simulation.