Estimation of size distribution in concentrated particle systems from light scattering measurements
AbstractWe consider the estimation of the particle size distribution (PSD) of concentrated particle systems with low contrast between particles and solvent from light scattering (LS) measurements. We follow Pedersen's monodisperse approximation, in which an effective particle volume fraction is used to take into account interference between particles. This parameter must be determined simultaneously with the PSD to characterize the system. To solve the inverse problem, we first assumed that the PSD is described by a log-normal function. We applied the Levenberg-Marquardt algorithm for the non-linear parameter estimation. We also approached the free-form case following a scheme by which Tikhonov's regularization method is used to estimate the PSD, simultaneously with a non-linear least-squares optimization used to estimate the effective parameter. The solutions obtained from the analysis of simulated measurements showed that a priori knowledge of the distribution form improves the quality of the estimation, but the problem can be solved properly when actual PSD form is not known.