Transfer of a nanoparticle product between different mixers using latent variable model inversion

An experimental nanoparticle preparation process by solvent displacement in passive mixers is considered. The problem under investigation is to estimate the operating conditions in a target device (Mixer B) in order to obtain a product of assigned properties that has already been manufactured in a source device of different geometry (Mixer A). A large his-torical database is available for Mixer A, whereas a limited historical database is available for Mixer B. The difference in device geometries causes a different mixing performance within the devices, which is very difficult to capture using mechanistic models. The problem is further complicated by the fact that Mixer B can only be run under an experimental setup that is different from the one under which the available historical dataset was obtained. A joint-Y projection to latent structures (JY-PLS) model inversion approach is used to transfer the nanoparticle product from Mixer A to Mixer B. The Mixer B operating conditions estimated by the model are tested experimentally and confirm the model predic-tions within the experimental uncertainty. Since the inversion of the JY-PLS model generates an infinite number of solu-tions that all lie in the so-called null space, experiments are carried out to provide (to the authors’ knowledge) the first experimental validation of the theoretical concept of null space. Finally, by interpreting the JY-PLS model parameters from first principles, the understanding of the system physics is improved.