  The movement of small particles and molecules through membranes is widespread
and has far-reaching implications. Consequently, the development of
mathematical models is essential for understanding these processes on a micro
level, leading to deeper insights. In this endeavour, we suggested a model
based on a set of empirical equations to predict the transport of substances
through a solid-state nanopore and the associated signals generated during
their translocation. This model establishes analytical relationships between
the ionic current and electrical double-layer potential observed during
ana-lyte translocation and their size, charge, and mobility in an electrolyte
solution. This framework allows for rapid interpretation and prediction of the
nanopore system's behaviour and provides a means for quantitatively determining
the physical properties of molecular analytes. To illustrate the analyt-ical
capability of this model, ceria nanoparticles were investigated while
undergoing oxidation or reduction within an original nanopore device. The
re-sults obtained were found to be in good agreement with predictions from
physicochemical methods. This developed approach and model possess
transfer-able utility to various porous materials, thereby expediting research
efforts in membrane characterization and the advancement of nano- and
ultrafiltra-tion or electrodialysis technologies.
