Soft sensors enable real-time ion concentration measurements

Analytical techniques such as Inductively Coupled Plasma Optical Emission Spectroscopy (ICP-OES) are widely used to measure ion concentrations, but are time-consuming, labor-intensive, and costly. The required sample collection, preparation, and offline, energy-intensive analysis render ICP-OES inadequate for real-time monitoring in membrane processes. Conductivity sensors provide rapid, in situ measurements of the electrical conductivity of ionic solutions, offering an attractive alternative for real-time tracking of ionic species during membrane processes; however, converting conductivity measurements into ion concentrations in multicomponent systems remains a significant challenge. This work addresses this limitation by developing soft sensors that estimate ion concentrations in real time using conductivity data from inexpensive sensors and mathematical models that map conductivity measurements to ion concentrations. Specifically, the Shedlovsky and mean spherical approximation (MSA) models are deployed, and their conductivity predictions are validated using experimental data representative of electronic waste and lithium-ion battery leachate. By capturing key physical phenomena in ion transport in the presence of the electric field generated by the conductivity sensor, such as electrophoretic and relaxation effects, these models accurately predict the conductivity of single, binary, and ternary salt feed solutions. Furthermore, Shedlovsky and MSA-based soft sensors are applied to estimate real-time ion concentrations in the permeate solution of a membrane-based separation, and the estimates are validated against ICP-OES analysis, demonstrating good agreement (within 5%). Overall, this study demonstrates that the development of scientifically rigorous and generalizable soft sensors is essential for enabling rapid, reliable, and efficient measurement of ion concentrations in complex ionic environments.