Simultaneous measurement of solubility and diffusion coefficient in partially miscible liquid systems using the liquid-core cylindrical lenses

Dissolution and diffusion in partially miscible liquid systems are prevalent physical phenomena. Parameters governing these processes, such as solubility ( S ) and diffusion coefficient ( D ), must be accurately measured for applications in biopharmaceuticals, chemical production, and food manufacturing. However, current common measurement methods are often time-consuming, require complex equipment, or lack accuracy, and they cannot measure both parameters simultaneously. In this study, we proposed a real-time optical image feature extraction method that utilizes the refractive-index spatiotemporal resolution capability of a compound liquid-core cylindrical lens to enable simultaneous assessment of S and D in partially miscible liquid systems. The D values of a glyceryl triacetate-water partially miscible system at five different temperature settings were measured using the equal-refractive-index thin-layer method based on the one-dimensional semi-infinite diffusion model, while S values were determined from the width of the image. The measured data at 298 K agreed with results obtained by other methods, confirming the reliability of the experiment and method. This method features a simple experimental setup and convenient operation, demonstrating broad application prospects.