Measurement of the concentration- and temperature-dependent diffusion coefficient and activation energy via diffusion image analysis

Problems associated with obtaining measurements of the concentration- and temperature-dependent liquid diffusion coefficient, D(C, T), and the concentration-dependent diffusion activation energy, Ea(C), include large experimental workload and time consumption. To account for these, this paper introduces an optical method for rapidly measuring D(C, T) and Ea(C), based on the imagery of a liquid-core cylindrical lens (LCL) and numerical calculation. This method requires only one diffusion image obtained from the diffusion experiment, and D(C) is measured at a particular temperature. First, we measured the D(C) coefficients of glycerin solution at 288.0, 293.0, 298.0, 303.0, 308.0, 313.0, and 318.0 K. Then, the ray tracing theory was used to study the ray propagation law in the LCL composed of an inhomogeneous solution, which simulated the diffusion images of the entire experimental process and provided a method to verify the measured values of D(C). Finally, the law of diffusion activation energy varying with concentration was discussed based on the Arrhenius theory and the acquired values of D(C, T). This study further improves the measurement technology for D(C, T) and Ea(C) and provides an efficient methodology to build extensive D(C, T) and Ea(C) databases in the biochemical, medical, semiconductor, and environmental protection industries.