Rapid Measurement of Liquid Diffusion Coefficients of β-Alanine Varying with Concentration at Different Temperatures

The liquid diffusion coefficient is a critical parameter for studying mass transfer processes, calculating mass transfer rates, and facilitating chemical engineering design and development, with its value strongly influenced by factors such as temperature and concentration. Conventionally, determining the concentration-dependent diffusion coefficient relationship D(C) requires multiple measurements across various concentrations followed by fitting, which is time-consuming and prone to cumulative errors, especially under varying thermal conditions encountered in industrial applications. To address this limitation, this study proposes an optimized finite difference numerical method that enables rapid determination of D(C) using only a single diffusion image, significantly enhancing measurement efficiency. This approach was validated by comparison with the shift of equivalent refractive index slice method and ray-tracing simulations. Diffusion coefficients for β-alanine aqueous solutions at different concentrations were measured over the temperature range of 288.15 K to 318.15 K using both techniques. The results from the two methods showed excellent consistency, with diffusion coefficients well described by the Arrhenius equation across temperatures, allowing for the rapid derivation of activation energies. Numerical simulations based on the derived D(C) relationship yielded images that closely matched experimental observations, confirming the accuracy and reliability of the finite difference method. This innovative technique not only offers a streamlined pathway for characterizing concentration-dependent diffusion in amino acid systems like β-alanine—relevant to pharmaceutical and biochemical processes—but also demonstrates broad applicability for obtaining diffusion coefficients and activation energies with minimal experimental effort.