Optical measurement of concentration-dependent diffusion coefficients of binary solution using an asymmetric liquid-core cylindrical lens

Abstract

An optical method for measuring concentration-dependent diffusion coefficients of binary solution is introduced in this paper. The concentration spatial and temporal profiles (Ce(z, t)s) are obtained from a single experiment using an asymmetric liquid-core cylindrical lens. The concentration-dependent diffusion coefficient is assumed to be a polynomial D(C) = D0 × (1 + α1C + α2C2 + α3C3 + …), where D0 is diffusion coefficient in infinite dilute solution, α1, α2 and α3 are under-determined parameters. The finite difference method (FDM) is applied to solve numerically Fick diffusion equation, the calculated concentration profiles (Cn(z, t)s) by varying the under-determined parameters are compared with the profile Ce(z, t), the parameters(α1, α2, α3, …) corresponding the minimum concentration standard deviation are selected to determine D(C). To verify the proposed method, we have carried out the diffusion experiment of ethylene glycol aqueous solution, the obtained concentration-dependent diffusion coefficients are in good agreement with literature values. On the other hand, the obtained polynomial D(C) has been used to calculate refractive index profiles (nn(z, t)s). Based on the nn(z, t)s, ray tracing method has been applied to simulate the diffusion images, which fit the experimental images very well over a wider range of diffusion time, demonstrating that the proposed method is reliable in rapidly measuring concentration-dependent liquid diffusion coefficients with high accuracy and stability.