An improved method for measuring the concentration dependence of Fick diffusion coefficient based on Boltzmann equation and cylindrical liquid-core lenses

Abstract

Liquid diffusion coefficient that depends on solution concentration (D(C))11D(C): Liquid diffusion coefficient that depends on solution concentration is an important basic data for calculating mass transfer rate and studying mass transfer process. To measure the D(C) of glucose aqueous solution, the spatial and temporal profiles of the experimental concentration (Cexpt(x,t)s)22Cexpt(x,t)s: Spatial and temporal profiles of the experimental concentration during diffusion process have been measured on the base of a combination liquid-core cylindrical lens. In theoretical analysis aspect, based on the analytical method proposed by Hall and the graphic method adopted by Matano and Sauer-Freise et al., Boltzmann-Matano (BM)33BM: Boltzmann-Matano semi-analytical method is proposed and used to solve the D(C) equation, the D(C) of glucose aqueous solution is calculated with the obtained Cexpt(x,t)s. In addition, using the Finite-Difference Time-Domain (FDTD)44FDTD: Finite-Difference Time-Domain method, the distribution functions of diffusion concentration (CFDTD(x,t)s)55CFDTD(x,t)s: Concentration profile calculated by FDTD method under different D(C) correlations are calculated and compared with the Cexpt(x,t)s. The results indicate that the BM semi-analytical method can be used to correctly measure the liquid diffusion coefficient, which has the advantages such as stable and reliable measurement results, high precision, fast speed, and it can avoid the error caused by determining the “Matano” plane. The profile calculated by FDTD method provides an effective verification for the correctness of the measured D(C) as comparing with the experimental profile.