Measuring Concentration-dependent Liquid Diffusion Coefficient Based On The Boltzmann-Matano Semi-analytical Method

Liquid diffusion coefficient is an important basic data for calculating mass transfer rate and studying mass transfer process.In experimental aspect of this paper,the spatial and temporal profiles of the experimental concentration(C_expt（x,t）s)of glucose and urea aqueous solution 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 et al.and the graphic method adopted by Matano and Sauer-Freise et al.,Boltzmann-Matano（BM）semi-analytical method is proposed and used to solve the concentration-dependent diffusion coefficient（D（C））equation according to C_expt（x,t）s.In addition,the Finite-Difference Time-Domain（FDTD）method is proposed and used to verify the correctness of the D（C）correlations in this paper.The main research contents and results of this paper are as follows:1.A method of measuring D（C）correlations—BM semi-analytical method is proposed.This method absorbs the advantages of the analytical method proposed by hall et al.,and sets the spatial and temporal profiles of diffusion solution concentration to meet the complementary Error function C_erfc（x,t）with undetermined parameters,by comparing C_expt（x,t）s,the undetermined parameters h and k are determined in the whole diffusion region.Then,D（C）correlations can be obtained by BM graphic method combined with the analytical form of C_erfc（x,t）.2.A method to verify the correctness of D（C）correlations is proposed.This method adopts the Finite-Difference Time-Domain method to solve the diffusion equation under different D（C）correlations,calculate the spatial profiles(C_FDTD（x,t）s)of numerical solution concentration at different times,and compare the graph and variance value with the experimental space-time profiles C_expt（x,t）s curve.The results indicate that the profile calculated by FDTD method provides an effective verification for the correctness of the measured D（C）correlations by comparing it with experimental profile.3.Based on a combination liquid-core cylindrical lens,an optical detection system for measuring the experimental curve of C_expt（x,t）was builted,and the C_expt（x,t）s of the liquid-phase diffusion process of glucose aqueous solution was measured at room temperature.The D（C）correlation of glucose aqueous solution was calculated by BM semi-analytical method.The correctness of the D（C）correlation is verified by using the FDTD method.4.Based on the optical detection system and the BM semi-analytical method,the diffusion coefficients of urea aqueous solution with concentration at different temperatures were measured.The results indicate that the diffusion coefficient of urea aqueous solution increases with the increase of temperature and decreases with the increase of concentration.The correctness of the D（C）correlations are verified by the FDTD method.5.The measurement results of liquid-phase diffusion coefficient of different diffusion systems varying with concentration at different temperatures indicate that the BM semi-analytical method can be used to measure the liquid diffusion coefficient,which has the advantages of stable and reliable measurement results,high precision and fast speed,and it can avoid the error caused by determining the"Matano"plane.