The Study On Rapidly Measuring Concentration-dependent Liquid Diffusion Coefficient Based On The Finite Difference Method

Diffusion coefficient(D)is the important datum for the study of liquid mass transfer process,and its accurate measurement has important scientific significance and application value for physics,chemical industry,medicine,environmental protection and other scientific fields.D value is generally concentration-dependent(D(C)),in view of the problems of large experimental workload and time consuming and difficulty in verifying measurement results in the measurement of D(C),an optical measurement for rapidly measuring the D(C)of binary solutions by the finite difference method is introduced in this paper.Combining by the finite difference method and imaging of liquid-core cylindrical lens,this method only requires an appropriate diffusion image collected by the imaging system,and compares with the calculated values of finite difference,the D(C)can be calculated rapidly,which greatly reduces the experimental workload and the measurement time.In this paper,the principle of this measurement,the design of liquid core lens,the numerical calculation of diffusion equation and the simulation verification of measurement results are studied in detail.The D(C)of the aqueous solutions of ethylene glycol(EG),triethylene glycol(TG)and glycerol have been measured.The concentration-dependent diffusion activation energy E_D(C)of glycerol solution was obtained by measuring the relation of liquid diffusion coefficient and temperature.The main research contents and results are as follows:1.The measuring platform of liquid diffusion coefficient has been built,and asymmetric liquid-core cylindrical lens(ALCL)has been designed and fabricated,which acts as the key imaging element of the measuring platform.The influences of aberration,refractive index measurement sensitivity,the measurement error of focal length and minimum resolution of refractive index change on the measuring accuracy of liquid diffusion coefficient are analyzed.Compared with the symmetrical liquid-core cylindrical lens used in the previous measurement platform,the spherical aberration of the ALCL is decreased greatly by 4 times within the refractive index range of1.3250-1.5000.In terms of refractive index measurement ability,the refractive index measurement sensitivity of ALCL can reach the accuracy of 0.0002 RIU within the refractive index measurement range of 1.3250e(z,t)s)are obtained from a single experiment using an ALCL.The concentration-dependent diffusion coefficient is assumed to be a polynomial.The finite difference method is applied to solve numerically Fick diffusion equation,the calculated concentration profiles(Cⁿ(z,t)s)by varying the underdetermined parameters are compared with the profile C^e(z,t),the parameters(?₁,?₂,?₃,…)corresponding the minimum concentration standard deviation are selected to determine D(C).In order to verify the correctness of D(C),the reliability of D(C)measurement results has been verified by using other experimental methods and comparing with reported values in literatures.3.The ray propagation in diffusion solution with inhomogeneous refractive index has been studied and the nonlinear second order differential ray equation has been established in the liquid core region,which shows that ray propagation law in homogeneous media can be used to calculate approximately the diffusion images in inhomogeneous media under the condition of small RI gradient of diffusion solution.The liquid diffusion process of TG aqueous solution in the ALCL has been experimentally carried out at room temperature,the reliability of D(C)measurement results is guaranteed by the method of concentration segmentation and the selection of appropriate diffusion images in the late stage.Using the obtained D(C),the diffusion images in the whole diffusion process(20 min-540 min)are calculated based on the ray equations,we simulate strictly the diffusion images in inhomogeneous solution,the simulated results are highly consistent with the experimental images in image contour,focal position and light intensity distribution,which not only verifies the correctness of D(C)measurement result,but also the reliability of treatment on ray propagation in the LCL composed of inhomogeneous diffusion solution.4.A semiconductor temperature control device is built around the ALCL.Based on the rapid measurement method of D(C)proposed in this paper and ray propagation law in inhomogeneous media,the temperature and concentration-dependent diffusion coefficient D(C,T)s of glycerin solution,over the range of 0-60%and at the temperature of 288.0 K,293.0 K,298.0 K,303.0 K,308.0 K,313.0 K and 318.0 K have been measured.The diffusion activation energies varying with concentration have been calculated based on the Arrhenius formula,which shows that the diffusion activation energy is positively correlated with the concentration.The empirical relationship between the diffusion activation energy of glycerin solution and concentration has been obtained based on the experimental data,which satisfies the parabolic conic relation.At the same time,the measurement results D(C)of the three alcohols shows that the molecular weight is the main factor affecting the diffusion rate of molecules at low concentration,while at high concentration,the solution viscosity is the main factor affecting the diffusion rate of molecules.