SONG Fang-xi, MENG Wei-dong,3, XIA Yan, CHEN Yan, PU Xiao-yun,2*

(1.Department of Physics and Astronomy,Yunnan University,Kunming 650091,China;2.International Joint Research Center for Photoelectronics Energy Materials,>Yunnan University,Kunming 650091,China;3.Key Laboratory of Quantum Information of Yunnan Province,Kunming 650091,China)

Abstract: Based on the consideration of the high resolution of the spatial resolution of the refractive index of the double liquid-core cylindrical lens(DLCL), the liquid-phase diffusion coefficients of different concentrations of aqueous sucrose solution are measured at room temperature(25 ℃) using two methods. Method 1:equivalent RI(refractive index) method is used to calculate the liquid phase diffusion coefficient by recording the time-dependent change of a specific refractive index layer during diffusion. Method 2:instantaneous diffusion analytical method is used to determine the liquid diffusion coefficient by reading the relationship between image width and diffusion position in an instantaneous diffusion image. The front liquid core of the DLCL serves as a diffusion cell and a main imaging element, and the rear liquid core serves as an aplanatic auxiliary system. The spherical aberration at a particular thin liquid layer can be reduced as needed with a DLCL, and the spherical aberration advantage within a certain range of refractive index can also be reduced. Both methods have the characteristics of high measurement accuracy. The relative errors between the measured results and the literature values of the two methods are less than 1.3% and 3.9%, respectively, indicating that the measurement system is stable and reliable and the measurement results are accurate when the liquid-phase diffusion coefficient is measured with a DLCL.

Key words: double liquid-core cylindrical lens;diffusion coefficient;diffusion imaging;spherical aberration;refractive index

1 Introduction

引 言

The diffusion coefficient is an important basic data for the study of mass transfer process, calculation of mass transfer rate, and chemical design and development. It is widely used in fields of chemical, pharmaceutical, food, biological and environmental protection fields[1-4]. Since the average distance between liquid molecules is much smaller than that of gas molecules, and the liquid molecules do not have regular arrangments like solids, the theoretical description and experimental measurement of the liquid phase diffusion coefficient are far more difficult than gas and solids. The liquid phase diffusion data of different systems is quite lacking[5-6]. At present, the liquid phase diffusion coefficient is mainly obtained by experimental methods. By measuring the concentration-dependent spatial and temporal distribution of the solution due to the diffusion process, the liquid phase diffusion coefficient is calculated according to Fick′s law[7]for describing the diffusion process. From the experimental method to measure the diffusion coefficient, the diaphragm pool method[8], optical interference method[9]and Taylor dispersion method[10]are widely used. In addition, measurement methods such as nuclear magnetic resonance[11], dynamic light scattering[12], fluorescent molecular tracing[13]and radioactive element tracing[14]can also be used. Diaphragm cell method[8]is a classical steady-state measurement method. This method measures the initial and steady state solution concentrations in the upper and lower parts of the diffusion cell, so the measurement time is longer.Optical interference method[9]measures interference fringes formed when target light and reference light meet in space, and inverts the spatial and temporal distribution information of diffusion solution concentration carried by the target light through fringes. The measurement accuracy of this method is high, but its requirements for the experimental environment are extremely demanding. The Taylor dispersion method[10]is to inject trace solute into the solvent flowing in the capillary. The solute diffuses in the solvent to form a Gaussian distribution of the solution concentration along the capillary axis. The diffusion coefficient is calculated by measuring the concentration distribution curves at different times. The method is fast, but the measurement accuracy is low. The NMR method[11]has the characteristics of anti-interference, fast speed,etc., but it is only suitable for measuring some special substances. The dynamic light scattering method[12]is suitable for the measurement of the diffusion coefficient of a polymer solution. There are other methods such as fluorescent molecular tracing[13]and radioactive element tracing[14]. However, they are not widely used. In order to solve these problems, according to the imaging principle of the liquid-core cylindrical lens focal plane, we proposed the equivalent RI(refractive index) method[15-16]and the instantaneous diffusion image analytical method[16-17]to measure the liquid-phase diffusion coefficient by analyzing the diffusion image. Spherical aberration is the main factor influencing the imaging quality of diffused images. The ability of the DLCL[18]to reduce the spherical aberration improves the imaging quality of the diffused image,and it is the key to accurately measure the liquid-phase diffusion coefficient. The front liquid core of the DLCL serves as a diffusion cell and the main imaging element, and the rear liquid core serves as an aplanatic auxiliary system[19-20]. In this paper, DLCL is used to reduce the spherical aberration at certain thin liquid layers as needed, and it can reduce the advantage of spherical aberration within a certain refractive index range. In this paper, the diffusion coefficients of different concentrations of aqueous sucrose solution at room temperature(25 ℃) are measured by combining the above two methods.

扩散系数是研究传质过程、计算传质速率及化工设计与开发的重要基础数据，广泛应用于化工、医药、食品、生物及环保等领域[1-4]。由于液体分子的平均间距远比气体分子小, 又不及固体那样有规则排列, 所以液相扩散系数的理论描述和实验测量远比气体及固体困难, 不同体系的液相扩散数据相当缺乏[5-6]。目前，液相扩散系数主要依靠实验方法获得，通过测量溶液由于扩散过程形成的浓度随空间和时间的分布，根据描述扩散过程的Fick定律[7]计算出液相扩散系数。从测量扩散系数的实验方法来看，广泛采用的是膜池法[8]、光干涉法[9]和泰勒分散法[10]。此外，还有核磁共振[11]、动态光散射[12]、荧光分子示踪[13]和放射性元素示踪[14]等测量方法。膜池法[8]是一种经典的稳态测量法，需要测量扩散池上下两个部分初始及稳态时的溶液浓度，测量时间较长。光干涉法[9]是测量目标光和参考光在空间相遇时形成的干涉条纹，通过条纹反演出目标光携带的扩散溶液浓度的空间和时间分布信息，该方法的测量精度较高，但其对实验环境的要求极为苛刻。泰勒分散法[10]是将微量溶质注入在毛细管中流动的溶剂中，溶质在溶剂中的扩散形成溶液浓度沿毛细管轴向的高斯分布，通过测量不同时刻浓度的分布曲线计算出扩散系数，该方法测量速度快，但测量精度较低。核磁共振法[11]具有抗干扰，测速快等特点，但只适用于测量一些特殊物质。光散射法[12]适用于测量高分子溶液的扩散系数。另……