Measuring liquid-phase diffusion coefficient of aqueous sucrose solution using double liquid-core cylindrical lens
doi: 10.3788/CO.20181104.0630
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摘要: 基于双液芯柱透镜的折射率空间分辨测量精度高的特点，本文采用两种方法在室温（25℃）下分别测量了不同浓度的蔗糖水溶液的液相扩散系数。方法一：等折射率薄层移动法，通过记录扩散过程中特定折射率薄层随时间的变化关系计算液相扩散系数。方法二：瞬态图像分析法，通过读取一幅瞬态扩散图像中图像宽度与扩散位置之间的关系确定液相扩散系数。双液芯柱透镜的前液芯作为扩散池和主要成像元件，后液芯作为消球差辅助系统。充分利用了双液芯柱透镜可以按需减小特定液体薄层处的球差以及能够在一定的折射率范围内同时减小球差，两种方法均具有测量精度高的特点。两种方法的测量结果与文献值的相对误差分别小于1.3%和3.9%，表明用双液芯柱透镜测量液相扩散系数时，测量系统稳定可靠，测量结果准确。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.
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图 4 不同折射率薄层球差与后液芯液体折射率的关系
Figure 4. Relationship between the refractive index thin layer spherical aberration and the refractive index of the rear liquid core
图 5 0.10→0.90 mol/L蔗糖水溶液扩散图像
Figure 5. Diffusion images of 0.10→0.90 mol/L aqueous sucrose solution
图 6 不同扩散体系球差之和与后液芯液体折射率的关系
Figure 6. Relationship between the sum of spherical aberrations of different diffusion systems and the refractive index of the rearliquid core
图 7 0.10→0.90 mol/L蔗糖水溶液的瞬态扩散图像
Figure 7. Transient diffusion image of 0.10→0.90 mol/L aqueous sucrose solution
表 1 Data record of equivalent refractive index location over time
Table 1. Data record of equivalent refractive index location over time
t/s 
Z′i/μm t/s Z′i/μm 1 200 34.64 2 249.5 4 500 67.08 4 350.5 1 500 38.73 2 442.0 4 800 69.28 4 488.0 1 800 42.43 2 673.0 5 100 71.41 4 614.5 2 100 45.83 2 948.0 5 400 73.48 4 730.0 2 400 48.99 3 157.0 5 700 75.50 4 829.0 2 700 51.96 3 366.0 6 000 77.46 5 016.0 3 000 54.77 3 613.5 6 300 79.37 5 131.5 3 300 57.45 3 800.5 6 600 81.24 5 203.0 3 600 60.00 3 965.5 6 900 83.07 5 307.5 3 900 62.45 4 130.5 7 200 84.85 5 417.5 4 200 64.81 4 224.0 - - - 
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表 2 Data of the equivalent refractive index method of aqueous sucrose solution for different concentrations
Table 2. Data of the equivalent refractive index method of aqueous sucrose solution for different concentrations
Concentration/
(mol·L-1)Fitting
result/μmCorrelation
coefficientD/
×10-6 cm2·s-1Dlit[24]/
×10-6cm2·s-1Relative
error/%0.30 Z′i=63.8 0.999 5 4.22 4.26 -0.94 0.50 Z′i=51.7 0.998 7 3.70 3.67 0.82 0.70 Z′i=42.9 0.997 1 3.07 3.11 -1.29
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表 3 Refractive index spatial distribution data at 2400 s
Table 3. Refractive index spatial distribution data at 2400 s
Z′i/μm Σi/μm ni Ci erfinv 3 311.0 38.5 1.338 7 0.115 6 1.459 1 3 349.5 44 1.338 6 0.113 6 1.499 6 3 415.5 55 1.338 6 0.113 6 1.499 6 3 470.5 60.5 1.338 5 0.111 5 1.545 7 3 536.5 66 1.338 5 0.111 5 1.545 7 3 591.5 77 1.338 4 0.109 5 1.599 6 3 674.0 82.5 1.338 4 0.109 5 1.599 6 3 756.5 93.5 1.338 3 0.107 4 1.664 7 3 822.5 99 1.338 3 0.107 4 1.664 7 3 899.5 110 1.338 2 0.105 4 1.748 0
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表 4 Data of transient methods for different concentrations of aqueous sucrose solution
Table 4. Data of transient methods for different concentrations of aqueous sucrose solution
Concentration/
(mol·L-1)Fitting
result/μmCorrelation
coefficientD/
×10-6 cm2·s-1Dlit[24]/
×10-6cm2·s-1Relative
error/%0.30 Z′i=2049.6x-59.8 0.970 6 4.38 4.26 2.82 0.50 Z′i=1908.2x-44.9 0.976 7 3.79 3.67 3.27 0.70 Z′i=1761.1x-69.2 0.977 9 3.23 3.11 3.86
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