Measuring liquid-phase diffusion coefficient of aqueous sucrose solution using double liquid-core cylindrical lens
doi: 10.3788/CO.20181104.0630
-
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.
-
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 - - - 
下载: 导出CSV
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
下载: 导出CSV
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
下载: 导出CSV
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
下载: 导出CSV
-
[1] CUSSLER E L. Diffusion:Mass Transfer in Fluid Systems[M]. 3rd Ed. London:Cambridge University Press, 2009. [2] CHHANIWAL V K, ANAND A, GIRHE S. New optical techniques for diffusion studies in transparent liquid solutions[J]. J. Opt. A:Pure & Appl. Opt., 2003, 5(5):S329-337. https://www.researchgate.net/publication/230994620_New_optical_techniques_for_diffusion_studies_in_transparent_liquid_solutions [3] WEISS N, LEEUWEN T G, KALKMAN J. Simultaneous and localized measurement of diffusion and flow using optical coherence tomography[J]. Opt. Express, 2015, 23(3):3448-3459. doi: 10.1364/OE.23.003448 [4] 王振中, 王楠, 姚文静.低扩散系数对Pd77Cu6Si17合金易非晶化的影响[J].物理学报, 2010, 59(10):7431-7436. https://www.researchgate.net/publication/286595500_Effect_of_low_diffusion_coefficient_on_glass_phase_formation_in_Pd77Cu6Si17_alloyWANG ZH ZH, WANG N, YAO W J. Effect of low diffusion coefficient on glass phase formation in Pd77Cu6Si17 alloy[J]. Acta Phys. Sin., 2010, 59(10):7431-7436.(in Chinese) https://www.researchgate.net/publication/286595500_Effect_of_low_diffusion_coefficient_on_glass_phase_formation_in_Pd77Cu6Si17_alloy [5] DONEV A, NONAKA A, BHATTACHARJEE A K, et al.. Low mach number fluctuating hydrodynamics of multispecies liquid mixtures[J]. Physics of Fluids, 2015, 27(3):1085-1105. http://adsabs.harvard.edu/abs/2015PhFl...27c7103D [6] 马友光, 朱春英, 何明霞, 等.氨基酸在水溶液中扩散系数的实验研究[J].激光技术, 2005, 29(2):145-147. https://www.sciencedirect.com/science/article/pii/S0065323308606270MA Y G, ZHU C Y, HE M X, et al. The experimental study about the diffusivities of amino acids in aqueous solution[J]. Laser Technology, 2005, 29(2):145-147.(in Chinese) https://www.sciencedirect.com/science/article/pii/S0065323308606270 [7] CRANK J. The Mathematics of Diffusion[M]. 2nd Ed. Oxford:Oxford University Press, 1975:2-26. [8] BREER J, GROOT K D, SCH NERT H. Diffusion in the diaphragm cell:continuous monitoring of the concentrations and determination of the differential diffusion coefficient[J]. Journal of Solution Chemistry, 2014, 43(1):71-82. doi: 10.1007/s10953-013-0020-z [9] HE M G, ZHANG S, ZHANG Y, et al.. Development of measuring diffusion coefficients by digital holographic interferometry in transparent liquid mixtures[J]. Opt. Express, 2015, 23(9):10884-10889. doi: 10.1364/OE.23.010884 [10] CIPELLETTI L, BIRON J P, MARTIN M, et al.. Measuring arbitrary diffusion coefficient distributions of Nano-Objects by Taylor dispersion analysis[J]. Anal. Chem., 2015, 87(16):8489-8496. doi: 10.1021/acs.analchem.5b02053 [11] MEREAU C, CAVALIER A. Sarcolemma phospholipid structure investigated by immunogold electron microscopy and P NMP spectroscopy with lanthanide ions[J]. FEBS Letters, 2001, 509(3):417-422. doi: 10.1016/S0014-5793(01)03199-4 [12] YANG C, LI W, WU C, et al.. Laser light-scattering study of solution dynamics of water/cycloether mixtures[J]. Journal of Physical Chemistry B, 2004, 108(31):1794-1801. http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.540.1295 [13] CULBERTSON C T, JACOBSON S C, RANSEY J M, et al.. Diffusion coefficient measurements in microfluidic devices[J]. Talanta, 2002, 56(2):365-373. doi: 10.1016/S0039-9140(01)00602-6 [14] WANG J H. Application of a radioactive tracer method for diffusion study in some liquids[J]. Pramana, 1991, 37(2) 105-114. doi: 10.1007/BF02875296 [15] 李强, 普小云.用毛细管成像法测量液相扩散系数-等折射率薄层测量方法[J].物理学报, 2013, 62(9):094206-6. http://wulixb.iphy.ac.cn/EN/Y2013/V62/I9/094206LI Q, PU X Y. Measuring the diffusion coefficient of liquids by capillary imaging method:equivalent refractive index method[J]. Acta Phys. Sin., 2013, 62(9):094206-6.(in Chinese) http://wulixb.iphy.ac.cn/EN/Y2013/V62/I9/094206 [16] 孟伟东, 孙丽存, 翟影, 等.用液芯柱透镜快速测量液相扩散系数-折射率空间分布瞬态测量法[J].物理学报, 2015, 64(11):114205-7.MENG W D, SUN L C, ZHAI Y, et al.. Rapid measurement of the diffusion coefficient of liquidsusing a liquid-core cylindricallens:a method foranalysing an instantaneous diffusive picture[J]. Acta Phys. Sin., 2015, 64(11):114205-7.(in Chinese) [17] SUNL C, MENG W D, PU X Y. New method to measure liquid diffusivity byanalyzing an instantaneous diffusion image[J]. Opt. Express, 2015, 23(18):23155-23166. doi: 10.1364/OE.23.023155 [18] MENG W D, XIA Y, SONG F X, et al.. Double liquid-core cylindrical lens utilized to measure liquid diffusion coefficient[J]. Opt. Express, 2017, 25(5):5626-5640. doi: 10.1364/OE.25.005626 [19] 李零印, 王一凡.液体变焦技术的发展与展望[J].中国光学, 2012, 5(6):578-582. http://www.opticsjournal.net/abstract.htm?id=OJ121224000186aGcJfLLI L Y, WANG Y F. Development and prospect of varifocal-liquid technique[J]. Chinese Optics, 2012, 5(6):578-582.(in Chinese) http://www.opticsjournal.net/abstract.htm?id=OJ121224000186aGcJfL [20] 张鹰, 张新, 史广维, 等.液体透镜在变焦系统中的应用[J].中国光学, 2013, 6(1):46-56. http://www.opticsjournal.net/Abstract.htm?id=OJ130206000061gNjQmSZHANG Y, ZHANG X, SHI G W, et al.. Applications of liquid lenses in zoom systems[J]. Chinese Optics, 2013, 6(1):46-56. http://www.opticsjournal.net/Abstract.htm?id=OJ130206000061gNjQmS [21] 邢曼男, 白然, 普小云.精确测量微量液体折射率的新方法[J].光学 精密工程, 2008, 16(7):1196-1202. https://www.researchgate.net/publication/292934966_Novel_measuring_method_for_refractive_index_of_micro-quantity_liquidXING MN, BAI R, PU X Y. Novel measuring method for refractive index of micro-quantity liquid[J]. Opt. Precision Eng., 2008, 16(7):1196-1202. https://www.researchgate.net/publication/292934966_Novel_measuring_method_for_refractive_index_of_micro-quantity_liquid [22] 张宗权, 徐铭, 任俊鹏, 等.封闭玻璃管道内液体折射率的非接触测量[J].光学 精密工程, 2016, 24(10):2408-2416. doi: 10.3788/OPE.ZHANG Z Q, XU M, REN J P, et al..Non-contact measurement for liquid refractive index in a closed pipe[J]. Opt. Precision Eng., 2016, 24(10):2408-2416. doi: 10.3788/OPE. [23] SUN L C, PU X Y. A novel visualization technique for measuring liquid diffusion coefficient based on asymmetric liquid-core cylindrical lens[J]. SCI Rep, 2016, 6(6):28264-1. https://www.researchgate.net/publication/305449483_A_novel_visualization_technique_for_measuring_liquid_diffusion_coefficient_based_on_asymmetric_liquid-core_cylindrical_lens [24] 马有光, 段志青, 朱春英.激光实时全息干涉法测量甘氨酸水溶液扩散系数[J].应用光学, 2004, 24(2):99-101.MA Y G, DUAN ZH Q, ZHU CH Y, et al.. Diffusivity measurement of glycine aqueous solution using real-time holographicinterferometry[J]. Applied Laser, 2004, 24(2):99-101.(in Chinese) [25] 孙丽存, 孟伟东, 李强, 等.电子目镜显微镜景深的确定与测量[J].光学 精密工程, 2013, 21(5):1151-1159. doi: 10.3788/OPE.SUN L C, MENG W D, LI Q, et al.. Calculation and measurement of depth of field for microscope with electronic ocular[J]. Opt. Precision Eng., 2013, 21(5):1151-1159. doi: 10.3788/OPE. -
下载:
点击查看大图
图(7) / 表(4)
计量
- 文章访问数: 1277
- HTML全文浏览量: 357
- PDF下载量: 114
- 被引次数: 0
