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本文提出了一种快速测量液相扩散系数的方法, 该方法以液芯柱透镜作为液相扩散池和成像元件, 利用柱透镜成像过程中特有的折射率空间分辨测量能力, 只需记录一幅瞬态扩散图像, 根据图像的像宽与折射率的对应关系, 基于扩散定律快速计算出液相扩散系数. 实验研究了室温(25℃)下乙二醇和纯水间的扩散过程, 用折射率空间分布法测量了扩散系数, 和其他测量方法得到的结果进行了分析对比, 结果表明:用折射率空间分布法测量液相扩散系数具有数据采集耗时短(～20 ms)、测量速度快(1 s)、精度高(相对误差3%)和操作简单的特点, 为快速测定液相扩散系数提供了一种有效的新方法.This paper studies the equivalent refractive index method and other methods to measure the liquid diffusion coefficient. Based on this, a quick method to measure the liquid diffusion coefficient is proposed, i.e. using a specially designed asymmetric liquid-core cylindrical lens as both diffusive pool and imaging element. By means of this system with the liquid-core cylindrical lens to measure the diffusion coefficient, we can eliminate the spherical aberration and improve the accuracy in refractive index measurement. Based on the spatially resolving ability of the cylindrical lens in measuring the refractive index, only one instantaneous diffusive picture is required. Depending on the correspondence between the image width and the refractive index, we thus can quickly calculate the diffusion coefficient D by the Ficks second law. Then the diffusive process of ethylene glycol in water at 25℃ is investigated by this method. We calculate the diffusion coefficient between 660-3000 s with the method to analyse an instantaneous diffusion picture. At the beginning, injection will cause the liquid turbulent, and thus create a larger diffusion coefficient. In the course of diffusion, the influence of turbulence on the diffusion coefficient gradually decreases, but the image narrowing can make inaccurate results. Therefore, this method is required to be used at an appropriate time and an appropriate position to reduce experimental errors. After repeated experiments we can conclude that, between 1500-2700 s we may select the appropriate measurement of location for measuring liquid diffusion coefficient by the method to analyze an instantaneous diffusive picture. This not only can avoid the effect of turbulence but also avoid the effect of fewer sampling points. Compared with other methods reported in the literature, the results show that this method is characterized by short time (~20 ms) in data acquisition, faster measurement ( 1 s), high-accuracy (relative error 3%), and easy operation, thus providing a new method for measuring the diffusion coefficient of liquids rapidly.
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Keywords:
- diffusion coefficient /
- fast measurement /
- spatial distribution of refractive index /
- liquid-core cylindrical lens
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[2] Zuo M, Han Y L, Qi L, Chen Y 2007 Chinese Science Bulletin. 52 3325
[3] Ju Y Y, Zhang Q M, Gong Z Z, Ji G F 2013 Chin. Phys. B 22 083101
[4] Ahmed A, Wu J T 2011 Chin. Phys. B 20 106601
[5] Zhang S Y, Bao S L, Kang X J, Gao S 2013 Acta Phys. Sin. 62 208703 (in Chinese) [张首誉, 包尚联, 亢孝俭, 高嵩 2013 62 208703]
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[7] Radi Z, L ábár J L, Barna P B 1998 Appl. Phys. Lett. 73 3220
[8] Bek W J, Muttzal M K 2006 Transport Phenomena (New York:Wiley) p75
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[10] Cheng Y, Wei L, Chi W 2004 J. Phys. Chem. B 108 11866
[11] Culbertson C T, Jacobson S C, Ransey J M 2002 Talanta 56 365
[12] WANG J H 1952 J. Am. Chem. Soc. 74 182
[13] Chhaniwal V K, Anand A, Girhe S, Patil D, Subrahmanyam N, Narayanamurthy C S 2003 J. Opt. A:Pure Appl. Opt. 5 S329
[14] Ghaleh K J, Tavassoly M T, Mansour N 2004 J. Phys.D:Appl. Phys. 37 1993
[15] Li Q, Pu X Y 2013 Acta Phys. Sin. 62 094206 (in Chinese) [李强, 普小云 2013 62 094206]
[16] Li Q, Sun L C, Meng W D, Pu X Y 2012 Chinese Journal Of Lasers 39 1008005 (in Chinese) [李强, 孙丽存, 孟伟东, 普小云 2012 中国激光 39 1008005]
[17] Li Q, Pu X. Y, Yang R. F Q, Zhai Y 2014 Chin. Phys. Lett. 31 054203
[18] Hills E E, Abraham M H, Hersey A 2011 Fluid Phase Equilib. 303 45
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[1] Cussler E L 1997 Diffusion-Mass Transfer in Fluid Systems (Cambridge:Cambridge University Press) 13
[2] Zuo M, Han Y L, Qi L, Chen Y 2007 Chinese Science Bulletin. 52 3325
[3] Ju Y Y, Zhang Q M, Gong Z Z, Ji G F 2013 Chin. Phys. B 22 083101
[4] Ahmed A, Wu J T 2011 Chin. Phys. B 20 106601
[5] Zhang S Y, Bao S L, Kang X J, Gao S 2013 Acta Phys. Sin. 62 208703 (in Chinese) [张首誉, 包尚联, 亢孝俭, 高嵩 2013 62 208703]
[6] Wang Z Z, Wang N, Yao W J 2010 Acta Phys. Sin. 59 7431 (in Chinese) [王振中, 王楠, 姚文静 2010 59 7431]
[7] Radi Z, L ábár J L, Barna P B 1998 Appl. Phys. Lett. 73 3220
[8] Bek W J, Muttzal M K 2006 Transport Phenomena (New York:Wiley) p75
[9] Zhao C W, Ma P S, He M X 2002 Chemical Industry and Engineering 19 374 (in Chinese) [赵长伟,马沛生,何明霞 2002 化学工业与工程 19 374]
[10] Cheng Y, Wei L, Chi W 2004 J. Phys. Chem. B 108 11866
[11] Culbertson C T, Jacobson S C, Ransey J M 2002 Talanta 56 365
[12] WANG J H 1952 J. Am. Chem. Soc. 74 182
[13] Chhaniwal V K, Anand A, Girhe S, Patil D, Subrahmanyam N, Narayanamurthy C S 2003 J. Opt. A:Pure Appl. Opt. 5 S329
[14] Ghaleh K J, Tavassoly M T, Mansour N 2004 J. Phys.D:Appl. Phys. 37 1993
[15] Li Q, Pu X Y 2013 Acta Phys. Sin. 62 094206 (in Chinese) [李强, 普小云 2013 62 094206]
[16] Li Q, Sun L C, Meng W D, Pu X Y 2012 Chinese Journal Of Lasers 39 1008005 (in Chinese) [李强, 孙丽存, 孟伟东, 普小云 2012 中国激光 39 1008005]
[17] Li Q, Pu X. Y, Yang R. F Q, Zhai Y 2014 Chin. Phys. Lett. 31 054203
[18] Hills E E, Abraham M H, Hersey A 2011 Fluid Phase Equilib. 303 45
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