液体折射率及液相扩散系数的测量方法研究
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摘要
液体折射率和液相扩散系数是物理、化学、化工、生物等学科的重要基础数据。本博士论文针对目前液体折射率和液相扩散系数测量中存在的一些问题,研究了几种可行的解决方法。利用透明玻璃毛细管测量液体的折射率,解决了传统液体折射率测量过程中样品需求量大的问题,实现了液体折射率的微量测量；设计并制作了一种对称结构液芯变焦柱透镜,提高了液体折射率的测量灵敏度,实现了液体折射率的高精度测量；基于毛细管测量液体折射率的方法,通过标准液体标定测量参数的方式,实现了透明毛细管管壁折射率的无损测量；利用毛细管测量液体折射率特有的空间分辨测量能力,发明了用毛细管成像法测量液相扩散系数的方法,该方法具有可以直接观测液相扩散过程,测量时间短的特点；在对称液芯变焦柱透镜基础之上,设计并制作了非对称结构的液芯变焦柱透镜,使其球差控制在不影响图像判断的范围内,实现了折射率差值较小的溶液之间的扩散系数测量,提高了液相扩散系数的测量精度。论文主要研究内容和结果如下：
1.用透明玻璃毛细管实现了微量液体折射率的测量。将透明玻璃毛细管视为一个由四个共轴圆柱面构成的光学系统,推导出了此光学系统的焦距和毛细管参数间的解析式。设计了液体折射率的“毛细管焦点测量法”和“毛细管成像测量法”,分别用这两种方法在室温下测量了多种液体的折射率,测量准确度达到千分位；测试液体用量为0.0015ml,是常规仪器(阿贝折射仪)用量的百分之一,实现了液体折射率的微量测量。为了进一步提高测量系统的准确度和测量数据的稳定性,提出了虚实像结合测量法,减小了测量系统晃动引起的误差；分析了测量系统景深和灵敏度的关系,并对毛细管内外径尺寸与测量折射率准确度关系进行了分析。
2.用对称液芯变焦柱透镜对液体折射率进行了精确测量。设计、加工并制作了一种对称液芯变焦柱透镜,解决了毛细管成像法焦距较短(≤2.35mm)造成折射率灵敏度不高(可分辨最小折射率变化量-0.001)以及光源宽度过窄(限制在毛细管内径范围内)造成的光线会聚角度不足,测距景深过大的问题；保证了折射率测量的准确度,使其折射率的单次测量误差值小于0.0002,提高了测量灵敏度。
3.用标准液体标定法实现了透明毛细管管壁折射率的无损测量。在“毛细管焦点测量法”的基础上,发明了一种近轴条件下无损测量毛细管管壁折射率的方法。利用两种标准液体样品标定毛细管的管轴位置,对多种管壁材料、以及同种管壁材料不同内外径尺寸的毛细管进行了测量,管壁折射率的测量准确度达到0.005。分析了毛细管内外径对管壁折射率测量的影响,并将近轴条件下的测量方法发展到在非近轴条件下的测量。
4.用透明玻璃毛细管实现了液相扩散系数的测量。基于Fick第二定律,用高斯误差函数表述了液相扩散系数D的计算解析式。将毛细管既作为成像元器件又作为扩散池,利用其特有的折射率空间分辨测量能力,设计了“等折射率薄层测量法”和“等观测高度测量法”,测量了室温下丙三醇溶液在纯水中的扩散系数。利用所设计的方法测量液相扩散系数具有测量时间短(-lh)和可以直观察扩散过程的特点。
5.用非对称液芯变焦柱透镜精确测量液相扩散系数。在原有对称液芯变焦柱透镜基础上,设计加工了非对称液芯变焦柱透镜,使其在芯区液体为纯水时球差≤0.02μm,折射率测量准确度达到1.7×10-5RIU。测量了乙二醇溶液在纯水中的扩散系数；验证了在“等折射率薄层测量法”中,折射率薄层的选取与扩散系数的计算是无关的；分析了“等观测高度测量法”中,不同高度选取对扩散计算误差的影响。利用测量不同浓度的乙二醇溶液的扩散系数,通过线性拟合取极限的方法,得出了乙二醇溶液在室温无限稀释条件下的扩散系数为1.069×10-5cm2/s,与文献值比较相对误差为8.6%,这种测量方法为无限稀释情况下溶液扩散系数的测量提供了一种新途径,在保证毛细管测量法优点的同时实现了液相扩散系数更加精确的测量。
The refractive index (RI) and diffusion coefficient (DC) of liquids are the fundamental data in Physics, Chemistry, Chemical Engineering and Biology Engineering. The dissertation aims at the study on the new measurement methods of the RI and DC of liquids. A new method for measuring the RI of micro-quantity liquid by using transparent capillary is elaborated, which is characterized by a micro-quantity liquid and spatial resolution. To measure the RI of liquid more accurately, a symmetric liquid-core-zoom cylindrical lens has been fabricated, with the sensitivity of RI of the measurement system further improving. Based on the method for measuring RI of liquid with a capillary, the approach of measuring the RI of a capillary wall without destruction is introduced by filling a standard liquid in the capillary, of which the accuracy of measurement under paraxial and non-paraxial conditions are analyzed, and which makes up the blank of this field. The spatially resolving ability of the capillary in measuring RI of liquid is utilized to observe and record diffusive process directly, the transparency capillary is used as both diffusive pool and imaging element, a novel method for measuring the DC of liquid is successfully invented. In order to measure the DC more accurately, an asymmetric liquid-core zoom cylindrical lens has been designed and fabricated, in which the spherical aberration can be ignored, and which has been achieved the measurement of DC of liquid with slight range of RI.
The main research contents and results of the dissertation are consisted of five aspects as following:
First of all, the measurement of RI of micro-quantity liquid is realized by using a capillary. Based on imaging principle of a coaxial spherical surface optical system, the function between the focal length of optical system and the RI of the liquid is deduced, and two methods, i.e. the focusing method and imaging method of capillary, have been designed to measure the RIs of some kinds of liquid are measured at room temperature. The measurement accuracy of0.001is achieved, and the liquid amount is less than0.0015ml, which is one percent of the amount with the common instrument (Abbe Refractometer). In order to improve the accuracy of the measuring system and the stability of the measured data, virtual-real imaging method is presented, which reduced the errors of the system caused by shaking. The relationship between depth of field and sensitivity and the relationship between radii of capillary and the accuracy of RI are analyzed.
Secondly, a symmetric liquid-core zoom cylindrical lens has been designed and fabricated to measure RI of liquid more accurately, which solves two problems in capillary imaging method, i.e. the sensitivity of RI is not so higher (the minimum resolved RI～0.001) due to a short focal length (≤2.35mm), and the depth of field is large caused by a narrow light source width (limited in the range of capillary diameter). Due to an improved sensitivity in measuring RI and a short depth of field in the measurement system, a high accuracy in measurement of RI is ensued, which is better than0.0002.
Thirdly, a method for measuring the RI of transparency capillary without destruction is invented, which calibrated the position of the axis of capillary by using the standard liquid samples. The capillaries with same material and different diameter size have been measured and the influence on measurement accuracy of the size of capillary is analyzed. The measurement accuracy of RI is better than0.005, which can meet the request of general scientific research and experiment. To make the calculative method for RI of capillary tube more convenient and accurate, reduce the effects of the spherical aberration and the depth of field on the measurement results, we developed the method in non-paraxial condition.
Fourthly, a new technology for measuring the DC of liquid is invented by using a transparent capillary, which is characterized by faster measurement (～1h) and observing diffusion process directly. The analytical solution of DC has been expressed as Gauss error function based on the Fick second law. Two methods, i.e."equivalent the RI of thin layer" and "fixed an observation height" are presented, the diffusion process of pure glycerol in water is investigated by using the two methods.
Finally, the DC has been measured accurately by using an asymmetric liquid-core zoom cylindrical lens. When water is filled within the core area of the lens, the spherical aberration of the used measurement system is less than0.02jum and the measurement accuracy is1.7×10-5RIU. In the method of "equivalent the RI of thin layer", we get the DC from recording the position of layer with fixed RI as time increases, and verify that the selection of RI of the thin layer is unrelated to the measurement result of DC. In the method of "fixed an observation height", we have discussed the relationship between the height and the calculation error of DC. Through measuring the DC values in different ethylene glycol (EG) concentrations, finding the simulated formula between DC values and EG concentrations, making a limit of the concentration to zero from the formula, the DC value (1.069×10-5cm2/s) of EG at infinite dilution solution at25℃is obtained with the relative error8.6%. This method may open a new way to measure DC of liquid quickly at the condition of infinite dilution solution.
1.用透明玻璃毛细管实现了微量液体折射率的测量。将透明玻璃毛细管视为一个由四个共轴圆柱面构成的光学系统,推导出了此光学系统的焦距和毛细管参数间的解析式。设计了液体折射率的“毛细管焦点测量法”和“毛细管成像测量法”,分别用这两种方法在室温下测量了多种液体的折射率,测量准确度达到千分位；测试液体用量为0.0015ml,是常规仪器(阿贝折射仪)用量的百分之一,实现了液体折射率的微量测量。为了进一步提高测量系统的准确度和测量数据的稳定性,提出了虚实像结合测量法,减小了测量系统晃动引起的误差；分析了测量系统景深和灵敏度的关系,并对毛细管内外径尺寸与测量折射率准确度关系进行了分析。
2.用对称液芯变焦柱透镜对液体折射率进行了精确测量。设计、加工并制作了一种对称液芯变焦柱透镜,解决了毛细管成像法焦距较短(≤2.35mm)造成折射率灵敏度不高(可分辨最小折射率变化量-0.001)以及光源宽度过窄(限制在毛细管内径范围内)造成的光线会聚角度不足,测距景深过大的问题；保证了折射率测量的准确度,使其折射率的单次测量误差值小于0.0002,提高了测量灵敏度。
3.用标准液体标定法实现了透明毛细管管壁折射率的无损测量。在“毛细管焦点测量法”的基础上,发明了一种近轴条件下无损测量毛细管管壁折射率的方法。利用两种标准液体样品标定毛细管的管轴位置,对多种管壁材料、以及同种管壁材料不同内外径尺寸的毛细管进行了测量,管壁折射率的测量准确度达到0.005。分析了毛细管内外径对管壁折射率测量的影响,并将近轴条件下的测量方法发展到在非近轴条件下的测量。
4.用透明玻璃毛细管实现了液相扩散系数的测量。基于Fick第二定律,用高斯误差函数表述了液相扩散系数D的计算解析式。将毛细管既作为成像元器件又作为扩散池,利用其特有的折射率空间分辨测量能力,设计了“等折射率薄层测量法”和“等观测高度测量法”,测量了室温下丙三醇溶液在纯水中的扩散系数。利用所设计的方法测量液相扩散系数具有测量时间短(-lh)和可以直观察扩散过程的特点。
5.用非对称液芯变焦柱透镜精确测量液相扩散系数。在原有对称液芯变焦柱透镜基础上,设计加工了非对称液芯变焦柱透镜,使其在芯区液体为纯水时球差≤0.02μm,折射率测量准确度达到1.7×10-5RIU。测量了乙二醇溶液在纯水中的扩散系数；验证了在“等折射率薄层测量法”中,折射率薄层的选取与扩散系数的计算是无关的；分析了“等观测高度测量法”中,不同高度选取对扩散计算误差的影响。利用测量不同浓度的乙二醇溶液的扩散系数,通过线性拟合取极限的方法,得出了乙二醇溶液在室温无限稀释条件下的扩散系数为1.069×10-5cm2/s,与文献值比较相对误差为8.6%,这种测量方法为无限稀释情况下溶液扩散系数的测量提供了一种新途径,在保证毛细管测量法优点的同时实现了液相扩散系数更加精确的测量。
The refractive index (RI) and diffusion coefficient (DC) of liquids are the fundamental data in Physics, Chemistry, Chemical Engineering and Biology Engineering. The dissertation aims at the study on the new measurement methods of the RI and DC of liquids. A new method for measuring the RI of micro-quantity liquid by using transparent capillary is elaborated, which is characterized by a micro-quantity liquid and spatial resolution. To measure the RI of liquid more accurately, a symmetric liquid-core-zoom cylindrical lens has been fabricated, with the sensitivity of RI of the measurement system further improving. Based on the method for measuring RI of liquid with a capillary, the approach of measuring the RI of a capillary wall without destruction is introduced by filling a standard liquid in the capillary, of which the accuracy of measurement under paraxial and non-paraxial conditions are analyzed, and which makes up the blank of this field. The spatially resolving ability of the capillary in measuring RI of liquid is utilized to observe and record diffusive process directly, the transparency capillary is used as both diffusive pool and imaging element, a novel method for measuring the DC of liquid is successfully invented. In order to measure the DC more accurately, an asymmetric liquid-core zoom cylindrical lens has been designed and fabricated, in which the spherical aberration can be ignored, and which has been achieved the measurement of DC of liquid with slight range of RI.
The main research contents and results of the dissertation are consisted of five aspects as following:
First of all, the measurement of RI of micro-quantity liquid is realized by using a capillary. Based on imaging principle of a coaxial spherical surface optical system, the function between the focal length of optical system and the RI of the liquid is deduced, and two methods, i.e. the focusing method and imaging method of capillary, have been designed to measure the RIs of some kinds of liquid are measured at room temperature. The measurement accuracy of0.001is achieved, and the liquid amount is less than0.0015ml, which is one percent of the amount with the common instrument (Abbe Refractometer). In order to improve the accuracy of the measuring system and the stability of the measured data, virtual-real imaging method is presented, which reduced the errors of the system caused by shaking. The relationship between depth of field and sensitivity and the relationship between radii of capillary and the accuracy of RI are analyzed.
Secondly, a symmetric liquid-core zoom cylindrical lens has been designed and fabricated to measure RI of liquid more accurately, which solves two problems in capillary imaging method, i.e. the sensitivity of RI is not so higher (the minimum resolved RI～0.001) due to a short focal length (≤2.35mm), and the depth of field is large caused by a narrow light source width (limited in the range of capillary diameter). Due to an improved sensitivity in measuring RI and a short depth of field in the measurement system, a high accuracy in measurement of RI is ensued, which is better than0.0002.
Thirdly, a method for measuring the RI of transparency capillary without destruction is invented, which calibrated the position of the axis of capillary by using the standard liquid samples. The capillaries with same material and different diameter size have been measured and the influence on measurement accuracy of the size of capillary is analyzed. The measurement accuracy of RI is better than0.005, which can meet the request of general scientific research and experiment. To make the calculative method for RI of capillary tube more convenient and accurate, reduce the effects of the spherical aberration and the depth of field on the measurement results, we developed the method in non-paraxial condition.
Fourthly, a new technology for measuring the DC of liquid is invented by using a transparent capillary, which is characterized by faster measurement (～1h) and observing diffusion process directly. The analytical solution of DC has been expressed as Gauss error function based on the Fick second law. Two methods, i.e."equivalent the RI of thin layer" and "fixed an observation height" are presented, the diffusion process of pure glycerol in water is investigated by using the two methods.
Finally, the DC has been measured accurately by using an asymmetric liquid-core zoom cylindrical lens. When water is filled within the core area of the lens, the spherical aberration of the used measurement system is less than0.02jum and the measurement accuracy is1.7×10-5RIU. In the method of "equivalent the RI of thin layer", we get the DC from recording the position of layer with fixed RI as time increases, and verify that the selection of RI of the thin layer is unrelated to the measurement result of DC. In the method of "fixed an observation height", we have discussed the relationship between the height and the calculation error of DC. Through measuring the DC values in different ethylene glycol (EG) concentrations, finding the simulated formula between DC values and EG concentrations, making a limit of the concentration to zero from the formula, the DC value (1.069×10-5cm2/s) of EG at infinite dilution solution at25℃is obtained with the relative error8.6%. This method may open a new way to measure DC of liquid quickly at the condition of infinite dilution solution.
引文
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[30]N. Manohar Reddy, D. Kothandan, S. Chandra Lingam, A. Ahmad, A study on refractive index of plasma of blood of patients suffering from tuberculosis[J], Int. J. Technol. Eng.2012,8:23-25.
[31]M. Friebel, M. Meinke, Determination of the complex refractive index of highly concentrated hemoglobin solutions using transmittance and reflectance measurements[J], J.Biomed.Opt.2005,10:064019.1-064019.5.
[32]G. N. Jham, R. Velikova, B. N. Damyavova, S. C. Rabelo, J. C. T. Silva, K. A. P. Souza, V. M. M. Valente, P. R. Cecon, Preparative silver ion TLC/RP-HPLC determination of coffee triacylglycerol molecular species[J], Food Res.Int. 2005,38:121-126.
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