Measurement and verification of concentration-dependent diffusion coefficient: Ray tracing imagery of diffusion process

doi:10.1088/1674-1056/ab9435

中国物理B ›› 2020, Vol. 29 ›› Issue (8): 84206-084206.doi: 10.1088/1674-1056/ab9435

• SPECIAL TOPIC—Ultracold atom and its application in precision measurement • 上一篇下一篇

Measurement and verification of concentration-dependent diffusion coefficient: Ray tracing imagery of diffusion process

Li Wei(魏利), Wei-Dong Meng(孟伟东), Li-Cun Sun(孙丽存), Xin-Fei Cao(曹新飞), Xiao-Yun Pu(普小云)

1 Department of Physics, Yunnan University, Kunming 650091, China;
2 Key Laboratory of Quantum Information of Yunnan Province, Yunnan University, Kunming 650091, China;
3 Department of Physics, Yunnan Normal University, Kunming 650504, China

收稿日期:2020-02-25 修回日期:2020-04-20 出版日期:2020-08-05 发布日期:2020-08-05
通讯作者: Xiao-Yun Pu E-mail:xypu@163.com
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 11804296), the Joint Key Project of Yunnan Province, China (Grant Nos. 2018FY001-020 and 2018ZI002), and the Fund from the Educational Department of Yunnan Province, China (Grant No. 2016CYH05).

Measurement and verification of concentration-dependent diffusion coefficient: Ray tracing imagery of diffusion process

Li Wei(魏利)¹, Wei-Dong Meng(孟伟东)^1,2, Li-Cun Sun(孙丽存)³, Xin-Fei Cao(曹新飞)¹, Xiao-Yun Pu(普小云)^1,2

1 Department of Physics, Yunnan University, Kunming 650091, China;
2 Key Laboratory of Quantum Information of Yunnan Province, Yunnan University, Kunming 650091, China;
3 Department of Physics, Yunnan Normal University, Kunming 650504, China

Received:2020-02-25 Revised:2020-04-20 Online:2020-08-05 Published:2020-08-05
Contact: Xiao-Yun Pu E-mail:xypu@163.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 11804296), the Joint Key Project of Yunnan Province, China (Grant Nos. 2018FY001-020 and 2018ZI002), and the Fund from the Educational Department of Yunnan Province, China (Grant No. 2016CYH05).

摘要/Abstract

摘要： Ray tracing method is used to study the propagation of collimated beams in a liquid-core cylindrical lens (LCL), which has dual functions of diffusion cell and image formation. The diffusion images on the focal plane of the used LCL are simulated by establishing and solving both linear and nonlinear ray equations, the calculated results indicate that the complex imaging results of LCL in inhomogeneous media can be treated by the law of ray propagation in homogeneous media under the condition of small refractive index gradient of diffusion solution. Guided by the calculation conditions, the diffusion process of triethylene glycol aqueous solution is experimentally studied at room temperature by using the LCL in this paper. The spatial and temporal concentration profile C^e(z, t) of diffusion solution is obtained by analyzing diffusion image appearing on the focal plane of the LCL; Then, the concentration-dependent diffusion coefficient is assumed to be a polynomial D(C)=D₀×(1+α₁C+α₂C²+α₃C³+…). The finite difference method is used to solve the Fick diffusion equation for calculating numerically the concentration profiles Cⁿ(z, t). The D(C) of triethylene glycol aqueous solution is obtained by comparing the Cⁿ(z,t) with C^e(z, t). Finally, the obtained polynomial D(C) is used to calculate the refractive index profiles nⁿ(z, t)s of diffusion solution in the used LCL. Based on the ray propagation law in inhomogeneous media and the calculated n(z,t), the ray tracing method is used again to simulate the dynamic images of the whole experimental diffusion process to varify the correctness of the calculated D(C). The method presented in this work opens up a new way for both measuring and verifying the concentration-dependent liquid diffusion coefficients.

关键词: concentration-dependent liquid diffusion coefficients, liquid-core cylindrical lens, nonlinear ray equation, ray tracing method

Abstract: Ray tracing method is used to study the propagation of collimated beams in a liquid-core cylindrical lens (LCL), which has dual functions of diffusion cell and image formation. The diffusion images on the focal plane of the used LCL are simulated by establishing and solving both linear and nonlinear ray equations, the calculated results indicate that the complex imaging results of LCL in inhomogeneous media can be treated by the law of ray propagation in homogeneous media under the condition of small refractive index gradient of diffusion solution. Guided by the calculation conditions, the diffusion process of triethylene glycol aqueous solution is experimentally studied at room temperature by using the LCL in this paper. The spatial and temporal concentration profile C^e(z, t) of diffusion solution is obtained by analyzing diffusion image appearing on the focal plane of the LCL; Then, the concentration-dependent diffusion coefficient is assumed to be a polynomial D(C)=D₀×(1+α₁C+α₂C²+α₃C³+…). The finite difference method is used to solve the Fick diffusion equation for calculating numerically the concentration profiles Cⁿ(z, t). The D(C) of triethylene glycol aqueous solution is obtained by comparing the Cⁿ(z,t) with C^e(z, t). Finally, the obtained polynomial D(C) is used to calculate the refractive index profiles nⁿ(z, t)s of diffusion solution in the used LCL. Based on the ray propagation law in inhomogeneous media and the calculated n(z,t), the ray tracing method is used again to simulate the dynamic images of the whole experimental diffusion process to varify the correctness of the calculated D(C). The method presented in this work opens up a new way for both measuring and verifying the concentration-dependent liquid diffusion coefficients.

Key words: concentration-dependent liquid diffusion coefficients, liquid-core cylindrical lens, nonlinear ray equation, ray tracing method

中图分类号: (Metrological applications; optical frequency synthesizers for precision spectroscopy)

42.62.Eh

07.60.-j (Optical instruments and equipment) 42.25.Dd (Wave propagation in random media) 42.15.Dp (Wave fronts and ray tracing)

魏利, 孟伟东, 孙丽存, 曹新飞, 普小云. Measurement and verification of concentration-dependent diffusion coefficient: Ray tracing imagery of diffusion process[J]. 中国物理B, 2020, 29(8): 84206-084206.

Li Wei(魏利), Wei-Dong Meng(孟伟东), Li-Cun Sun(孙丽存), Xin-Fei Cao(曹新飞), Xiao-Yun Pu(普小云). Measurement and verification of concentration-dependent diffusion coefficient: Ray tracing imagery of diffusion process[J]. Chin. Phys. B, 2020, 29(8): 84206-084206.

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Measurement and verification of concentration-dependent diffusion coefficient: Ray tracing imagery of diffusion process

Measurement and verification of concentration-dependent diffusion coefficient: Ray tracing imagery of diffusion process

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