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中国物理学会期刊

宽浓度范围扩散系数与关联黏度结果的测定及计算验证

Determination and calculation verification of diffusion coefficients over a wide concentration range and associated viscosity results

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  • 液相扩散系数与黏度是表征液体物质输运性质的关键参数,二者均随浓度变化,实现其快速测量对于化学工程与生物医药等领域具有重要意义。针对宽浓度范围内相关参数连续获取及结果验证问题,本文基于液芯柱透镜成像与有限差分反演方法,对二元溶液扩散过程进行了非接触、可视化监测。液芯柱透镜兼作扩散池与成像单元,通过分析采集的瞬态浓度场数据,反演获得扩散系数随浓度的变化函数D(C),并在斯托克斯-爱因斯坦关系近似适用的前提下,进一步计算出随浓度变化的黏度系数函数η(C)。以甘氨酸-水体系(0~3.0 mol/L, 298.15 K和303.15 K)为对象进行实验,结果表明,D(C)和η(C)测量结果与文献值接近。进一步地结合D(C)测量结果,对扩散图像进行光线追迹仿真,成功复现了实验观测的动态扩散图像,验证了测量结果的可靠性。本研究为宽浓度范围液体体系浓度相关输运参数的实验表征与结果验证提供了参考。

     

    The liquid-phase diffusion coefficient and viscosity are important physical parameters for characterizing mass transfer and transport behavior in liquid systems, and both generally depend on solute concentration. Conventional methods usually require multiple experiments or contact-based measurements, making it difficult to continuously obtain concentration-dependent transport parameters over a wide concentration range. In this work, a non-contact and visual optical method is proposed for determining concentration-dependent diffusion coefficients and associated viscosity results over a wide concentration range. A liquid-core cylindrical lens was used simultaneously as a diffusion cell and an imaging element. By analyzing the transient diffusion images of a binary solution, the relationship among image width, refractive index, and concentration was established, and the spatial and temporal concentration profiles were obtained from the same continuous diffusion process. On this basis, the concentration-dependent diffusion coefficient was expressed as a polynomial, D(C)=D0(1+αC+βC2+γC3), where D0is the diffusion coefficient at infinite dilution and α, β, and γ are undetermined coefficients. The finite difference method was applied to numerically solve Fick’s diffusion equation, and the calculated concentration profiles were compared with the experimental profiles. The coefficients corresponding to the minimum concentration deviation were selected to determine D(C). Under the approximate applicability of the Stokes-Einstein relation, the concentration-dependent associated viscosity η(C) was further calculated from the obtained D(C). Experiments were carried out for the glycine-water system over a concentration range of 0~3.0 mol/L at 298.15 K and 303.15 K. At 298.15 K, the measured diffusion coefficient was D(C)=1.071×10-5(1-0.083C+0.010C2)cm2×s-1, and the associated viscosity increased from 0.8870 mPa×s to 1.0547 mPa×s with increasing concentration. At 303.15 K, the measured diffusion coefficient was D(C)=1.167x10-5(1-0.068C+0.006C2)cm2×s-1. The obtained diffusion coefficients and associated viscosity results are in close agreement with reported values. Furthermore, the measured D(C) was used to calculate the spatial and temporal refractive-index profiles, based on which ray-tracing simulations were performed to reproduce the dynamic diffusion images. The simulated images closely match the experimental images in terms of the sharp imaging position, overall contour, and image-width profiles along the diffusion direction, further demonstrating the reliability of the proposed method. The results indicate that this method provides an efficient and visual approach for characterizing concentration-dependent transport parameters of liquid systems with high accuracy and stability.

     

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