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Knudsen diffusion differs from Fickian diffusion
Physics of Fluids ( IF 4.6 ) Pub Date : 2021-04-21 , DOI: 10.1063/5.0048978
Jun Li 1 , Chunpei Cai 2 , Zhi-Hui Li 3
Affiliation  

We investigate the gas transport enhancement through nanotubes, relative to the prediction by the prevailing century-old Knudsen diffusion model. This enhancement is usually attributed to the partly specular molecular reflections at the smooth nanotube surface, which break the model assumption of completely diffusive reflections. However, an oversighted cause of the discrepancy between the measurement and theory that we found is that even for the gas transport with completely diffusive reflections, the Knudsen diffusion model based on Fick's first law is accurate only for long nanotubes. Additionally, for smooth nanotubes with partly specular reflections, the Knudsen diffusion model is also invalid even if the diffusion coefficient is corrected to account for the atomic-scale surface smoothness. On the other hand, the Knudsen diffusion model might be used for interpretations instead of predictions, and then the diffusion coefficient inferred from the measured mass flow rate could be completely different from the actual value. All those discrepancies and confusions stem from the implementation of Fick's first law can be avoided by using the molecular transmission probability obtained by the kinetic theory to quantify the flow rate of the Knudsen diffusion process. This work provides the correction to the Knudsen diffusion model for accurate predictions of gas diffusion through nanotubes and better interpretations of experimental measurements.

中文翻译:

Knudsen扩散与Fickian扩散不同

相对于流行的已有百年历史的克努森扩散模型的预测,我们研究了通过纳米管的气体传输增强作用。这种增强通常归因于光滑纳米管表面的部分镜面分子反射,这打破了完全漫反射的模型假设。但是,我们发现测量值与理论之间存在差异的一个疏忽原因是,即使对于具有完全扩散反射的气体传输,基于菲克第一定律的Knudsen扩散模型也仅适用于长纳米管。另外,对于具有部分镜面反射的光滑纳米管,即使校正了扩散系数以解决原子尺度的表面光滑度,Knudsen扩散模型也无效。另一方面,Knudsen扩散模型可用于解释而不是预测,然后从测得的质量流量推断出的扩散系数可能与实际值完全不同。通过使用动力学理论获得的分子传输概率来量化Knudsen扩散过程的流速,可以避免因实施菲克第一定律而引起的所有这些差异和混淆。这项工作对Knudsen扩散模型进行了校正,以准确预测通过纳米管的气体扩散,并更好地解释实验测量结果。通过使用动力学理论获得的分子传输概率来量化Knudsen扩散过程的流速,可以避免因实施菲克第一定律而引起的所有这些差异和混淆。这项工作对Knudsen扩散模型进行了校正,以准确预测通过纳米管的气体扩散,并更好地解释实验测量结果。通过使用动力学理论获得的分子传输概率来量化Knudsen扩散过程的流速,可以避免因实施菲克第一定律而引起的所有这些差异和混淆。这项工作对Knudsen扩散模型进行了校正,以准确预测通过纳米管的气体扩散,并更好地解释实验测量结果。
更新日期:2021-04-30
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