Zhu Zhongfan, Wang Hongrui, Peng Dingzhi, Dou Jie
Beijing Key Laboratory of Urban Hydrological Cycle and Sponge City Technology, College of Water Sciences, Beijing Normal University, Xinjiekouwai Street 19, Beijing 100875, China.
Public Works Research Institute, Minamihara 1-6, Tsukuba, Ibaraki-ken 305-8516, Japan.
Entropy (Basel). 2019 Jan 11;21(1):55. doi: 10.3390/e21010055.
The settling velocity of a sediment particle is an important parameter needed for modelling the vertical flux in rivers, estuaries, deltas and the marine environment. It has been observed that a particle settles more slowly in the presence of other particles in the fluid than in a clear fluid, and this phenomenon has been termed 'hindered settling'. The Richardson and Zaki equation has been a widely used expression for relating the hindered settling velocity of a particle with that in a clear fluid in terms of a concentration function and the power of the concentration function, and the power index is known as the exponent of reduction of the settling velocity. This study attempts to formulate the model for the exponent of reduction of the settling velocity by using the probability method based on the Tsallis entropy theory. The derived expression is a function of the volumetric concentration of the suspended particle, the relative mass density of the particle and the particle's Reynolds number. This model is tested against experimental data collected from the literature and against five existing deterministic models, and this model shows good agreement with the experimental data and gives better prediction accuracy than the other deterministic models. The derived Tsallis entropy-based model is also compared with the existing Shannon entropy-based model for experimental data, and the Tsallis entropy-based model is comparable to the Shannon entropy-based model for predicting the hindered settling velocity of a falling particle in a particle-fluid mixture. This study shows the potential of using the Tsallis entropy together with the principle of maximum entropy to predict the hindered settling velocity of a falling particle in a particle-fluid mixture.
沉积物颗粒的沉降速度是模拟河流、河口、三角洲及海洋环境中垂直通量所需的一个重要参数。据观察，与在清水中相比，流体中存在其他颗粒时颗粒沉降得更慢，这种现象被称为“受阻沉降”。理查森和扎基方程是一个广泛使用的表达式，用于根据浓度函数及浓度函数的幂来关联颗粒在受阻沉降时的速度与在清水中的沉降速度，该幂指数被称为沉降速度降低指数。本研究尝试基于Tsallis熵理论，采用概率方法来构建沉降速度降低指数的模型。推导得出的表达式是悬浮颗粒的体积浓度、颗粒的相对质量密度以及颗粒雷诺数的函数。该模型与从文献中收集的实验数据以及五个现有的确定性模型进行了对比测试，结果表明该模型与实验数据吻合良好，且预测精度优于其他确定性模型。还将基于Tsallis熵推导的模型与现有的基于香农熵的模型针对实验数据进行了比较，在预测颗粒 - 流体混合物中下落颗粒的受阻沉降速度方面，基于Tsallis熵的模型与基于香农熵的模型相当。本研究展示了结合使用Tsallis熵和最大熵原理来预测颗粒 - 流体混合物中下落颗粒受阻沉降速度的潜力。
