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Entropy 2019, 21(1), 55; https://doi.org/10.3390/e21010055

Modelling the Hindered Settling Velocity of a Falling Particle in a Particle-Fluid Mixture by the Tsallis Entropy Theory

1
Beijing Key Laboratory of Urban Hydrological Cycle and Sponge City Technology, College of Water Sciences, Beijing Normal University, Xinjiekouwai Street 19, Beijing 100875, China
2
Public Works Research Institute, Minamihara 1-6, Tsukuba, Ibaraki-ken 305-8516, Japan
*
Authors to whom correspondence should be addressed.
Received: 30 November 2018 / Revised: 3 January 2019 / Accepted: 9 January 2019 / Published: 11 January 2019
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Abstract

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. View Full-Text
Keywords: entropy; Tsallis entropy; probability distribution; hindered settling velocity; particle-fluid mixture entropy; Tsallis entropy; probability distribution; hindered settling velocity; particle-fluid mixture
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Zhu, Z.; Wang, H.; Peng, D.; Dou, J. Modelling the Hindered Settling Velocity of a Falling Particle in a Particle-Fluid Mixture by the Tsallis Entropy Theory. Entropy 2019, 21, 55.

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