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A Simple Explicit Expression for the Flocculation Dynamics Modeling of Cohesive Sediment Based on Entropy

Zhongfan Zhu1

  • 1College of Water Sciences, Beijing Normal University, Xinjiekouwai Street 19, Beijing 100875, China.

Entropy (Basel, Switzerland)
|December 3, 2020
PubMed
Summary

This study introduces a new probabilistic model for cohesive sediment flocculation in turbulent water, using entropy theories to predict floc size over time. The model shows good agreement with experimental data, especially for logarithmic growth patterns.

Keywords:
Shannon entropyTsallis entropycohesive sedimententropyflocculationprobability distribution

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Area of Science:

  • Environmental science
  • Fluid dynamics
  • Sedimentology

Background:

  • Cohesive sediment flocculation impacts coastal morphology, dredging, and water quality.
  • Existing turbulence-induced flocculation models lack probabilistic approaches.
  • Understanding flocculation dynamics is crucial for various environmental and engineering applications.

Purpose of the Study:

  • To derive a probabilistic model for cohesive sediment flocculation in turbulent fluids.
  • To develop an explicit expression for characteristic floc size as a function of flocculation time.
  • To compare the derived model with existing deterministic models and experimental data.

Main Methods:

  • Application of Shannon entropy and Tsallis entropy theories.
  • Maximization of entropy function with constraint equations.
  • Hypothesis on the cumulative distribution function of floc size.
  • Validation with experimental data from existing literature.

Main Results:

  • Both Shannon and Tsallis entropy theories yield the same explicit expression for floc size.
  • The derived model demonstrates good agreement with experimental data.
  • The model shows superior prediction accuracy for logarithmic floc size growth patterns compared to existing models.
  • An empirical power relationship was found between maximum floc size capacity and flow shear rate.

Conclusions:

  • The developed probabilistic entropy-based model provides a novel approach to flocculation dynamics.
  • The model's performance varies with data patterns; existing models may be better for sigmoid growth.
  • Flow shear rate is a key factor influencing the maximum floc size achievable.