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

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.