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

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.

Evaluating GIS-Based Multiple Statistical Models and Data Mining for Earthquake and Rainfall-Induced Landslide Susceptibility Using the LiDAR DEM

“…where Υ and γ denote factors of kernel functions. During these four types of kernel functions, RBF usually provides a better predictive capability for LSM than other kernel functions in non-linear classification [23,64]. Additionally, a novel ensemble model was proposed by integrating normalized InV values from the bivariate analysis with BF-SVM kernel.…”

“…An unverified prediction model and susceptibility maps are nonetheless meaningless and hence do not have any scientific significance [57]. Several studies have addressed the issue of LSM validation [13,64].…”

Entropy Generation for Negative Frictional Pressure Drop in Vertical Slug and Churn Flows

“…The frictional pressure drops were calculated by Equations (16) and (17) and the entropy generation rates due to mechanical energy loss were calculated with Equation (18) from the data in Table 1. The mean velocity vm in Equation (18) was determined by Equations (3) and (23). The results are plotted against superficial gas velocity in Figures 3 and 4.…”

Evaluating scale effects of topographic variables in landslide susceptibility models using GIS-based machine learning techniques

“…Landslide susceptibility assessment is a useful task for landslide hazard management and mitigation 8,9,50 . However, landslide is a complex natural phenomenon which is controlled by several geo-environmental factors; thus, it is not easy to be modeled accurately 8,9 .…”