Hindered Settling Velocity in Particle-Fluid Mixture: A Theoretical Study Using the Entropy Concept

Abstract

In the study of mechanics of sediment transport, settling velocity is one of the important parameters because it is needed to solve the governing equations. It has been established that the presence of particles in the flow reduces the settling velocity of a particle, and this phenomenon is commonly known as hindered settling. The clear water settling and hindered settling of a particle are mathematically connected by a concentration function and a term in the power of concentration function, which is known as the exponent of reduction of settling velocity. Based on several turbulent features, a number of experimental and theoretical investigations have been carried out to formulate deterministic mathematical models on the exponent of reduction of settling velocity. However, a probabilistic study to formulate such models is still lacking in the literature. The present study therefore focuses on the modeling of exponent of reduction of settling velocity in a sediment-laden flow probabilistically, which is explored using the concept of entropy theory. The model is shown to be a function of particle Reynolds number, volumetric concentration, and relative mass density of sediment particles through the inclusion of these parameters in a hypothesized cumulative distribution function. The authors tested the model using experimental data from the literature and also compared these data with those of existing models. Relative percentage error between the observed and computed values of all the models shows the better prediction accuracy of this model in comparison to the others.