Settling velocity for particle sets and its dependence on the sediment concentration - a study based on the kinetic energy quantification

Abstract

This paper presents analytical solutions for settling velocity of particle sets, considering the volumetric concentration, the kinetic energy of the set and its dissipation in the fluid. The concept of drag coefficient is used to evaluate the energy consumed during the particle movement (work done). Two different situations are considered: constant drag coefficient and drag coefficient proportional to the inverse of the particle Reynolds number. The solutions appear, at the first case, as a product of factors which include the free space between the particles. At the second case, the solutions appear like a sum of parcels which also involve the free space. The mass conservation principle is guaranteed by the present formulation. Comparisons between experimental data of the literature and the theoretical solution presented here show good agreement between data and predictions, and also between results of semi empirical formulations and of the present formulation, covering a wide range of sedimentation scenarios. Keywords: settling velocity, sedimentation, sediment volumetric density, particle suspensions.