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Estimation of hindered settling velocity of suspensions
Sangkyun Koo 한국공업화학회 2009 Journal of Industrial and Engineering Chemistry Vol.15 No.1
Four effective-medium models (EM-I, II, III, IV) are utilized and compared for determining hindered settling velocity of equi-sized particles in a viscous fluid. Among the models, EM-IV model is found to accurately predict the effective viscosity and the hindered settling velocity of monodisperse suspensions. In EM-IV model which was developed for determining the diffusivity of proteins in a biological membrane by Dodd et al. [T.L. Dodd, D. A. Hammer, A.S. Sangani, D.L. Koch, J. Fluid Mech. 293 (1995) 147], the effective-medium region begins at the distance R = a[(1 - S(0))/Φ]1/3 from the origin where the center of the test particle is located, where a is the radius of the particle, f is the volume fraction of the particles in the suspension, and S(0) is the zero wavenumber limit of the structure factor. The estimations by EM-IV model agree very well with the exact calculations and the experimental observations. The hindered settling velocity U of the particles is given, in Richardson–Zaki form, by U/U0 = (1-Φ)5.5, where U0 is the settling velocity for an isolated particle.
Direct numerical simulations of inertial settling of non-Brownian particles
Ali Abbas Zaidi,Takuya Tsuji,Toshitsugu Tanaka 한국화학공학회 2015 Korean Journal of Chemical Engineering Vol.32 No.4
The dynamics of particles settling at moderate Reynolds number is studied with periodic boundary conditions. The particle Reynolds number ranges from 0.1 to 50, and the solid volume fraction ranges from single sphere to0.4. Particle-fluid interactions are solved by immersed boundary method and particle-particle interactions are solved bydiscrete element method. The principal results are the average settling velocity and the structure formation of particles. The average sedimentation velocities of particles for moderate Reynolds number showed deviation from the well-knownpower law, and the difference keeps on increasing with decrease in solid volume fractions. This deviation is removed byproposing the division of the power law into three regions of Reynolds number for dilute and non-dilute regimes. Byanalyzing the particle structures, this difference is due to the particle arrangements by the wake interactions at moderateReynolds number.
Numerical simulation of bidisperse hard spheres settling in a fluid
구상균 한국화학공학회 2011 Korean Journal of Chemical Engineering Vol.28 No.2
Average settling velocity of non-uniform hard spheres in a viscous fluid is determined by using a largescale numerical simulation that is carried out for over 103 spheres in a periodic unit cell which extends infinitely. An efficient calculation scheme is used for reducing the computation cost which steeply increases with the number of the spheres. The calculation scheme is based on a fast summation method for far-field hydrodynamic interaction among spheres. It is applied in the computation of hindered settling velocity of hard spheres with bidisperse size distribution in a viscous fluid. The simulation results are compared with the theoretical predictions by Batchelor [8] and Davis and Gecol [9]. It is found that the prediction by Davis and Gecol reasonably agrees with the numerical results.