Fluid‐particle drag in low‐Reynolds‐number polydisperse gas–solid suspensions

Abstract

Lattice-Boltzmann simulations of low-Reynolds-number fluid flow in bidisperse fixed beds and suspensions with particle-particle relative motions have been performed. The particles are spherical and are intimately mixed. The total volume fraction of the suspension was varied between 0.1 and 0.4, the volume fraction ratio / 1 // 2 from 1:1 to 1:6, and the particle size ratio d 1 /d 2 from 1:1.5 to 1:4. A drag law with improved accuracy has been established for bidisperse fixed beds. For suspensions with particleparticle relative motions, the hydrodynamic particle-particle drag representing the momentum transfer between particle species through hydrodynamic interaction is found to be an important contribution to the net fluid-particle drag. It has a logarithmic dependence on the lubrication cutoff distance and can be fit as the harmonic mean of the drag forces in bidisperse fixed beds. The proposed drag laws for bidisperse fixed beds and suspensions are generalized to polydisperse suspensions with three or more particle species.

Characterization of fluid-particle interactions in poly-disperse systems

“…Its presence could include the dependence observed in Fig. 2 at the higher voidage values and, at the same time, avoid the previously-mentioned problem identified by Yin and Sundaresan [6].…”

“…(6,8)) rather than approaching a corrected drag force on isolated particles. Note that both the original formulation [5] and the discussion of Yin and Sundaresan [6] refer to expressions similar to Eq. (6) but with reference to the force in monodisperse system of the same size rather than the average force and in dimensionless terms.…”

“…On the other hand, there are cases that cannot be contemplated within the derivation recalled above. One of these concerns the tendency of the force on an individual particle when its y k is vanishingly small: Yin and Sundaresan [6] noted that the resulting force tends to zero (see Eqs. (6,8)) rather than approaching a corrected drag force on isolated particles.…”

“…One of these concerns the tendency of the force on an individual particle when its y k is vanishingly small: Yin and Sundaresan [6] noted that the resulting force tends to zero (see Eqs. (6,8)) rather than approaching a corrected drag force on isolated particles. Note that both the original formulation [5] and the discussion of Yin and Sundaresan [6] refer to expressions similar to Eq.…”

“…Even semi-analytical treatments of low-Reynolds-number flow through periodic arrays have been proposed in the literature [1][2][3]. In the last decade, fully resolved numerical simulations have allowed developing more accurate expressions for the drag force acting on individual particles [4][5] and to introduce useful elements for a formulation of the problem in poly-disperse systems [5][6]. However, the problem of a sufficiently general and validated theory for modelling the fluid-particle interaction in poly-disperse systems is still open, as will be discussed below.…”