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For “Drag Force of Intermediate Reynolds Number Flow Past Mono- and Bidisperse Arrays of Spheres” by Beetstra et al. (pp. 489–501, February 2007, DOI: 10.1002/aic.11065), the authors request the following Erratum:

The total gas-particle interaction force Fg[RIGHTWARDS ARROW]s,i can be split into a drag force Fd,i and a force from the pressure gradient:

  • equation image(1)

with Vi the volume of particle i. In literature both forces Fg[RIGHTWARDS ARROW]s,i and Fd,i are defined as the drag force, which has been the source of some confusion. The lattice Boltzmann method yields data for Fg[RIGHTWARDS ARROW]s,i. Nevertheless, in the paper we have chosen to present all results in terms of Fd,i, using the relation:

  • equation image(2)

with ϕ the packing fraction. However, relation (2) is only correct (that is, consistent with Eq. (1)) for monodisperse systems, and not for polydisperse systems. As a consequence, all results on Fd,i for binary systems are in fact valid for the total gas-particle interaction force Fg[RIGHTWARDS ARROW]s,i (multiplied by (1 − ϕ)), and not for the drag force Fd,i as defined by Eq. (1). This means that the correction factor to the drag force that we present for polydisperse systems is valid for Fg[RIGHTWARDS ARROW]s,i. Specifically, the equation for the normalized total gas-particle force Ftot,i = Fg[RIGHTWARDS ARROW]s,i/3πμdiU is1:

  • equation image(3)

with Ftot the normalized total gas-particle force of a monodisperse system. The equation for the normalized drag force Fi = Fd,i/3πμdiU, consistent with (1), is then equal to:

  • equation image(4)

with F the normalized drag force of a monodisperse system (note that F = (1 − ϕ)Ftot). For the precise definitions of the symbols we refer to the original paper. Note that when applying (4), the contribution from the pressure gradient has to be added seperately. Our claim that the deviation with the drag force that follows from the ad-hoc modification for polydispersity (replacing d by di) can be as much as a factor 3–5 is only true for the total gas-particle force. With regard to the drag force, the deviation is less.

  • 1

    when neglecting the yi3 term