Abstract
The lift force on a circular particle in plane Poiseuille flow perpendicular to gravity is
studied by direct numerical simulation. The angular slip velocity Ωs=Ωp+½γ˙, where
−½γ˙ is the angular velocity of the fluid at a point where the shear rate is γ˙ and Ωp
is the angular velocity of the particle, is always positive at an equilibrium position at
which the hydrodynamic lift balances the buoyant weight. The particle migrates to its
equilibrium position and adjusts Ωp so that Ωs > 0 is nearly zero because Ωp ≈ −1/2γ˙
No matter where the particle is placed, it drifts to an equilibrium position with a
unique, slightly positive equilibrium angular slip velocity. The angular slip velocity
discrepancy defined as the difference between the angular slip velocity of a migrating
particle and the angular slip velocity at its equilibrium position is positive below the
position of equilibrium and negative above it. This discrepancy is the quantity that
changes sign above and below the equilibrium position for neutrally buoyant particles,
and also above and below the lower equilibrium position for heavy particles. The
existence and properties of unstable positions of equilibrium due to newly identified
turning-point transitions and those near the centreline are discussed.The long particle model of Choi & Joseph (2001) that gives rise to an explicit
formula for the particle velocity and the velocity profile across the channel through
the centreline of the particle is modified to include the effect of the rotation of the
particle. In view of the simplicity of the model, the explicit formula for Up and the
velocity profile are in surprisingly good agreement with simulation values. The value
of the Poiseuille flow velocity at the point at the particle's centre when the particle is
absent is always larger than the particle velocity; the slip velocity is positive at steady
flow.
Publisher
Cambridge University Press (CUP)
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics
Cited by
64 articles.
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