The effect of a vertical gas flow on the dynamics of a coulombic granular material
moving over a horizontal rigid porous surface has been studied experimentally and
theoretically. The presence of a fluidizing gas significantly alters the granular flow
dynamics. When the gas velocity, ug, is below the
minimum fluidization velocity, umf,
the effect of the gas is to reduce the angle of repose θ from the value measured in the
absence of a gas flow. When material is poured from a point source onto a horizontal
surface it forms a pile, which adjusts through episodic avalanching to a self-similar
conical shape. Under these conditions, the development of the pile is determined by
the local force balance on individual particles and its extent may be expressed in
terms of the volume of particles added and the angle of repose. A volume of material
is poured continuously from a point source onto a surface according to Qtα. Below
the minimum uidization velocity, a quasi-static description gives the encroachment
distance of the granular pile as l = (2Q/(2π/3)n−1
tan θ)1/n+1tα/n+1 where n = 1 for a
planar release and n = 2 for an axisymmetric release.A continuum description of fluidized granular flow has been developed by vertically
averaging the mass and momentum conservation equations and including the
momentum exchange between the gas and granular flow. The bulk movement is
driven along the ground by horizontal gradients of particle pressure and is resisted
by a viscous drag force due to the particles moving horizontally through a vertical
gas flow. Above the minimum fluidization velocity the character of the granular
flow is significantly altered and takes on fluid-like properties. The model predicts the
shape of the fluidized granular pile and that the encroachment distance grows as
l = λnα (Q(ug
+ umf) / ε)1/n+2tα+1/n+2, where ε is the void fraction in the bed and
λnα is a constant. Below the conditions for fluidization
(ug < umf), the pile of granular material
grows quasi-statically when t > t∗, where
t∗ ∼ (εn+1Qug
+ umf) / μ2+n
(umf − ug)2+n)
1/1+n−α corresponds to the critical time when frictional forces are comparable
to gradients of particle pressure and the drag force. Numerical solutions describing the granular flow are presented.Experimental observations of the shape and extent of planar and axisymmetric
granular flows when α = 1 compare well with theoretical predictions for various
values of particle volume flux Q, time t, and gas flow rate ug. The
mathematical description of fluidized granular flows along rigid surfaces indicates a strong analogy
with buoyancy-driven flows in a porous medium. This analogy permits extension of
our description to include flows down slopes and the effect of internal stratification.
Aerated granular flow over a horizontal rigid surface
