Eur. Phys. J. E 8, 517-529 (2002)
DOI: 10.1140/epje/i2002-10042-0
Foam drainage on a sloping weir
P. Grassia, S.J. Neethling and J.J. CilliersDepartment of Chemical Engineering, UMIST, P.O. Box 88, Manchester M60 1QD, UK Paul.Grassia@umist.ac.uk
(Received 8 March 2002 and Received in final form 27 June 2002 Online publication 8 October 2002)
Abstract
Foam drainage is considered in a froth flotation tank
with a sloping weir.
The drainage is shown to be gravity dominated in
most of the foam, except for thin boundary layers at the
base of the froth, and along the sloping weir.
The mathematical reason for the boundary layers is that
capillary suction is a much weaker effect
than gravity, but cannot be ignored altogether,
because it represents a singular perturbation.
The relative weakness of capillary suction with respect
to gravity is represented by a
key dimensionless parameter, denoted
K,
which satisfies
.
The volumetric flow at any point along the weir boundary layer
is the accumulation of all liquid that has rained onto
the weir above the point in question:
typically, this flow is linear
in distance measured downward from the weir lip.
All liquid raining onto the weir is ultimately returned to
the pulp phase as a high-speed jet. The jet velocity
scales with the
power of distance from the weir lip,
and is O
(K-2/3) times larger than the
typical velocity in
the gravity-dominated
flow in the bulk of the flotation tank.
The liquid volume fraction in the jet
is likewise O
(K-2/3) larger than that in
the bulk.
Across the jet, the foam exhibits a
known profile of liquid fraction vs.
distance from the weir: this is known as the equilibrium profile.
The foam requires a distance equivalent to
O
(K4/3) weir lengths to dry out significantly from the
wetness value on the weir,
but a larger O
(K) distance to fall back to a wetness comparable
with that in the bulk of the froth.
47.55.Dz - Drops and bubbles.
82.70.Rr - Aerosols and foams.
83.80.Iz - Emulsions and foams.
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2002
