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Small fluid element
z
Disc surface
θ
r
Centrifugal force
Viscous shear force
ω
Figure 3.5
Schematic of film flow on a rotating disc with forces exerted on the fluid in the
centrifugal flow model.
3.2.1 Hydrodynamics
The flow of thin liquid films on a smooth horizontal rotating disc is fully described by the
modified Navier-Stokes equations for the conservation of momentum and the equation
of continuity for the conservation of mass [8]. The centrifugal model represents a much
simplified version of the Navier-Stokes equation, derived on the basis of a number of
assumptions applicable to steady-state, symmetrical flow of thin liquid films on the rotating
disc [8]. The model, represented by Equation 3.1, is based on a force balance between
the body force, which is governed by the centrifugal force directed radially away from
the centre of the disc, and the opposing viscous shear force, as shown schematically
in Figure 3.5.
2
v
r
¼ n
@
2
r
v
(3.1)
@
z
2
Expressions for various parameters of interest for SDR processing, such as radial velocity
distribution, v
r
, mean radial velocity, u
m
, film thickness,
,andmean
residence time, t
res
, for flow on the spinning disc can be derived from Equation 3.1 and
are as follows [8,9]:
d
,shearrate,
g
2
r
n
z
2
2
Þ¼
v
v
r
ð
r
;
z
d
z
(3.2)
1
=
Q
2
2
v
3
u
m
ð
r
Þ¼
(3.3)
12
p
2
r
n
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