5 Development of a Dynamic-Physical Process Model for Sieving
163
Table 2 (continued)
Model number and
origin
Major equations
Adjustable
parameters
λ. Nakajima/Whiten
[116]
E = 1 − exp(−N P); N = kt
P =
cos 4 (θ − π/8)α
1 −
d
a0
×
a1
a2
2
sin 2 θ + cos 2 θ
0.5
2
θ = tan −1 (d t /d w ); d t , d w : particle thickness/width;
a 0 =
a 2
1 + a 2
2
k
μ. Dehghani et al.
[103]
E = 1 − exp(−N P); N = kt
P = α
a 1 −
√
2d cos θ
a 2 −
√
2d sin θ
/(a 1 a 2 )
θ = tan −1 (d t /d w ); d t , d w : particle thickness/width;
α: fraction open area
k
ν. Ferrara et al. [117]
m 0
n
j=1 y j,0
1
X ji
E i (t)
X ji − 1
+ ln E i (t)
r
j=n+1 y j,0
=
−k2 σ
1 −
di
a
σ
t
y j,0 : initial weight fraction of particle fraction j
X ji =
a − d j
/(a − d i )
σ
d i , d j : studied/other present particle diameters
n, r: number of undersized/undersized + oversized particle
classes
k
σ (screen
mesh
dependent)
ξ. Soldinger; without
undersized fractions
[9]
E j+1 = k j B j
t j+1 − t j
+ E j
B j+1 = B j +
c j
1 − S j
− k j B j
t j+1 − t j
j: time index
k j = b
1 − E j
; c j = f
w q , w d
B: fractional mass of undersized particles in bottom layer
S: fractional mass of undersized particles stratified into bottom
layer
E: fractional mass of undersized particles passed through
apertures
w q
(dependent
on
proportion
of undersize
material)
w d
(dependent
on width of
particle size
distribution)
b
(dependent
on particle
size)
(continued)
size class E i (t) is calculated on the basis of the fractional initial undersize mass m i,0
and fractional actual undersize mass m i .