5 Development of a Dynamic-Physical Process Model for Sieving
161
the screening process and thus do not provide any further insight into other related
subprocesses [119].
In contrast, some phenomenological screening models account for concurrent
subprocesses by providing additional input parameters, e.g. the opposing processes
of stratification and particle passage through the screen apertures [7, 9, 10]. In this
sense the original model of Soldinger [9] was extended by the influence of the
particle layer thickness and the consideration of the bulk material composition [10].
The prediction of the conveyance speed of the bulk material on the screen as a further
extension of this model was dealt with in another paper by the same author [121].
Table 1 gives an overview of all investigated screening process models including
the name of the author and a model number (Arabic numerals), including the main
equations and the adjustable model parameters used. A more detailed description of
all investigated models can be found in [109].
All models outlined in Table 1 have in common that they rely on the overall
screening efficiency E as a screen length dependent variable for continuous screening.
It is given as
E = E(l) = ( ˙
m 0 − ˙
m)/ ˙
m 0 ,
(27)
where ˙
m 0 is the initial undersized mass flow at l = 0 and ˙
m is the remaining mass flow
of the undersized material at the screen position l. In the case when the undersized
particles are considered as different fractions, the screening efficiency is stated per
particle size class i
E i = E i (l) =
˙
m i,0 − ˙
m i
/ ˙
m i,0 ,
(28)
where ˙
m i,0 is the initial fractional and ˙
m i is the actual fractional undersized mass
flow. This is related to the overall screening efficiency by E =
n
i=1
E i · ˙
m i,0 / ˙
m 0
,
where n is the number of undersized particle classes.
3.2.3 Transient Screening Models
In Table 1 presented steady state spatially resolved screening models can also be
applied to transient discontinuous screening by replacing length l by time t. In addition to the thirteen models listed in Table 1 two other models by Shimosaka et al. [118]
and Yoshida et al. [7] become applicable. The complete list of models is presented in
Table 2 (for details see [122]). The models allow the calculation of the overall screening efficiency E which is a time dependent variable during batch screening given as
E = E(t) = (m 0 − m)/m 0 , where m 0 is the initial undersize mass at t = t 0 and m is
the actual mass of the undersize material on the screen at time t. Often the screening
efficiency is stated per particle size class i as E i = E i (t) =
m i,0 − m i
/m i,0 , which
is related to the overall screening efficiency by E =
n
i=1
E i · m i,0 /m 0
, where n is
the number of undersize particle classes. The screening efficiency for each particle
161
the screening process and thus do not provide any further insight into other related
subprocesses [119].
In contrast, some phenomenological screening models account for concurrent
subprocesses by providing additional input parameters, e.g. the opposing processes
of stratification and particle passage through the screen apertures [7, 9, 10]. In this
sense the original model of Soldinger [9] was extended by the influence of the
particle layer thickness and the consideration of the bulk material composition [10].
The prediction of the conveyance speed of the bulk material on the screen as a further
extension of this model was dealt with in another paper by the same author [121].
Table 1 gives an overview of all investigated screening process models including
the name of the author and a model number (Arabic numerals), including the main
equations and the adjustable model parameters used. A more detailed description of
all investigated models can be found in [109].
All models outlined in Table 1 have in common that they rely on the overall
screening efficiency E as a screen length dependent variable for continuous screening.
It is given as
E = E(l) = ( ˙
m 0 − ˙
m)/ ˙
m 0 ,
(27)
where ˙
m 0 is the initial undersized mass flow at l = 0 and ˙
m is the remaining mass flow
of the undersized material at the screen position l. In the case when the undersized
particles are considered as different fractions, the screening efficiency is stated per
particle size class i
E i = E i (l) =
˙
m i,0 − ˙
m i
/ ˙
m i,0 ,
(28)
where ˙
m i,0 is the initial fractional and ˙
m i is the actual fractional undersized mass
flow. This is related to the overall screening efficiency by E =
n
i=1
E i · ˙
m i,0 / ˙
m 0
,
where n is the number of undersized particle classes.
3.2.3 Transient Screening Models
In Table 1 presented steady state spatially resolved screening models can also be
applied to transient discontinuous screening by replacing length l by time t. In addition to the thirteen models listed in Table 1 two other models by Shimosaka et al. [118]
and Yoshida et al. [7] become applicable. The complete list of models is presented in
Table 2 (for details see [122]). The models allow the calculation of the overall screening efficiency E which is a time dependent variable during batch screening given as
E = E(t) = (m 0 − m)/m 0 , where m 0 is the initial undersize mass at t = t 0 and m is
the actual mass of the undersize material on the screen at time t. Often the screening
efficiency is stated per particle size class i as E i = E i (t) =
m i,0 − m i
/m i,0 , which
is related to the overall screening efficiency by E =
n
i=1
E i · m i,0 /m 0
, where n is
the number of undersize particle classes. The screening efficiency for each particle