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Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
359
DOI: 10.4408/IJEGE.2011-03.B-041
FLOW PATTERNS FOR MUDDY MATERIAL IN A ROTATING DRUM
k
o
-f
ei
liu
(*)
& y
i
-a
n
ai
(**)
(*)
Professor, Department of Civil engineering, National Taiwan University, Taiwan ROC
(**)
Master, Department of Civil engineering, National Taiwan University, Taiwan ROC
must be understood. However, before we can actually
use experimental data to calibrate any formulae, it is
essential to understand if the flow conditions in a ro-
tating drum are suitable for rheological measurements
and to develop corresponding theories. This paper
therefore concentrates on describing the phenomenon
that observed in the experiments. It can be seen that,
many of the phenomena are actually not expected
from the theoretical point of view. Even the usual as-
sumed “steady state” is not always true.
Often rheological experiments are conducted in a
vertical rotating drum similar to what is shown in Fig. 2.
H
enein
et alii (1983) has shown that there are
six different patterns of motion: Slipping, Slumping,
Rolling, Cascading, Cataracting, and Centrifuging
(Fig. 1). They used granular material of small sizes.
ABSTRACT
We perform rheological measurements in a ro-
tating drum. As a starting point for using formula to
calibrate rheological measurements, we first identify
the possible flow phenomenon in the drum. The ex-
periments were conducted in a drum with 0.5 m inner
radius and 0.2 m width. The material used is a Kaolin/
water mixture. The rotating speeds varied from 0 rpm
to 40 rpm. The sample amount used in experiments
must be large enough to assure that the flow length
is much larger than its height. The three flow pat-
terns discovered are Sliding, Swinging, and Circling.
Among the three basic categories, there are other
variations in each category. Some ofthe variations are
unsteady patterns. We delineate the occurrence of the
observed motion patterns in a diagram asa function of
rotation speed and kaolin concentration.
K
ey
words
: kaolin mixed with water, rotating viscometer
INTRODUCTION
Taiwan is an island with fragile geology and lo-
cated in the subtropical area. Frequent abundant and
intensive rainfall usually induces massive soil erosion,
mudflows and landslides. These flows have velocities
typically in the order 10m/s and usually appear in the
shape of long waves. Long travel distance up to 5 to
10Km is usual and devastating damage can be induced
along the path. In order to estimate the disaster caused
by mudflows, the rheological properties of such flows
Fig 1 - The possible motion patterns of the mud and sand
granules in the upright rotating sink by H.Henein
(1983)
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k.-F. LIU & Y.-A. AI
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5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
transparent glass. There are 12 rotating speed used
in the experiments. 3.23rpm, 6.97rpm, 10.62rpm,
14.28rpm, 17.91rpm, 21.66rpm, 25.17rpm, 28.74rpm,
32.52rpm, 36.00rpm, 39.66rpm, and 43.37rpm (the
max speed). To maintain the long wave characteris-
tics, the testing material is filled less than 1/4 of the
full drum capacity.
We use Kaolin/water mixture in this study. Dif-
ferent volumes ranging form 6000 ml to 15000 ml
were used in our experiments. All volumes produces
flow characteristics corresponding to a long wave and
yet thick enough for meaningful observation. In this
In our experiments, we focus on muddy material and
similar but different flow patterns are found.
There are other experiments using slurries like
material to perform rheological experiments such as
H
uizinGa
(1996), m
aJoR
(1997) and k
aitna
& R
iCk
-
enmann
(2007 a, b). H
uizinGa
(1996) concluded that
different volume put into the rotating drum is not im-
portant and the phenomena would be the same. How-
ever, this is not what we have encountered during our
experiments. As the first step, we shall point out that
steady flow patterns may not always be possible and
the different velocity profiles of the flows may explain
the experimental data.
EXPERIMENTAL METHODS
In this study, we use the equipment from l
iu
&
C
HanG
(2008) as show in Fig. 2. The drum has 0.5 m
inner radius, 0.2 m width and rotates clockwise. The
bottom of the rim is made of iron and has strips of
0.5cm width and 0.1cm height attached to increase the
bottom friction. The side walls are made of reinforced
Fig. 2a - Front view of the vertical rotating viscometer ac-
cording to l
iu
& c
hANG
(2008)
Fig. 2b - Front view of the vertical rotating viscometer ac-
cording to l
iu
& c
hANG
(2008)
Fig. 3 - Flow for a mixture with kaolin concentration
25.38% and 3.51rpm rotating speed. The surface
velocity is counter-clockwise. This can be seen
from the movement of the bubbles on the free sur-
face. Two consecutive location of the same bubble
is marked in the photos
Fig 4 - Sliding motion: shape of the rear and front end of
the moving mass
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FLOW PATTERNS FOR MUDDY MATERIAL IN A ROTATING DRUM
Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
361
of the material was 10.9cm and located approximate
at the mid point of the whole pile
After observing different phenomena in the drum,
we can first divide these phenomena into three basic
categories: Sliding, Swinging, and Circling, the ba-
sic motion patterns which are illustrated in the Fig.
5. Within each category, there are further variations
according to the free surface conditions..
SLIDING
This flow pattern is just the standard case discussed
before. Mixture contains two flow regions with lower
region flow upward by bottom stress and upper region
flow downward by gravity. The front position remains
at the same location for all time. The maximum thick-
ness of the mixture varies from 6.7cm to 10.9cm for
different concentrations and different rotating speeds.
This flow pattern is similar to the rolling phenomenon
among the six motion patterns observed by H
enein
(1983). We defined the phenomena with stable fronts
as Sliding. In Fig. 6, we mark all runs with this pattern
in the rotating speed vs. concentration graph.
The pattern does not exist for high rotating speed
or very high concentration. For high rotating speed, the
bottom stress is high enough to break the balance. For
very high concentration, the yield stress and viscosity
preventssignificant flow motion.
SWINGING
As the concentration increases, the viscosity in-
creases, so the bottom stress becomes larger. It is not so
easy for gravity to balance the stress, so the whole pile
of mixture will rise to even higher position (the rear
end in Fig. 4) before gravity can be effective. Since
the total volume of sample is fixed, the front is pulled
paper we shall describe the observations made for a
total sample volume 9000 ml. All patterns reported in
this paper were also observed for other volumes but
at different rotation speeds and concentrations. As
the concentration of mixture reaches 47.96% for to-
tal volume 9000 ml, all the materials would simply
adhere with the drum wall. Therefore, 47.96% was
the highest concentration in our study. 9 different con-
centrations were used in our experiments, i.e. 25.38%,
31.47%, 37.19%, 38.76%, 41.30%, 43.63%, 45.27%,
47.13%, and 47.96%.
EXPERIMENTAL RESULTS
We first use the result form Kaolin concentration of
25.38% and rotating speed of 3.57rpm as an example
to describe our experimental procedure. After mixing
of /water mixture, we put the sample in the drum and
start the drum with the highest rotating speed. Then we
reduce the rotating speed gradually to desired speed and
maintain that speed for 5~10 minutes until steady state
is reached. All the measuring can be done after that.
In the experiment with a Kaolin concentration
of 25.38% and 3.51rpm rotating speed, it was found
that the free surface moved counter-clockwise down-
ward. This is confirmed by observing small bubbles
on the free surface which moves counter-clockwise as
shown in Fig. 3. Since mixture must move clockwise
in the bottom so there must be a boundary with zero
velocity. When the motion reaches a steady state, the
bottom material is brought up by the rotation of drum
and brought down by gravity. In this case, the mixture
forms a steady pile with a front and a tail as shown in
Fig. 4. The measurement is done with the central part
of flow without the front and the tail influence. At this
particular case, the front and the tail span 80° apart
respect to the center of drum. The maximum thickness
Fig 5 - The 3 basic flow patterns observed during the ex-
periments
Fig 6 - Domain for stable Sliding patterns observed
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k.-F. LIU & Y.-A. AI
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5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
becomes more uniform. After the speed increased to
22.67rpm, the fluid distributed evenly at the entire bot-
tom as shown in Fig. 9. This phenomenon was similar
to the Circling phenomenon among the six motion pat-
terns by Henein (1983). So it is named Circling. All
cases with this pattern is marked in Fig. 10
SPECIAL SUB-PATTERNS
Besides the three basic categories, there are oth-
er variations in each category. Some variations are
steady, we refer them as sub-patterns. But there are
also unsteady patterns.
SLIDING SUB-PATTERN 1
Sliding means the whole pile remains at the same
location with bottom layer going upward and top
layer going downward. However, for high concentra-
tion and low rotating speed, there are cases where the
steady pile looked the same as in other Sliding case,
but with some small amplitude wave on the free sur-
face travelling UPWARD! Placing a very light float
on the free surface reveals the fact that the velocity of
the free surface is travelling in the same direction as
the bottom, i.e. upward (Fig. 11). However, this free
surface velocity is much less than the bottom velocity
and can be considered as stationary. This means there
higher also. As a result, the front position will move
upward and then drop downward to form a periodical
motion. The motion patterns were illustrated in Fig.
7 This is not a steady state but a quasi steady state.
This type of phenomena is similar to the Swinging
phenomenon among the six motion patterns by H
enein
(1983). Therefore, it was named Swinging. All runs
with Swining pattern are marked in Fig. 8. As can be
seen, this pattern only occurs for high concentration
and high rotating speed which can produce relative
large bottom stress..
CIRCLING
When the concentration of the fluid is really high,
all mixture actually is distributed along the wall. There
is no “flow” phenomenon. As the rotating speed in-
creases, the thickness of the mixture along the wall
Fig 7 - The red line indicates the front of the pile and
dashed red line is the original front location.
Photo 1 to 6 are the consecutive photos at time
interval 0.33sec. This sequence demonstrates a
complete period of the front (kaolin concentration
45.27%. Rotating speed 28.57rpm)
Fig 8 - Domain for periodic Swinging patterns observed
Fig 9 - The even distribution of the fluid in the phenome-
na of Circling (47.13% concentration; 32.68rpm)
Fig 10 - Domain for Circling patterns observed
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FLOW PATTERNS FOR MUDDY MATERIAL IN A ROTATING DRUM
Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
363
can conclude that this is a one layer structure with
whole layer travelling clockwise. Since the longitu-
dinal profile remains unchanged so the vertical inte-
grated flux rate must be the same through longitudinal
direction. A schematic graph of the velocity profile is
drawn in Fig. 12.
SLIDING SUB-PATTERN 2
There are runs with two dimensional flow pat-
terns. These runs are usually for low concentration
and high rotating speed. The typical 2-D pattern can
be observedthrough the bobbles on the free surface
(Fig. 14).
is no reverse velocity through out the depth. Hence
this Sliding phenomenon has only one layer and the
whole pile is moving upward. Detailed observation
even shows that the small wave is produced due to
piling effect at the front.
The flow depth for these phenomenon ranges
from 4.1 cm to 6 cm and varies with concentration
and rotating speed. All runs of this type appear on the
lower right corner of Fig. 13. These points are close to
the boundary between Sliding and Circling.
This is a steady case and can last as long as one
hour, which is the maximum observation time for all
our runs.After testing the velocity through depth, we
Fig. 11 - Sliding Sub-pattern 1 (kaolin concentration
43.62%, 10.46rpm rotating speed). These three
photos are consecutive photos in time interval
1sec. The float (marked with red circle) was
observed to travel upward with small velocity
Fig. 12 - The schematic velocity profile for Sliding Sub-
pattern 1. The flow rate through every section is
the same
Fig 13 - Domains for Sliding Sub-pattern 1 & 2 and Un-
steady flow pattern 1 & 2
Fig. 14 - Sliding Sub-pattern 2: Photos are consecutive
pictures at time interval is 0.36sec (kaolin con-
centration 25.38% and 29.06rpm rotating speed).
Different colours indicate motion for different
bubbles. It can be seen that bubbles are moving in
circles on free surface
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k.-F. LIU & Y.-A. AI
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5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
The whole pile moves just as the standard case.
Top layer moves downward with a steady front.
However these bubbles on free surface have 2-D cir-
cling trajectories
The bubbles were generated at the tail. When mix-
ture was brought up to the tail region, it would fall and
merge to the whole pile. But the falling generates bub-
bles, and bubbles show this 2-D Circling motion. It
is possible that the falling is affected by sidewall and
thus creates this 2-D motion. All runs with this feature
are marked in Fig. 13.
UNSTEADY FLOW PATTERN 1 -INTER-
MITTENT
For runs with condition close to the Sliding sub-
pattern 1, it is possible to have unsteady motion. It
looked like when the free surface has a small velocity
in the same direction of the bottom, mass transported
with bottom can be blocked. When blocked mass ac-
cumulated to a threshold, the top layer is forced to
move faster. But once the blocking situation is re-
leased, it returns to sub-pattern 1. Points with this fea-
ture are marked in Fig. 13 with
..
UNSTEADY FLOW PATTERN 2 - WAVES
In our experiment, when the concentration is high, it
is possible to have lobe of mixture been brought up and
fall as a whole. This falling is typically 2-D and creates
waves on the free surface. As waves travel to the front,
these waves can affect the distribution of the front. The
influence depends on the amount of the lobe that falls.
Typical surface disturbance is shown in Fig. 15. All runs
with this feature are marked in Fig. 13 with ▲
CONCLUSION
The motion of fluid in the rotating viscometer would
vary according to different rotating speeds and Kaolin
concentrations. We divided the observed phenomena
into three categories, namely Sliding, Swinging, and
Circling, and we further divided them into sub-catego-
ries according to their different motion characteristics.
Sliding can have two more sub-patterns.
Combing the results for the three major patterns in
one graph allows us to delineate the boundaries of the
domains (in terms of rotation speed and concentration)
in which these patterns appear. Red lines in Fig. 16 are
the two boundaries separating the three major patterns.
The two boundaries lines will vary for different
total volumes and of course for different material such
as Kaolin/water or Bentonite/water mixture. Experi-
ments reported in H
uizinGa
(1996) may all fall within
our sliding case.
The important discovery is that the Sliding sub-
pattern 1 is a one layer structure other than commonly
believed two opposite moving layers. Also, the dis-
covery of unsteady pattern and 2d pattern (Sliding
sub-pattern 2) indicate that assuming a steady 1-D
flow may not always be true
. As the next step, we will try to complete a three
dimensional graph with concentration, rotation
speed and total volume as three parametric axes. This
can give us a more complete understanding of the var-
iation. With the full understanding of the variation of
phenomenon, then accurate theoretical treatment for
motion in rotating drum is possible.
ACKNOWLEDGEMENTS
We gratefully appreciate National Science Coun-
cil (Grant NSC 96-2625-Z-002-006-MY3) in Taiwan
for supporting this research.
Fig 15 - Unsteady flow pattern 2: Surface waves affect the
position of the front. kaolin concentration was
41.30%, and the rotating speed was 39.52rpm
Fig 16 - The boundary lines separating Sliding, Swinging
and Circling. Results are for kaolin/water mixture
and total volume of 9000ml
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FLOW PATTERNS FOR MUDDY MATERIAL IN A ROTATING DRUM
Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
365
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enein
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iu
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