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Granular ows through vertical pipes controlled by an electric eld Granular ows through vertical pipes controlled by an electric eld
Wei Chen, Meiying Hou, and Kunquan Lu
Center for Condensed Matter Physics & Institute of Physics, Chinese Academy of Sciences, Beijing 100080, China
Zehui Jiang
Department of Applied Physics, Harbin Institute of Technology, Harbin 150001, China
Lui Lam
Nonlinear Physics Group, Department of Physics, San Jose State University, San Jose, California 95192-0106
Received 24 February 2001; published 21 November 2001
The ow of granular nickel particles moving down vertical pipes from a hopper in the presence of a local,
horizontal ac electric eld is studied experimentally. The ow is initiated by opening the bottom outlet of the
pipe after the pipe is fully lled with particles from the hopper. The mass of particles owing out of the pipe
is measured as a function of time by an electronic balance. The time dependence of the steady-state ow rate
Q, under each xed voltage V, is obtained. Depending on the magnitude of V, two types of ow behaviors are
observed. For low V (
V
c
2.0 kV , a downward-moving interfaceseparating a dense particle region below
it from a low-density region aboveexists between the hopper and the electrodes. Two prominent peaks exist
in the Q(t) curve for V in the range of 1.4 kV
V
V
c
, reulting in two clearly dened ow rates Q
A
2
and,
later in time, Q
B
. The particles measured by Q
A
2
originate from the pipe above the electrodes, and those by Q
B
coming initially from the hopper. For high V (
V
c
), no interface exists and the whole region between the
hopper and the electrodes are densely lled; only one constant ow rate Q
A
2
is observed. The precise meaning
of Q
A
2
and Q
B
are dened in the text. The steady-state ow rates Q
A
2
and Q
B
measured for each V, are plotted
as a function of V. The ow rate Q
A
2
is a monotonically decreasing function of V, which can be approximately
tted by a power law, with an exponent of
0.8, while Q
B
is found to be voltage independent. These features
result from a competition between the blocking effect of the electric-eld region and the gravity-driven pushing
effect from the hopper outlet. The local electric eld is able to retard the downward movement of a dense
column existing above it, but is ineffective in doing so when the column above is dilute in density.
DOI: 10.1103/PhysRevE.64.061305
PACS number s : 45.70.Mg, 81.05.Rm, 97.10.Ld
I. INTRODUCTION
Granular matter is a subject of intense interest 15 in
recent years. In this eld, many important topics in nonlinear
physics
6 such as pattern formation
5 , solitons
7 ,
chaos 8 , and cellular automata 911 were studied. In
particular, nonlinear waves in granular ow have been ob-
served and computationally simulated 1219 .
This discrete, compressible system has distinct features
when compared with classical uids. Density uctuation is
an important character of granular ow and has been broadly
noticed. Many interesting phenomena related to it were ob-
served in different experiments using x-ray imaging 19 ,
spatiotemporal diagrams 14 , and light detector 15 . Inter-
mittent and kinematic shock wave 12 was found in a small-
angle two-dimensional funnel when the funnel angle was
changed. Different kinds of wave regimes 14 in the vertical
pipe were observed when the mass-ow rate was changed by
adjusting the stopcock at the bottom end of the tube. The
power spectra of density waves were shown to assume a
stable power-law form, when the air outow rate was con-
trolled 15,17 . Jamming phenomenon of granular ow in a
two-dimensional hopper was studied experimentally 20 .
In this paper, a new granular ow control mechanism
by applying a local, ac electric eldis introduced to study
the nickel particle ow in a vertical pipe attached to a hop-
per. Different density patterns in the ow were observed at
different electric-eld strengths. Due to the dipole-dipole in-
teraction induced by the electric eld, particle clusters were
formed near the eld and the granular ow rate was reduced
nonlinearly with the applied voltage.
II. EXPERIMENTAL SETUP AND METHOD
A hopper with open angle 60� is joined to a short tube of
9 cm long with inner diameter of 7 mm. The tube is then
joined to a long pipe of length 85 cm and inner diameter 3
mm. The vertical length between the tube and the pipe is 1
cm see Fig. 1 . All these parts are made of glass. The pres-
ence of the short tube practically prevents the ow rate in the
pipe from being inuenced by how particles are piled up in
the hopper.
Most of the particles are spherical in shape of average
diameter 0.25 mm . The nickel particles are metallic; how-
ever, they are covered with a thin lm of oxide after exposed
in air for a long time. The particles are thus electrically in-
sulated from each other.
Two copper electrode plates of vertical length 10 cm, and
1.2 cm in width, are xed upon the outside wall of the long
pipe. The distance between the two electrodes is 5 mm,
which is equal to the outer diameter of the long pipe. The
upper ends of the electrodes are at a distance of 60 cm from
the top of the pipe see Fig. 1 . An ac electric voltage V of 50
Hz in frequency is applied across the electrodes.
PHYSICAL REVIEW E, VOLUME 64, 061305
1063-651X/2001/64 6 /061305 6 /$20.00
�2001 The American Physical Society
64
061305-1 In our experiments, the applied voltage V is xed in a
range of 0 6 kV. The voltage V is increased by 0.2 kV for
each different run. For each xed voltage V applied across
the two electrodes, the total mass on the balance M is mea-
sured as a function of time t.
Since nickel is a weak ferromagnetic element, we have
used a magnet as a stopper to block or initiate the ow. In
fact, an electromagnet placed 1 cm above the bottom end of
the pipe, outside of and in contact with the glass pipe is
used. In the beginning of the experiment, we turn on the
control current of the electromagnet. We then ll the hopper
and the pipe with the nickel particles, up to a xed height in
the hopper. The magnet keeps the particle column from fall-
ing out of the pipe. When the control current is switched off,
the particles fall down from the pipe and are collected in a
container placed on an electronic balance. A thin layer of
nickel particles is initially placed inside the container to ab-
sorb the impact of the falling masses. The balance sends data
to a personal computer at a time interval of 0.4 sec. The
resolution of the balance is 10
3
g, and the maximum mass
allowed by the balance is 200 g.
During the experiments, the humidity is maintained at
4755 %. This is one of our efforts to reduce the static elec-
tric caused by low humidity and, at the same time, to prevent
the formation of particle aggregations due to high humidity.
III. EXPERIMENTAL RESULTS
For each experimental run, the mass M collected by the
electronic balance as a function of time t is given in Fig. 2.
At time t
t
0
, the measured mass of 40 g is the total mass of
the container and the initial thin layer of particles placed
there. After the ow reaches the balance, the recorded mass
M increases with time. At a different voltage the slope of the
recorded mass vs time curve is different, as can be easily
seen in Fig. 2. The lower the voltage, the faster the ow. It is
an immediate evidence that the application of an external
electric eld is able to affect and retard the granular ow.
The ow rate Q (
d M /dt), as a function of t, is obtained
from the slope of the M (t) curve, and is plotted in Fig. 3
with V as a parameter. For viewing convenience, each Q(t)
curve at different voltage has been shifted vertically upward
by 10 g/s from the one below it. When the voltage is zero,
the ow rate increases from zero rapidly and uctuates for a
FIG. 1. Sketch of apparatus.
FIG. 2. Dependence of mass M on time t. The voltage difference
between two adjacent curves is 0.2 kV.
FIG. 3. Steady-state ow rate Q(t), obtained from the slope of
M (t) at large t in Fig. 2. For viewing convenience, each of the
curves with V
0.4 kV has been shifted upward by 10 g/s from the
curve below it. Each horizontal line represents Q
5 g/s, and is
drawn to guide the eye to show that Q
B
does not change, while Q
A
2
decreases with voltage. A dotted line connects all the second peaks
separating regime A from regime B in the Q(t) curves.
CHEN, HOU, LU, JIANG, AND LAM
PHYSICAL REVIEW E 64 061305
061305-2 few seconds before it goes steady. As the eld is increased,
the uctuating part of the curve expands and eventually sepa-
rates into two distinct peaks at about V
1.4 kV. The rst
peak stays at the same location, while the second peak moves
to the right when V is increased. At V
2.0 kV, the second
peak disappears