Nagaashi et al. Progress in Earth and Planetary Science
https://doi.org/10.1186/s40645-018-0205-6(2018) 5:52

Progress in Earth andPlanetary Science

RESEARCH ARTICLE

Open AccessLaboratory experiments on agglomerationof particles in a granular stream
Yuuya Nagaashi1*, Tomomi Omura1, Masato Kiuchi1, Akiko M. Nakamura1, Koji Wada2 and Sunao Hasegawa3

Abstract
Inelastic collisions occur among regolith particles, such as those in the ejecta curtain from a crater, and may cause
clustering or agglomeration of particles and thus produce discrete patterns of ejecta deposits around a crater.
Previous studies have shown that clusters, and even agglomerates, are formed via mutual, inelastic collisions ofspherical particles due to adhering forces between particles in granular streams. To investigate the condition of
agglomerate formation in granular streams, we conducted laboratory experiments of granular streams using bothspherical and irregular, non-spherical particles. Measurements of particle adhesion in this study were performed
using a centrifugal separation method, in contrast to the previous study in which atomic force microscopy (AFM)
was used. This enabled simultaneous measurements of multiple particles of various shapes for a statistical analysisof the results. With similar relative velocities and adhesion values, irregular particles were found to form agglomerates
much more easily than spherical particles. The axial ratio of the agglomerates of spherical particles and irregularparticles was similar and was in accordance with those observed in previous laboratory studies, whereas the size of theagglomerates of irregular particles was larger than the size of spherical particles. The degree of agglomeration and thesize of agglomerates can be used as an indicator of the shape or adhesive force of the particles in granular stream. Ourfindings on agglomeration in granular streams could provide new insights into the origin of rays on airless bodies andgrooves on Phobos.
Keywords: Regolith, Granular stream, Cohesion, Agglomerate

Introduction
The flow of granular material enables the formation of
discrete structures due to inelastic collisions between
particles. For example, high-speed camera observationsof the ejection of glass beads and silica sand from craters
recorded in laboratory impact experiments have revealed
mesh-like patterns in the ejecta curtain (Kadono et al.
2015). Such patterns have also been reproduced using
numerical simulations of particles with non-unity restitution coefficients (Kadono et al. 2015). It is possiblethat this process is relevant to the origin of rays aroundfresh craters on the Moon or other planetary bodies(Kadono et al. 2015).
The simplest granular flow is a stream of particles. A
laboratory observation of free-falling streams of sphericalparticles has shown that uniform streams initially form
* Correspondence: yuuya.nagaashi@stu.kobe-u.ac.jp
1
Graduate School of Science, Kobe University, 1-1 Rokkodaicho, Nada-ku,
Kobe 657-8501, Japan
Full list of author information is available at the end of the article

clusters as they fall under Earth’s gravity (Royer et al.
2009). The clusters are connected by bridges, and thebridges become thinner as the clusters fall downward,
breaking apart from one another to form discrete clusters. A numerical simulation (Waitukaitis et al. 2011)
has shown that particles forming droplets have a verysmall relative velocity and that the average coordination
number (i.e., the number of contacts of each particle
with other particles) is approximately 4. A previous laboratory experiment (Royer et al. 2009) showed that
discrete clusters do not change their shape significantly
after formation until they are destroyed via air drag;based on the above information, these are most likely
agglomerates, not just clusters. Here, “cluster” is defined
as a group of particles regardless of whether or not they
adhere, and “agglomerate” is defined as a group of particles that adhere to one another. Henceforth, this paper
refers to the groups of particles formed in granularstreams as agglomerates, although Royer et al. (2009) refers to them as clusters. Royer et al. (2009) indicated that

© The Author(s). 2018, corrected publication October/2018. Open Access This article is distributed under the terms of theCreative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits
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(2018) 5:52

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the formation of agglomerates is due to the adhesive
force produced by a combination of van der Waals interactions and capillary forces between nanoscale surface
asperities and not due to hydrodynamic interactions
with ambient gas. It has also been experimentally implied that the formation of agglomerates is insensitive tothe restitution coefficient of particles (Royer et al. 2009).
A subsequent numerical study showed that a lower restitution coefficient of particles acts to increase collimationof the stream and that the adhesive force drives agglomerate formation (Waitukaitis et al. 2011), which agrees
with laboratory experiments (Royer et al. 2009).
To obtain a better understanding of the conditions required for the formation of agglomerates in a granularstream and to apply the conditions of impact phenomena on asteroids and other celestial bodies, we conducted laboratory experiments of granular streams with
an emphasis on irregular, non-spherical particles, which
are a more suitable analogue of regolith particles thanspherical particles are. As mentioned above, mesh-likepatterns have been observed in the ejecta curtain in laboratory impact experiments (Kadono et al. 2015). Keeping this in mind, we turned our attention to the ejecta
curtain produced by an artificial impactor, such as thesmall carry-on impactor (SCI) of the Hayabusa2 asteroid
mission of ISAS/JAXA (Arakawa et al. 2017), or that was
produced by natural collisions of meteoroids on theregolith surface of small bodies. The ejecta curtain fromthe surface of a small body is expected to show discrete
structures, such as mesh patterns, clusters, or agglomerates of regolith particles. In this study, we attempted todemonstrate how the study of these structures could reveal valuable information about the physical propertiesof regolith particles.

using an optical microscope (Nikon ECLIPSE ME600) anda digital camera (Nikon D300), shown in Fig. 1. Both size
distributions are consistent. Figure 2 shows scanning electron microscopy (SEM) images of the particles. The
roughnesses of the glass bead were examined using a laser
confocal refractometer. The vertical height of the surface
was measured with 1 μm spacing and a vertical resolutionof 0.1 μm (0.2 μm reproducibility is guaranteed by the
supplier). According to Gadelmawla et al. (2002), the average roughness of a surface, Ra, is defined as follows:

Nagaashi et al. Progress in Earth and Planetary Science

Methods/Experimental
Particles

We used poly-dispersed spherical glass beads with median
diameters of 55 μm (hereafter called 50 μm beads) and93 μm (100 μm beads) (Fujikihan Co., Ltd.). To examine
the effect of the shape on the agglomeration of particles in
granular streams, we also used irregular alumina particles
with a median diameter of 77 μm (The Association of
Powder Process Industry and Engineering, JAPAN) andsilica sand grains (Miyazaki Chemical Co., Ltd.) with a
median diameter of 73 μm, which were prepared using asieve with a 45 μm mesh opening to reduce fine particles,
as in a previous study (Omura et al. 2016). Among theparticles, the silica sand grains are the most representativeof the regolith particles on asteroids in terms of composition, size, and shape (e.g., Omura and Nakamura 2017).
We also show the size distributions of the samples determined by two methods: using a laser diffractometer (SHIMAZU SALD-3000S) installed at Kobe University, and

Ra ¼

1 Xn
jy j
i¼1 i
n

ð1Þ

where yi is the vertical deviation from the mean line. We
approximated the mean curved line by a polynomial
function. Ra was 1.13 ± 0.24 μm for the 50 μm beads and3.82 ± 0.45 μm for the 100 μm beads. The restitution coefficient of a glass sphere (diameter 3.2 mm) against a
10-mm-thick glass plate measured using an acoustic
emission sensor (Higa et al. 1996) was 0.957 ± 0.012 fora collision velocity in the range of 0.5–1.3 ms− 1. The
restitution coefficient of an alumina sphere with a diameter of 4 mm against a 10-mm-thick alumina plate wasalso measured and found to be 0.975 ± 0.006. Table 1
summarizes the physical characteristics of the particles.
Measurement of adhesive force

In the previous study of granular streams (Royer et al.
2009), the adhesive force between micron-sized sphericalsilica particles was measured using an atomic force
microscope cantilever. In this study, however, we used acentrifugal separation method (centrifugal method) (e.g.,
Krupp 1967) to measure the adhesive force between aparticle and a plate. This method can directly measure
the adhesive force of multiple particles simultaneously,
including those of different shapes, enabling a statisticalanalysis of the results.
All measurements of particle adhesive force were conducted in air. A schematic diagram of the experimental
configuration used for the force measurements is shownin Fig. 3a, and the apparatuses are shown in Fig. 3b, c.
First, we deposited particles over Petri dishes, or in somecases optical glass plates, using a cotton bud. Before particle deposition, the Petri dish surface was washed withethanol. We then took an image of the particles adheringto the Petri dish using an optical microscope (Nikon
ECLIPSE ME600) and a digital camera (Nikon D300).
We were able to see that oil and other factors were notattached to the Petri dish. With this measurement approach, it was not necessary to sieve particles because
the size of each particle could be determined from theimage. ImageJ software (Image Processing and Analysis
in Java: https://imagej.nih.gov/ij/) was used to analyze
the images. Figure 4a shows an example of an image of aNagaashi et al. Progress in Earth and Planetary Science(2018) 5:52

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Fig. 1 Particle size distributions. Cumulative volume fractions plotted against the particle diameter. a 50 μm glass beads, b 100 μm glass beads,
c alumina particles, and d silica sand. Solid and dashed lines are the size distributions determined using a laser diffractometer and optical
microscope images, respectively. In the latter, the diameter of the equivalent sphere of the projected area of the microscope image is used

Fig. 2 Scanning electron microscopy images of each particle. a 50 μm glass beads, b 100 μm glass beads, c alumina particles, and d silica sandgrains. Scale bar is 500 μm

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Table 1 Physical characteristics of particles
Particle type
Glass bead 50 μm

3Density (kg m−)

2

Surface energy (J m−)Poisson’s ratio,νYoung’s modulus, ε(Pa)

Roughness, Ra(μm)

Restitution
coefficient

2.5 × 103

0.025a0.17b

7.3 × 1010b

1.13 ± 0.24

0.957 ± 0.013

3

a

b

10b

Glass bead 100 μm

2.5 × 10

0.025

0.17

7.3 × 103.82 ± 0.45

0.957 ± 0.013

Silica sand 73 μm

2.645 × 103c

0.025a0.17b

7.3 × 1010b––

Alumina particle
77 μm

4.0 × 103

0.041d0.24e3.85 × 1011e–

0.975 ± 0.006

aHeim et al. (1999)
Spinner (1962)c
The silica sand grains were used in a previous study (Omura et al. 2016), but we updated the density of the grain according to a measurement of true density
made using a pycnometer (SEISHIN ENTERPRISE MAT-7000)
dBurnham et al. (1990)
eWong and Bollampally (1999)b

Petri dish with particles. Some particles were in contact
with one or more particles; these particles were not included in the measurement results.
Next, the Petri dish was placed in a cylindrical basket
with its surface normally aligned with the axis of thebasket, as shown in Fig. 3a. The basket was then put in atable-top centrifuge (Kubota KN-70) at Kobe University,
as shown in Fig. 3b. The distance from the axis of rotation to the surface of the Petri dish was set at 0.08 m or
0.12 m, according to the height of the gypsum filler
shown in Fig. 3c. The basket was rotated at 300 rpm toapply a centrifugal force to particles adhered to the Petridish. After a few minutes, the rotation was stopped andthe Petri dish was gently removed from the basket. We
took an optical microscope image at the same locationof the dish as before applying the centrifugal force, as
shown in Fig. 4b. The Petri dish was then once again
placed in the basket and rotated faster than before. This
process was repeated, as the rotational speed was increased in 15 steps to 5000 rpm, which was the maximum rotational speed of the centrifuge used in thisexperiment. The centrifugal force acting on the particles
increased with the rotation speed. The particles subsequently separated from the glass plate when the resultant force of two forces, i.e., the centrifugal force and theforce of gravity, which was approximately equal to theFig. 3 a Schematic diagram of the experimental configuration used for the adhesive force measurements. b Image inside the centrifuge. There
are four baskets (marked “B”), each of which can be tilted freely from vertical to horizontal. c Image inside the basket. A Petri dish of diameter3.3 cm and height 1.5 cm was placed on a gypsum filler

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Fig. 4 Optical microscope images of alumina particles (a) before and (b) after applying a centrifugal force at a rotation speed of 300 rpm. A particle ina circle in image (a) detached during the rotation and did not exist on the Petri dish in image (b)centrifugal force, became larger than the adhesive force
between the particle and the dish. Measurements wereconducted four times for each particle type. The numberof detached particles for which the measurement wascompleted was 29, 98, 262, and 596 for the 50 μm beads,
100 μm beads, alumina particles, and silica sand grains,respectively. In the case of small particles, the centrifugal
force applied was smaller than the adhesive force between the particle and the Petri dish; thus, 71, 0, 92, and29 particles remained on the Petri dish for the 50 μm
beads, 100 μm beads, alumina particles, and silica sandgrains, respectively.
We measured the vibration acceleration of the centrifuge using an accelerometer placed on the top cover ofthe centrifuge and found that it was up to 0.21 G, which isconsiderably smaller than the centrifugal acceleration. In
addition, because the basket could tilt freely from a vertical to horizontal position, the vertical direction of the Petridishes should have been in the direction of the resultant
force of the centrifugal force and gravity, which was approximately in the direction of the centrifugal force. Adhesive forces measured in this experiment included vander Waals, electrostatic forces, and the effects of moistureadsorption from the atmosphere on the particle surface.
Regarding the electrostatic force, previous studies, such asthat of Royer et al. (2009), involving granular streams indicated that this force is very small; as such, the electrostaticforce contribution was assumed to be negligible in thisstudy. As another concern, as indicated in the electron microscopy image of Fig. 2, it is conceivable that fine objectsof a sub-micron to micron scale adhered to the particles;
however, the essential point is that the adhesion of particles in this state was measured and that granular stream
experiments in the air were also conducted with the particles in the same state.
The possible range of rotation speeds at which the particle separated from the plate was determined based on

optical microscope images to estimate the adhesive force
between the particle and the Petri dish. The mass ofeach particle, which was used for the calculation of thecentrifugal force, was estimated using the size of the particle from the images and the mass density value. The
optical microscope images were then translated into binary data using ImageJ software to measure the area
based on the major and minor axes of each particle. Fora glass bead, we assumed the shape to be a perfectsphere and determined the radius from the projected
area, which enabled calculation of the volume. For an irregularly shaped particle of either alumina particles orsilica sand, we assumed that the shape was instead ellipsoidal. The axial ratios of the two-dimensional (2D)
projections were 0.63 ± 0.16 with a median of 0.64 and0.66 ± 0.16 with a median of 0.67 for the alumina particles and silica sand grains, respectively. These values are
smaller than the value of the medium to the maximum
axial ratio (0.73) and larger than the minimum to the
maximum axial ratio (0.50) of collisional fragments(Fujiwara 1978). We assumed that the axial ratio of theirregularly shaped particles was similar to that of collipﬃﬃﬃ
sional fragments as 2c : 2c : c, where c is the minimumaxis. We determined the value of c from the projectedarea S of the microscope image and calculated the volume of particle V on the assumption that the minimum
axis was along the line of sight, i.e., that the minimum
axis was vertical to the Petri dish:πc2
S ¼ pﬃﬃﬃ ;2

ð2Þ

pﬃﬃﬃ 3
2πc
:
V ¼
3

ð3Þ

Using this method, we were able to estimate the centrifugal force Fcen(ω) applied to each particle using the(2018) 5:52

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calculated volumes together with the density of the material (shown in Table 1), the distance from the axis ofrotation, and the rotation speed ω. The adhesive force
between the particle and the Petri dish was then obtained as the geometric mean of the two subsequentcentrifugal forces applied to the particle aspﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
F cen ðωi Þ F cen ðωiþ1 Þ, where Fcen(ωi) denotes the force at
the maximum rotation speed ωi at which the particle
remained on the Petri dish and Fcen(ωi + 1) denotes theforce at the rotation speed ωi + 1 at which the particle nolonger remained on the dish. Note that if we assume theextreme case of the maximum axis of a particle being
along the line of sight when the optical microscope
pﬃﬃﬃ
image is acquired, the volume estimate becomes 2 2times larger than the above. Therefore, adhesive forces
may be a few times larger than the current estimates.
The surface roughness (Ra) of the Petri dish was
0.18 μm. We used two optical glass plates with surface
roughnesses of 0.032 and 0.046 μm, respectively, toexamine the effect of the surface roughness on the cohesive force and particle shape.

University experiments, respectively. The particles exitedthe bottom of the funnel through an aperture (diameter8 mm). Following the opening of an electromagneticallysealed shutter at the bottom of the funnel, the particles
fell freely from the aperture as a granular stream.
We used a digital camera (Casio EXILIM PRO EX-F1)
to take images (432 × 192 pixels) of granular streams in
the ISAS chamber at 600 fps in air and at a reduced ambient pressure. An additional 6400 fps high-speed camera (Photron FASTCAM Mini AX) was used to acquire
more detailed images (1024 × 1024 pixels) in air for the
ISAS experiments. The cameras were initially held at theheight of the aperture with an electromagnet. After the
shutter of the funnel aperture was opened, the electromagnet for the camera was deactivated, and the camera
was allowed to slide along two perpendicular shafts together with the stream. The granular stream was illuminated over its entire length using taped light-emitting
diodes (LEDs). We used a high-speed camera (Photron
FASTCAM SA1.1) fixed at vertical distances of 0 m and
0.9 m from the aperture to obtain high-resolution images (1024 × 1024 pixels) in the experiments conducted
at Kobe University. The camera did not move along the
granular stream. The spatial resolution was 0.02 mm/
pixel, and the frame rate was 5400 fps.

Nagaashi et al. Progress in Earth and Planetary Science

Granular stream experiments

The granular stream experimental setup is shown in
Fig. 5a, b. The experiments were performed in a vacuum
chamber with a diameter of 1.5 m and a height of 2.0 m
in ISAS/JAXA and in a chamber with a diameter of
0.15 m and a height of 1.5 m at Kobe University. Wechanged the ambient pressure in the vacuum chamber
to examine the effect on agglomeration. The ambientpressure was set to between 3 and 105 Pa for the ISAS
experiments, and between 10 and 105 Pa for Kobe University experiments. A plastic funnel containing the sample particles was placed at a height of 1.8 m and 1.5 mfrom the bottom of the chambers for the ISAS and Kobe

Results and discussion
Adhesive force

In Fig. 6, the ratio of the experimentally measured valueof the adhesive force to the calculated theoretical reference value, described below, is shown as a function of
the cumulative percentage of particles for which we determined the adhesive force. The range of the measured
adhesive force is shown in Table 2. As mentioned previously, the centrifugal force generated at 5000 rpm in thisstudy was not sufficient to separate all of the particles

Fig. 5 Experimental setup of the granular stream experiments conducted at Kobe University. a Overall view and b detailed view of the top part

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Fig. 6 Measurement results of the adhesive force. The ratio of the measurement value of the adhesive force using a Petri dish to the theoreticalreference value against the cumulative percentage. Solid, dashed, dotted, and dashed and dotted lines show the 50 μm glass beads, 100 μm
glass beads, alumina particles, and silica sand, respectively. a The percentage reflects the number of detached particles/total number of detachedparticles ratio. b The percentage reflects the number of detached particles/total number of observed particles ratio

from the Petri dish for the 50 μm glass beads, while allof the 100 μm glass beads were separated successfully
from the Petri dish before the maximum centrifugal
force was achieved. The percentage of the residual
50 μm glass beads on the Petri dish was 71%; hence, thecurve in Fig. 6a for 50 μm glass beads shows the lower
limit of the adhesive force distribution. The percentageof the residual alumina particles and silica sand grains
were 26 and 5%, respectively. Most of the residual particles and grains had small diameters of approximately
30 μm; thus, the curves for the alumina particles and silica sand in Fig. 6a can be regarded as representative foralumina particles and silica sand (approximately 75 μm
particles).
We refer to the theoretical value of the adhesive force
based on Johnson–Kendall–Roberts (JKR) theory(Johnson et al. 1971), although the capillary force is significant at atmospheric pressure, as discussed later. The
force required to separate two spheres in contact, Fc, isgiven byF c ¼ 3πγR;

ð4ÞTable 2 Range of measured adhesive force between eachparticle and a Petri dishParticle type

Diameter rangea (μm)

Adhesive forceb (μN)

Glass bead 50 μm

44–66

0.16–5.6

Glass bead 100 μm

74–1120.027–13

Alumina particle 77 μm

62–92

0.0062–13

Silica sand 73 μm

58–88

0.0069–8.0

a

80–120% of the median diameter (see Fig. 1)b
The corresponding range of values for the particles within the diameter
range shown in the left column

where γ is the surface energy of the particle, and R is the
reduced radius of two spheres with radii of R1 and R2,
respectively:
1=R ¼ 1=R1 þ 1=R2 :ð5Þ

In this case, the contact is between a glass plate and aparticle. Thus, R is simply equal to the radius of the particle. We calculated the force for perfect spheres of radius R for glass beads, alumina, and silica sand grainsaccording to Eq. (4) as reference values. In the calculation, we used the radius R for each particle determinedfrom the 2D projected area by
S ¼ πR2 :ð6Þ

We assumed a value of γ = 0.025 J/m2 of SiO2 particles (Heim et al. 1999) for the glass beads, silica sand,and the glass plate; γ = 0.041 J/m2 was used for alumina
particles (Burnham et al. 1990). We adopted the formulapﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
for the adhesive force, γ ¼ γ 1 γ 2 , between different materials with surface energies of γ1 and γ2 (Burnham et al.
1990). The adhesive forces between the Petri dish andthe 50 μm glass beads, 100 μm glass beads, 77 μm alumina spheres, and 73 μm silica spheres were 5.9, 12, 12,
and 8.6 μN, respectively.
Figure 6a shows that approximately 80% of the 50 μm
glass beads that detached from the Petri dish had an adhesive force that exceeded 10% of the theoretical reference value. If we take the percentage of residual glass
beads on the Petri dish, the distribution of adhesive
forces of the 50 μm glass beads had a higher medianvalue than that shown in Fig. 6a (shown in Fig. 6b). On
the other hand, more than half of the 100 μm glass

Nagaashi et al. Progress in Earth and Planetary Science(2018) 5:52

beads had values less than 5% of the theoretical reference values of perfect spheres. From the different shapesof the curves of irregular particles compared with thoseof the glass beads in Fig. 6, it can be said that the adhesive force is likely influenced by the macroscopic shapeof the particle. On the other hand, the data for the
100 μm glass beads were much smaller than the theoretical reference values compared with those for the 50 μm
glass beads; this is likely due to the high roughness (Ra)of the 100 μm glass beads in comparison with the 50 μm
beads. The compression length of a sphere (delta in JKR
theory) is 0.54 nm for the 50 μm glass beads and0.69 nm for the 100 μm glass beads. Compared with theone order of magnitude larger surface roughness, which
is approximately 1 μm for the 50 μm beads and 4 μm
for the 100 μm beads, it can be said that perfect contact
was not achieved. Figure 7 shows that the spread in themeasurement values of the 100 μm glass beads with theoptical glass plates was smaller than the case in which
the Petri dish was used, implying that the microscopic
surface roughness has a significant effect on adhesive
forces.
We calculated the effective surface energy of particles,
γeff, which reproduces the measurement value. Table 3
summarizes the range of the γeff values of the particles
corresponding to 10–90% of the total number of particles; note that the percentage of the residual particles on
the Petri dish is not taken into account. The measured
values in this study were considerably smaller than the

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Table 3 Range of effective surface energy
Particle typeγeffa (J m− 2)

vcra (cm s− 1)

Glass bead 50 μm

0.00061–0.017

0.20–2.8

Glass bead 100 μm

0.000071–0.017

0.025–2.1

Alumina particle 77 μm

0.00012–0.011

0.022–0.98

Silica sand 73 μm

0.00034–0.010

0.099–1.7

The range of the γeff and vcr values of the particles corresponding to 10–90%
of the total number of particlesareference values, based on the previous measurementsof surface energy (Heim et al. 1999; Burnham et al.
1990). As mentioned above, this is probably because thecontact between the particles and the Petri dish was lessthan perfect due to the high surface roughness. The root
mean square deviation from the ideal sphere of a
micron-sized SiO2 particle used in the previous study
was 0.13 nm (Heim et al. 1999).
Horizontal particle velocity just below the aperture

We analyzed the motion of the particles just below theaperture via particle image velocimetry (PIV), using the
fixed high-speed camera images shown in Fig. 8. The
analysis was only applied to particles at the outer sectionof the stream because the optical depth of the central
part of the stream was too large for the motion of theparticles to be tracked. Fig. 9 shows the cumulative percentage of the horizontal particle velocities of the 50 μm
and 100 μm glass beads within 20.4 mm from theFig. 7 Effect of surface roughness. The ratios of the measurement values of the adhesive force of the 100 μm glass beads obtained using a Petri
dish and two optical glass plates having different surface roughnesses to the theoretical values plotted against the cumulative percentage. Solidline, dashed, and dotted lines correspond to the results of the Petri dish, smoother optical glass plate, and another optical glass plate, respectively. The
numbers in parentheses show the roughness (Ra)Nagaashi et al. Progress in Earth and Planetary Science(2018) 5:52

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Fig. 8 Granular streams at the funnel aperture in air. a 50 μm glass beads, b 100 μm glass beads, c 77 μm alumina particles, and d 73 μm
silica sandaperture in the vertical direction, and those for the alumina particles and silica sand within 19.4 mm and17.9 mm from the aperture, respectively. The four typesof particles had similar horizontal velocity distributions,typically about 1 cm s− 1.
According to Chokshi et al. (1993), the critical collision velocity between the monomers of radius R iswhere ν is the Poisson ratio, ε is Young’s modulus, and ρ
is density. On the other hand, we assume that agglomerates, not monomers, collide with each other in a granular stream, based on the fact that tiny agglomerates
consisting of a small number of monomers are recognized in the images of Fig. 8. The critical collision velocity for equal-size agglomerates was shown to be5

vcr ≅3:86

γ6½ð1−v2 Þ=ε−3 R6 ρ2
1

5

1

;

ð7Þ

vcr ≅15

pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
E break =m;

Fig. 9 Horizontal particle velocity distribution just below the funnel aperture plotted against cumulative percentage for a 50 μm glass beads, b
100 μm glass beads, c alumina particle, and d silica sand. Quadrangles show the ranges of the critical collision velocity for equal-size agglomerates
corresponding to 10–90% of the total number of monomers

ð8Þ

Nagaashi et al. Progress in Earth and Planetary Scienceh2 i1=3
E break ≅23 γ 5 R4 1−ν2 =ε2;(2018) 5:52

ð9Þ

5vcr ≅35γ6½ð1−v2 Þ=ε−3 R6 ρ2
1

5

1

;

ð10Þ

where Ebreak is the energy of breaking a single contact
between two (identical) particles and m is the mass ofthe constituent monomer (Wada et al. 2018). Thus, thecritical collision velocity between agglomerates is aboutnine times higher than the critical velocity between
monomers. If we substitute the value of the effective surface energy, γeff, obtained in the previous section into γ
in Eq. (10), we obtain the critical velocities for the virtual
agglomerates consisting of identical monomers withvalues of R and γeff. Figure 10 shows the calculated critical collision velocity for equal-size agglomerates versus
the cumulative percentage. The critical collision velocity
is a few centimeter per second. The maximum criticalcollision velocity between agglomerates exceeds the typical horizontal velocity of the particles in the stream (approximately 1 cm s− 1). Although we did not measure
the typical horizontal velocity of the agglomerates, itwould be similar to or lower than the individual particle
horizontal velocity and therefore even lower than the
maximum critical collision velocity between agglomerates. Consequently, agglomerates in a stream may growvia agglomerate-agglomerate collisions. The range of thecritical velocity for agglomerates of each type of particle,
based on Fig. 10, is shown in Table 3. The range of thecritical collision velocity for agglomerates is indicated by
the quadrangles in Fig. 9. We adopted the values of ν

Fig. 10 Calculated critical collision velocity for equal-size agglomerates
versus the cumulative percentage. This percentage is based on thenumber of detached particles/total number of detached particles ratio,
as shown in Fig. 6a. Solid, dashed, dotted, and dashed and dotted lines
show 50 μm glass beads, 100 μm glass beads, alumina particles, andsilica sand, respectively

Page 10 of 14and ε shown in Table 1. A relatively large number of the
50 μm glass beads had horizontal particle velocities
lower than the critical collision velocity, indicating favorable conditions for agglomerate growth. On the other
hand, most but not all of the 100 μm glass beads, alumina particles, and silica sand grains had higher horizontal velocities than the critical collision velocity.
Agglomeration of these particles is expected to be moredifficult.

Observation of granular streams

The state of granular streams at 0.9 m of vertical distance from the funnel aperture at each ambient pressure
is summarized in Fig. 11. Because the transparent partof the vacuum chamber at Kobe University is 1.0 mhigh, the maximum drop height of the particles for taking images from outside of the chamber is approximately
0.9 m. In air, all particles except for the 100 μm glass
beads formed millimeter-size agglomerates at 0.9 m. Although the 100 μm glass beads did not form agglomerates at 0.9 m from the funnel aperture, agglomeration
was initiated at approximately 1.2 m from the aperture.
Based on Fig. 9a, b, the 50 μm glass beads can form agglomerates more easily than the 100 μm glass beads.
The observational results of the granular streams werein accordance with predictions based on the critical collisional velocity. Contrary to the prediction from thecritical collision velocity, although the prediction was forspherical particles, alumina particles and silica sandgrains were able to form agglomerates in air. A previous
study showed that irregularly shaped particles have ahigher probability of sticking and a higher capture velocity than spherical particles (Poppe et al. 2000). The
reason was thought to be due to multiple opportunities
of hitting and the resultant energy dissipation allowed by
the irregular shape. Royer et al. (2009) also conductedlaboratory experiments with irregularly shaped particles
and found less agglomeration of irregular particles, atendency opposite to that observed in the current study.
The irregularly shaped particles used in Royer et al.
(2009) were quite rounded, that is, not angular, while
those used in this study were elongated and angular.
This difference in irregularity would result in the different degrees of agglomeration. In fact, the irregularity of
diamond particles of 1.3–1.9 μm in diameter (average
diameter 1.5 μm) used by Poppe et al. (2000) exhibiting
higher sticking velocity than the spherical particles issimilar to those used in our study, although the collisionvelocity in the current study was lower than that ofPoppe et al. (2000) and the energy dissipation mechanism may have been different. Further study is required
to reveal the formation process of the agglomerates in a
granular stream.

Nagaashi et al. Progress in Earth and Planetary Science(2018) 5:52

Page 11 of 14

Fig. 11 State of granular streams at 0.9 m from the funnel aperture at each level of ambient pressure

Figure 12 shows the ratio of the local minimum to the
local maximum widths of granular streams, determinedusing ImageJ software versus the ambient pressure.
When agglomerates form perfectly, the ratio becomeszero. As shown in Fig. 11, the formation of agglomerates

becomes more difficult as the ambient pressure decreases. This is likely due to a decrease in the adhesive
force, i.e., capillary forces, at lower pressures. Because
the capillary force relates to the surface energy of water,which is 0.072 J/m2 (Butt and Kappl 2009), it contributes

Fig. 12 Ratio of the local minimum width to the local maximum width of granular stream versus ambient pressure(2018) 5:52

Page 12 of 14

significantly to adhesive forces in air. However, there
was no influence of the atmosphere in the previous
study (Royer et al. 2009). The reason why the ambient
gas pressure dependence in our study is different fromthat in the previous one remains unclear; however, it
may be due to differences in the experimental conditions, such as the funnel aperture and humidity.
Figure 13 shows the length (λ) and width (w) of agglomerates at 0.90 ± 0.01 m from the aperture in air. We
used ImageJ software for the measurement. The length
to width ratio was between approximately 1 and 2.5,
which roughly agrees with the ratio (between 1 and 3)
shown in the previous study (Royer et al. 2009); however,
the absolute size of the agglomerates formed was larger.
This does, however, agree with the correlation observedin the previous study (Royer et al. 2009): specifically, thata larger aperture leads to a larger agglomerate size. Agglomerates of irregular particles had a larger overall size
than agglomerates of spherical particles.

and numerically that clear mesh patterns form in
impact-generated ejecta during flight. They also demonstrated in the laboratory that the characteristic angle ofspaces between radial patterns was a few degrees, which issimilar to that of the rays around two craters on theMoon. If crater rays are formed via ejecta from primarycraters, the morphology of the rays can be discussed interms of the agglomerating process of ejecta particles. The
pattern of rays may be compared directly with the undulation of the granular streams shown in Fig. 11, although a
dedicated study of the formation of discrete patterns in
the ejecta curtain is required.
A study of agglomeration in a granular stream would
also provide new insights into the origin of grooves on
Phobos. The grooves, or striations, are often parallel depressions, and many have a pitted appearance (Veverka
and Duxbury 1977). Hypotheses regarding their origin
include secondary impacts from the Stickney Crater, secondary impacts from primary impact events on Mars,
impact crater chains from debris in Mars’s orbit, tracks
formed by boulders from the Stickney Crater, and fractures caused by impacts or tidal forces into which regolith has drained (Murchie et al. 2015). According to the
hypothesis of secondary impacts from primary impact
events on Mars, an ejecta melt jet derived from a large
impact on Mars breaks up into droplets and causes a
chain of impact craters on the surface of Phobos (Murray and Heggie 2014). Even if melt droplets do not form,
the ejecta particles may gather together, as seen in the

Nagaashi et al. Progress in Earth and Planetary Science

Application to planetary surfaces

Crater rays have bright albedo features that extend from
fresh craters, forming radially oriented filaments and diffuse patches (Melosh 1989). Rays have been observed onairless bodies, i.e., the Moon, Mercury (Allen 1977), andicy satellites (Wagner et al. 2011). Various processes, including deposition of ejecta from primary craters, havebeen proposed as the production mechanism of rays
(Allen 1977). Kadono et al. (2015) showed experimentally

Fig. 13 Agglomerate length λ (mm) versus agglomerate width w (mm). Filled circle, open square, and triangle show 50 μm glass bead, silica sand, andalumina particles, respectively. The solid line is the ratio λ/w = 1, and the dashed line is λ/w = 3

(2018) 5:52

Page 13 of 14

granular stream of this study, impact Phobos with abeaded structure, and thus create pitted grooves. By
comparing the aspect ratio of the pits of the grooves
with that of the agglomerates in granular streams, thisformation hypothesis may be evaluated.
Moreover, our study showed that both the adhesive
force of particles and the particle shape greatly influence
agglomerate formation. Tsuchiyama et al. (2011) showedthat the shape distribution of the particles of asteroid(25143) Itokawa is not significantly different from thatof laboratory experimental fragments, while the shapesof lunar regolith particles are more spherical than experimental impact fragments. Such information on the
shape of ejecta particles may be obtained from ejecta
curtains and crater rays originating from natural collisions or artificial collisions like the SCI experiment of
Hayabusa2 (Arakawa et al. 2017; Ogawa et al. 2017) byapplying the results of our study. The grain size of thesurface of asteroid Ryugu, the target of Hayabusa2, is estimated to be 3–30 mm (Wada et al, 2018); however,there may be particles of smaller size, and even a
depth-dependence of size and shape of regolith particles
due to, for example, vibrational size sorting (Miyamoto
et al. 2007) or thermal fatigue (Delbo et al. 2014) and alteration, caused by either solar radiation heating (Michel
and Delbo 2010) or space weathering (Le Corre et al.
2018). The macroscopic pattern of ejecta from the surface to subsurface may show a microscopic property of
the constituent particles.
Finally, apart from its significance for planetary surfaces, understanding the agglomeration phenomenon
in the granular stream may be useful for understanding particle shape effects of the agglomeration processof solid particles in protoplanetary disks and debris
disks.

measured adhesion, the critical collision velocity for agglomerates of these particles was up to a few centimeter
per second, while the typical horizontal velocity of theparticles just below the aperture of the funnel was approximately 1 cm s− 1.
Agglomerate formation for the 50 μm glass beads occurred much more easily than for the 100 μm glass
beads, which agrees with predictions based on a comparison between the horizontal velocity and critical collision velocity for agglomerates. However, irregularly
shaped particles also formed agglomerates, althoughthese showed less adhesion. It seems that more efficientenergy dissipation occurs during the collisions among irregularly shaped particles. The sizes of the agglomerates
were larger than in the previous study (Royer et al.
2009), likely due to the larger aperture of the funnel
used in this study. The length and width ratios of the agglomerates were approximately between 1 and 2.5,
which roughly agrees with the previous study (Royer et
al. 2009), although it is notable that the agglomerates ofirregular particles had a larger size than those of spherical particles.
The granular stream allows constituents to collide atvelocities low enough for clusters or agglomerates togrow and therefore can be used to study the agglomeration of solid particles. Our study showed that both theadhesive force of particles and the particle shape greatly
influence agglomerate formation. Therefore, informationon the shape or adhesive force of ejecta particles may beobtained from ejecta curtains and crater rays originatingfrom natural collisions or artificial collisions, like that of
the SCI experiment of Hayabusa2. Further study of theagglomeration of solid particles in a granular stream
would allow new insights into cratering ejecta patterns,
rays on planetary bodies, and grooves on Phobos. Laboratory granular stream experiments may also be usefulfor examining the effects of the particle shape on otheragglomeration processes, such as those in protoplanetarydisks and debris disks.

Nagaashi et al. Progress in Earth and Planetary Science

Conclusions
We conducted laboratory experiments of granularstreams using poly-dispersed glass beads with median diameters of 55 μm (50 μm glass beads) and 93 μm(100 μm glass beads), alumina particles, and silica sandgrains to investigate the formation conditions of agglomerates in granular streams. The glass beads were spherical, whereas the alumina particles and silica sand grains
had irregular, non-spherical shapes. We measured theadhesion of the particles using a centrifugal separation
method. The 50 μm glass beads had a relatively smaller
range of adhesion, which was closer to theoretical expectations than the other particles. The other particles
showed discrepancies of orders of magnitude from thetheoretical values of perfect spheres, as well as a large
spread in the values, which was likely due to the microscopic roughness of the particle surfaces, in addition to
the macroscopic irregularity in their shape. Based on the

Abbreviations
ISAS: Institute of Space and Astronautical Science; JAXA: Japan Aerospace
eXploration Agency; PIV: Particle image velocimetry; SEM: Scanning electron
microscope
Acknowledgements
We would like to thank K. Ogawa and A. Suzuki for their support with thelaboratory experiments. We are also grateful to the Hypervelocity Impact
Facility (former facility name, The Space Plasma Laboratory), ISAS, and JAXA
for their support.
Funding
This research was supported by the Hosokawa Powder Technology Foundationand grants-in-aid for scientific research from the Japanese Society for
the Promotion of Science (nos. 25400453 and 18K03723) of the Japanese
Ministry of Education, Culture, Sports, Science, and Technology (MEXT).
Availability of data and materials
Please contact author for data requests.

(2018) 5:52

Page 14 of 14

Authors’ contributions
YN conducted the measurements and experiments, analyzed the data, andconstructed the manuscript. TO prepared the regolith analogues and helped
measure the cohesive force of the particles. MK helped with the granularstream experiments. AMN proposed the topic, conceived the study, andhelped in the interpretation of the results. KW provided the theoreticalbackground of the study. SH supported the granular stream experiments
conducted in the vacuum chamber in ISAS. All authors read and approved
the final manuscript.

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Nagaashi et al. Progress in Earth and Planetary Science

Competing interests
The authors declare that they have no competing interests.

Publisher’s NoteSpringer Nature remains neutral with regard to jurisdictional claims in publishedmaps and institutional affiliations.
Author details
1
Graduate School of Science, Kobe University, 1-1 Rokkodaicho, Nada-ku,
Kobe 657-8501, Japan. 2Planetary Exploration Research Center, Chiba Instituteof Technology, 2-17-1 Tsudanuma, Narashino, Chiba 275-0016, Japan.
3
Institute of Space and Astronautical Science, Japan Aerospace Exploration
Agency, 3-1-1 Yoshinodai, Chuo-ku, Sagamihara, Kanagawa 252-5210, Japan.
Received: 30 November 2017 Accepted: 17 August 2018

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