J. Jpn. Soc. Soil Phys.
土壌の物理性No. 156 p.7 ∼ 14 (2024)

Analysis of sedimentation behavior of ﬂocculated
Na-montmorillonite in a semi-dilute regime— effects of the container height —Jiawei LI1 and Yasuhisa ADACHI2

Abstract: A systematic observation of the sedimentation
behavior of montmorillonite suspension coagulated in 1.00
M NaCl solution was made using glass cylinders of different heights in the semi-dilute regime which starts from avery slow rate followed by gel collapse ending slow consolidation. Intensive analysis was done for the maximum
interface settling rate (Q) as a function of the volume fraction of montmorillonite (ϕ ) using cylinders of different
heights. The velocities were plotted against the reciprocal height of the cylinder to obtain the velocity of inﬁnite height as a function of the volume fraction of montmorillonite. On the basis of Richardson-Zaki’s equation;
Q = Qf (1 − αϕ )4.65 , the swelling ratio of α , and the velocity of zero limit dilution (Qf ) were obtained from the slopeof the plot and the intercept of the abscissa, respectively.
Using the obtained values of α and Qf , the representative
diameter of the ﬂoc, df , is determined by the application of
Stokes’ Law. The obtained values of Qf and df were conﬁrmed to be consistent with the result of the measurementof the settling velocity of a single ﬂoc against diameter independently determined by the method of Two-way camera.
Key Words : ﬂocculated suspension. Na-montmorillonite,settling velocity, container height, sedimentation turbulence

1. Introduction
Colloidal materials and soil exist throughout aquatic environments. Their sedimentation behaviors are closely related to the solid-liquid separation process such as water treatment, and the transportation of the cohesive sediment in rivers and estuaries (Adachi and Iwata, 2003;
Chassagne, 2019). Although these substances are foundto be aggregated ﬂocs and they play an important role in
1 Graduate School of Science and Technology, University of Tsukuba, 11-1 Tennodai, Tsukuba, Ibaraki 305-8572, Japan.
2 Faculty of Life and Environmental Sciences, University of Tsukuba, 11-1 Tennodai, Tsukuba, Ibaraki 305-8572, Japan. Corresponding author:
Yasuhisa Adachi.
2023 年 8 月 18 日受稿 2023 年 12 月 13 日受理

the transport in aquatic environments, the settling behavior is hardly noticed. In paddy ﬁeld agriculture, this phenomenon is seen in the plowing process (Adachi, 2019).
The ﬁne sediment discharged from the surface of the paddy
ﬁeld by the excess water moving to the river raises the water turbidity in the downstream region (Wakai et al., 2005;
Sudo et al., 2009). On the other hand, in the process of
irrigation, the cohesive sediment tends to be temporarily
deposited in the stagnation of the irrigation drainage canal.
At the time of the commencement, chemical substances
derived from agricultural chemicals such as fertilizer wereadsorbed on the surface of the clay particles constituting
the aggregates, and polluted river water. Such contaminants may endanger the entire ecosystem (Winterwerp andWalther, 2004). In these natural water environments, mostparticles exist as ﬂocs. Therefore, ﬂocs are very importanttransport units rather than individual particles and may inﬂuence various environmental phenomena. Thus, the settling process of ﬂocs under gravity is considered to be oneof the most fundamental problems in the transport of chemicals.
In order to understand the sedimentation of ﬂocculated
suspension, it is necessary to correlate the hindered sedimentation to the single ﬂoc sedimentation. The velocity ofa single ﬂoc settling under gravity can be derived by theforce balance applying Stokes’ Law:

Qf =g(ρf − ρw )df 2
18µ

(1)

Where Qf , g, ρf , ρw , df , and µ , denotes the settling velocity of a single ﬂoc (mm s−1 ), the gravitational constant (ms−2 ), the density of the ﬂoc (g mm−2 ), the density of thesolution (g mm−2 ), the ﬂoc diameter (mm), and the viscosity of the solution (Pa·s), respectively. In this derivation, aﬂoc is assumed to be an impermeableand rigid sphere with

土壌の物理性

8equal projected area.

When the concentration of ﬂocculated material increases, the settling velocity will be hindered due to theinterference from the neighboring ﬂocs. The presence ofneighboring particles will increase apparent viscosity andreduce the difference in density. In the case of a solid
sphere, Richardson and Zaki (hereinafter R-Z) obtained thefollowing equation for the hindered sedimentation basedon the intensive measurement using a ﬂuidized bed ofmonodispersed particles (Richardson and Zaki, 1954):
Q = Qo (1 − ϕ )4.65(2)

Where Q denotes the maximum interface settling rate (mms−1 ), Qo is the settling velocity of a single sphere (mms−1 ), and ϕ is the solid volume fraction. It should be notedthat equation (2) is only targeted on mono-dispersed particles. In the ﬂocculated suspension, the sedimentation
behavior is more complicated. The formed ﬂocs are obviously far from mono-diapered spheres. For this problem, Michaels and Bolger (hereinafter M-B) did a comprehensive analysis using the suspension of kaolinite ﬂocs
(Michaels and Bolger, 1962). They have demonstrated that
R-Z’s equation is widely applicable to the sedimentationof ﬂocculated kaolinite, introducing the concept of effective volume fraction of solid which is expressed by theswelling ratio due to ﬂocculation. It’s worth noting that the
ﬂocculated material of kaolinite is far from monodispersed
spheres, nevertheless, M-B demonstrated the validity of RZ’s equation. Regarded as a settling unit, ﬂoc holds its
structure with the consist of primary clay particles and porewater. The solid volume fraction (ϕ ) and the swelling ratioof the ﬂoc (α ) can be expressed in the following relationship:

α=

ϕf
ϕ

(3)

On the basis of equation (2), Michael and Bolger showed
the relationship between the ﬂoc characteristics and the interference settling rate as,
Q = Qf (1 − αϕ )4.65(4)Imai (1981) classiﬁed the sedimentation behavior of
ﬂocculated sediments into three regimes corresponding to
the concentration of the suspension. They are dilute, semidilute, and concentrated regimes. In the ﬁrst dilute regime,
ﬂocs settle freely interacting with each other very weakly.
The motion of each ﬂoc seems hydrodynamically independent. The larger ﬂocs settle faster than the smaller ﬂocs,
thus the interface between the formed supernatant and the

第 156 号（2024）

region of settling ﬂoc present becomes unclear. In the second semi-dilute regime, on the other hand, the interaction
between suspending ﬂocs seems to inﬂuence the whole region generating a network-like structure. A clear interface
between transparent supernatant and a region occupied by
the suspended ﬂocs can be recognized. It should be notedthat suspended ﬂocs are not rigidly connected. However,the duration of the ﬁrst stage is reﬂected by the colloidal
interaction (Wu and Adachi, 2016). The movement of theinterface is very slow and after a while, the initially formed
network-like structure will collapse due to gravity. This is
the onset of the second stage results in a rapid rate of sedimentation which will end with the accumulation of settled
ﬂocs in the bottom. The formed bottom sediment will start
to consolidate at a very slow rate which is regarded as thethird stage. In the last concentrated regime, the initiallyformed ﬂocculated sediment network structure settles very
slowly from the beginning. The slow process is essentiallythe consolidation process that continues very long period.
Among all, the semi-dilute regime is a very characteristic
regime that reﬂect the presense of ﬂocs which is very fragile. This domain is important in the sedimentation process
in the esturaly (Wolanski and Gibbs, 1995). In this study,
we mainly focused on the second stage of the semi-dilute
regime.
Montmorillonite is a kind of alkaline clay. The ﬂocculation of montmorillonite coagulated in NaCl solution is
also suitable for the analysis of sedimentation experiments
because of the easy generation of visibly big ﬂocs. The
cohesive force between particles and the resulting size of
ﬂocs under a certain shear rate can be simply controlled
by the concentration of sodium chloride (Miyahara et al.,
1998; Miyahara et al., 2001; Di et al., 2019). The resulting
size of ﬂocs is approximately ten times larger than the caseof kaolinite (Kuroda et al., 2003; Kinoshita et al., 2017).
In our previous study, we demonstrated the signiﬁcant effect of cylinder heights on the rate of sedimentation by thegeneration of so-called sedimentation turbulence (Ghazali
et al., 2020). Increasing the initial height will promote therate of interface sedimentation due to the development oflarge ﬂocs during the sedimentation period, which was regarded as the feed-forward mechanism. That is, once thecollision between two ﬂocs is taken place due to the difference of settling velocity, it will result in the formationof bigger ﬂoc. The generation of bigger ﬂoc will result inincrease of rate of sedimentation thus the more frequentcollision between ﬂocs will be induced. This iteration process will be acccelrated during sedimentation process andmore probable development of ﬂoc size will be predicted inthis duration, settling velocity and rate of collision can bepredicted in heigher settling container which allows longer

論文：Analysis of sedimentation behavior of ﬂocculated Na-montmorillonite in a semi-dilute regime

travel distance. It is necessary to investigate this effect toobatain the representative rate by the experiment under different initial height conditions.
Miyahara et al. (2001) tried to conﬁrm the consistencyof the rate of hindered sedimentation of the ﬂocculated suspension of Na-montmorillonite with the rate of single ﬂoc
sedimentation referring to the analytical method reportedby M-B. However, their trial was not quantitatively successful due to the incomplete consideration of the cylinder
heights. A similar trial was reported by Kinoshita et al.
(2017) using ﬂocculated materials of Na-kaolinite. They
concluded the validity of the analytical method of M-B toevaluate the state of suspension. However, they are notable to conclude the consistency between the rate of hindering sedimentation and that of single ﬂocs. As their research pointed, although many studies have been carriedout to use microscopy combined with image analysis andphotography to deﬁne the shape, porosity, and structure of
the ﬂoc, the difﬁculty of measuring the settling velocity ofsingle ﬂocs with high accuracy still needs to be improved.
In the analysis of M-B, it was found that the settlingrate is inﬂuenced by the height of the container. For thisproblem, they proposed the method to obtain the settling
velocity of sedimentation by considering inﬁnite containerheight (from the plot of the results vs the reciprocal valueof interface height H). That is, it is necessary to carry out
the experiment as a function of container height and establish the inﬁnite container height condition though M-B’s
method. In addition, to prevent the accurate analysis ofsingle ﬂoc sedimentation, we applied the method of Twoway camera in the present study, which two cameras are
positioned in orthogonal directions in the horizontal plane
to obtain accurate data on settling ﬂocs. By the applicationof this method, the scatter of ﬂoc diameter measured forthe ﬂoc settling velocity is reduced by approximately 20–
30 % evaluated by the coefﬁcient of variation (Adachi andDaitokurin, 2020). In order to verify the effectiveness of
the R-Z formula on the hindered sedimentation of ﬂocculated Na-montmorillonite and consistency with the single
ﬂoc sedimentation, we conducted systematic analysis of
sedimentation behavior of ﬂocculated suspension of Namontmorillonaite with different height of cylinder and asingle ﬂoc sedimentation using Two-way camera.

9

dispersed in deionized water, and the suspension was left
undisturbed to remove the coarse components by sedimentation. The upper part of the dispersion was siphoned into a
NaCl solution of sufﬁciently high concentration to replace
the exchangeable cation with Na+ . Dialysis procedures
were done to remove sulfur and glycerol. The dispersion
was dialyzed against distilled water until the electrical conductivity of the percolate decreased to 2.00 µS cm−1 withwater renewal. Then, the gel-like dispersion was stored ina refrigerator at 4.0 ◦ C as the stock solution. The volume
fraction of the dispersion was measured gravimetrically.
2.2 Measurement of the rate of hindered sedimentation
The relationship between interface height (H) and settling time under different solid volume fractions in 1.00
M NaCl solution is measured. Na-montmorillonite suspension and NaCl solution were gently mixed by the endover-end method using two cylindrical measuring cylinders inverted 7 to 8 times. Through this mixing procedure,
ﬂoc was generated in standard size and distributed evenly(Michaels and Bolger, 1962). The suspension was left tostand for the observation of settling behavior in circularmeasuring cylinders of different heights from 200 mm to
500 mm as shown in Fig. 1. The change of interface settling height H was recorded as a function of elapsed time, t.
The inner diameter of the settling cylinders was 50.00 mm.
Solid volume fraction (ϕ ) was adjusted as 1.00 ×10−4 ,1.25 ×10−4 , 1.50 ×10−4 , 1.75 ×10−4 , 2.00 ×10−4 and2.50 ×10−4 . The lower limit of volume fraction is thelimit value of the interface that can be visually obtained.
The ultimate NaCl concentration was 1.00 M. During themeasurement, the temperature was controlled at 20.0 ◦ C ±0.5.

2. Materials and Methods
2.1 Sample preparation
In this study, we made ﬂocs from the suspension of the
Na-montmorillonite (Miyahara et al., 1998). Montmorillonite powder (Kunipia-F) was purchased from Kunimine
Industry Co. Ltd., Japan. Montmorillonite powder wasFig. 1 Experimental setup of the hindered sedimentation measurement.

10

土壌の物理性第 156 号（2024）

Fig. 2 Experimental setup for measuring the single ﬂoc sedimentation observed by the Two-way
camera and its cross-section view. 1 and 2 are the cameras, 3 is the illumination source, 4 is thecomputer, 5 is the octagonal settling tube, and 6 is the ﬂoc sampler for releasing ﬂocs.

Fig. 3 Interface height as a function of elapsed time for different initial heights in the 5 cm cylinders.
1.0 M NaCl, Na-Montmorillonite 2.5×10−4 .

2.3 Measurement of the single ﬂoc sedimentation
In order to obtain an accurate relation between the ﬂoc
diameter and the settling velocity, the single ﬂoc sedimentation experiment was conducted by applying the methodof Two-way camera (Adachi and Daitokurin, 2020) installed in an octagonal settling tube (1200.00 mm Height;
80.00 mm inner diameter). The Two-way camera system
consists of two CCD cameras (DU657M, Toshiba Teli Co.,
Japan) coupled with image processing software. Two cameras were orthogonally installed on the same horizontal

plane as shown in Fig. 2. During the settling of a single ﬂoc, images from two directions were captured. The
mean value obtained from the projections taken from two
different directions was used for the analysis. The digital
camera could acquire images with 4080-3072 pixels. DIPP
macro II software (DITECT Co., Ltd., Japan), was used forthe image processing. The settling rate of the single ﬂoc(Qf ) was calculated by the vertical displacement of the ﬂoc
centroid moved between two points at a certain time. Floc
diameter (df ) was obtained as the diameter of a sphere withthe equivalent area of the binarized projection.

論文：Analysis of sedimentation behavior of ﬂocculated Na-montmorillonite in a semi-dilute regime

11

Fig. 4 Plot of maximum settling rate with the reciprocal of initial height.

Fig. 5 Relations between the settling velocity of the interface (Q1/4.65 ) and volume fraction of solid(Φ) at 1.0 mol L−1 NaCl concentration with inner diameter of cylinder 28 and 50 mm.

3. Results
3.1 Hindered sedimentation
Here, the result under a solid volume fraction of 2.50
×10−4 was demonstrated in Fig. 3. Sedimentation curves
under different initial settling heights were plotted, showing a similar trend as a sigmoidal curve, which is the descending speed of the interface changes from slow at the
beginning to intense and then continues to slow as described in the introduction. The maximum interface settling rate (Q) was obtained from the slope of the relation
curve between interface settling height and elapsed time

during the rapid sedimentation stage. It was conﬁrmed thatthe results match our earlier ﬁndings, in which the settling
velocity increased linearly with an increase in the initial
settling height (Ghazali et al., 2020).
The maximum interface settling rate (Q) with respect
to the reciprocal of the initial settling height (Ho −1 ) under different solid volume fractions is presented in Fig.
4. The maximum interface settling rate under inﬁnite container height condition (Q′ ) was obtained directly from theintercept of the tendency line. It is obvious that Q′ increased sharply with the decrease of solid volume fractions
from 1.75 ×10−4 to 1.00 ×10−4 . In the more concentrated

土壌の物理性

12

第 156 号（2024）

cases, which are solid volume fractions under 2.00 ×10−4
and 2.50 ×10−4 , Q′ obtained from the data plots demonstrates a remarkable level of congruence.

termined as 1.97 from the value of power of this relationship.

3.2 A single ﬂoc sedimentation test using themethod of Two-way camera
In this study, the direct measurement of a single ﬂoc settling experiment was also carried out to examine the validity of the obtained values through R-Z’s modiﬁed equation.
Typical images of the observed Na-Montmorillonite obtained by the method of Two-way camera are shown in Fig.
6. The ﬂoc diameters were calculated from the mean valueof the two directions’ projections. Our research proposesa novel approach to ﬂoc analysis by utilizing a two-way
camera system to observe individual ﬂocs from two different directions. By capturing images of ﬂocs from multiple
directions, we can obtain a more comprehensive and accurate understanding of their physical properties, including
size, shape, and settling velocity. It is obvious that, evenon the same ﬂoc the sizes we observed from two directions were different. This is particularly important given
the complex and heterogeneous nature of ﬂocs in water
treatment processes, which can exhibit signiﬁcant variation in their properties even within a single sample.

4. Discussion

By assuming that the settling ﬂoc can be approximatedas an impermeable sphere with a fractal structure, i, thenumber of primary montmorillonite particles composing a
ﬂoc can be described as
i=(

Df D
)
do

(5)

Where d0 , Df and D denotes the number of montmorillonite particles composing a ﬂoc (mm), the diameter of themontmorillonite particle (mm), and the fractal dimension,respectively. So, the swelling ratio of the ﬂoc (α ) can befurther expressed asα=

Df 3−D
ϕf
=( )
ϕ
do

4.1 Sedimentation behavior under different
initial settling heights
The hindered sedimentation behavior can be characterized as a very slow ﬂocculation stage in the beginning, followed by rapid sedimentation, and entirely comes back to

Fig. 6 Typical images of the ﬂoc projections taken from the
Two-way Camera observation in the single Na- montmorillonite
ﬂoc sedimentation in 1M NaCl. Here we show ﬁve sets of images, each set horizontally, of the same ﬂocs viewed from different directions. The left column represents camera number
one, and the right column represents camera number two.

(6)

This equation means, that the volume fraction will increase
with the increase of the ﬂoc diameter. So, equation (1) canbe simply modiﬁed asVf =g(ρs − ρw )d0 3−D Df D−1
18µ

(7)

Where ρs denotes the density of the montmorillonite particle (g mm−2 ). The relationship between the ﬂoc diameterand settling velocity from the single ﬂoc sedimentation wasplotted on a log-log paper in Fig. 7. The settling velocity
increased with the increase of ﬂoc diameter, and the obtained relationship was conﬁrmed to follow a power law.
On the basis of equation (7), the fractal dimension was de-

Fig. 7 Relationships between the settling velocity and diameter of a single Na-montmorillonite ﬂoc in 1M NaCl.

論文：Analysis of sedimentation behavior of ﬂocculated Na-montmorillonite in a semi-dilute regime

a very slow consolidation process. With the help of wellestablished visualization techniques in this study, detailed
descriptions of this phenomenon could be given. The initial stage can be understood as the formation of a loosely
connected network structure between ﬂocs. However, theinterface starts to move rapidly by the self-weight of the
network. In the rapid settling stage, the ﬂocs continuouslytransfer downward, and the liquid in the lower depositionis squeezed upward, resulting in strong convection. Then,in the third stage of the consolidation, the settling rate of
the interface becomes relatively slow. This typical phenomenon of the three stages settling in the hindered sedimentation of the semi-dilute regime was clearly displayedusing Na-montmorillonite suspension. Once the sedimentation starts, the whole system takes into action. As long as
the settling continued the force was transferred upwards.
The starting point of the rapid sedimentation period wasclariﬁed by our previous study (Wu and Adachi, 2016).
To deﬁne the beginning of the consolidation stage, we can
employ a straightforward procedure utilizing the standard
sedimentation curve. This curve illustrates the relationship between the interface settling height and elapsed time.
Firstly, we extract the ﬁtting line from the rapid sedimentation stage, which provides the interface settling velocity based on its slope. Subsequently, we draw the ﬁtting
line representing the ﬁnal consolidation stage. By determining the abscissa of the intersection point between these
two lines, we can accurately identify the starting point ofconsolidation. While this method provides a quick way
to determine the beginning of the consolidation stage, it isimportant to note that more precise research is required for
accurate results. Determining the starting point of consolidation is crucial for predicting the formation of the ﬁnal
sediments’ structure. Furthermore, the compression settlement stage is a common occurrence in nature, and analyzing it can offer a better understanding of physical phenomena in natural environments.

13

1.00 × 10−4 and 1.75 × 10−4 in Fig. 5. A linear relationship between Q1/4.65 and ϕ can be obtained through equation (4). Therefore, corresponding values of α , Qf , and Df
can be derived from the slope of this relation, which was
obtained as 2497.74, 0.93 mm s−1 , and 1.64 mm respectively. Eventually, the value obtained from hindered sedimentation matches the results of the single ﬂoc sedimentation Fig. 8. Miyahara’s previous result was below the ﬁtting line because the inﬂuence of the container height was
not considered in the hindered sedimentation experimentat that time, 150.00 mm was adopted as a uniﬁed containerheight. So, in the present result, taking advantage of the inﬁnite height measurement through M-B’s method, the calculated value falls exactly on the ﬁtting line of the relationship between ﬂoc diameter and settling velocity. We cansee that the hindered sedimentation of Na-montmorillonite
is highly correlated with the single ﬂoc sedimentation under 1.00 M NaCl condition.

5. Conclusion
To investigate the validity of R-Z’s equation through MB’s method on Na-montmorillonite suspension, we systematically analyzed the sedimentation behavior of the
ﬂocculated suspension of Na-montmorillonite. The relationship between the interface sedimentation rate andthe effective volume fraction of the suspension was determined. The estimated result using R-Z’s equation obtained
from hindered sedimentation was conﬁrmed by the direct

A same conditioned experiment was done in thinnercylinders (28.00 mm inner diameter) was conducted separately in Fig. 5, in which the Q′ was smaller than the
thicker cylinders’ case. While in the less concentrated part1.00 ×10−4 and 1.50 × 10−4 the slope shows nearly thesame tendency as the thicker cylinders’ condition. These
results showing the disturbance by the formation of thelarge aggregates illustrate the evidence of a long-chain network structure that yields a long-distance stress chain in
the ﬂocculated sediment.
4.2 The validity of Michaels and Bolger’s
methods
Estimated results using R-Z’s equation from hinderedsedimentation were obtained from the ﬁtting line between

Fig. 8 Relations between the settling velocity and diameter ofsingle ﬂocs sedimentation. Estimated results using R-Z’s equation obtained from the hindered sedimentation was plotted. Previous’ result done by Miyahara was also shown (Miyahara et al.,2001).

土壌の物理性

14

measurement of single ﬂoc sedimentation. The estimatedvalue is exactly in line with the measured results. Compared with our previous research done by Miyahara, theconcept of inﬁnite height was used for taking no inﬂuenceof container height in this study. We could conclude that
R-Z’s equation is applicable to the clay suspension of Namontmorillonite under 1.00M NaCl condition. The effectof container diameter on the settlement was conﬁrmed, thatis, thicker cylinders (50.00 mm diameter) have no effectwhile thinner cylinders (28.00 mm diameter) will greatly
hinder the sedimentation due to the long-chain network
structure of Na-montmorillonite. Furthermore, the uniqueapproach of the Two-way camera observation to the single ﬂoc sedimentation provides an effective way for theaccurate measurement of ﬂocs. Analyzing the sedimentation behaviors of Na-montmorillonite under different conditions and the consolidation period in the hindered sedimentation will further elucidate the study on ﬂoc structure
and illustrate the ﬂoc packing phenomenon.

第 156 号（2024）(2020): Effect of the concentration of NaCl and cylinder
height on the sedimentation of ﬂocculated suspension of
Na-montmorillonite in the semi-dilute regime. Paddy andWater Environment, 18(2): 309–316.
Imai, G. (1981): Experimental studies on sedimentation mechanism and sediment formation of clay materials. Soil andFoundation, 21(1): 7–20.
Kinoshita, T., Nakaishi K. and Kuroda Y. (2017): Determination of kaolinite ﬂoc size and structure using interface
settling velocity, Appl. Clay Sci., 148: 11–16.
Kuroda, Y., Nakaishi, K. and Adachi, Y. (2003): Settling velocity and structure of kaolinite ﬂoc in sodnm chloride solution. Clay Science, 12: 103–107.
Michaels, A.S., Bolger, J.C. (1962): Settling rates and sediment volumes of ﬂocculated kaolin suspensions. Industrial
and Engineering Chemistry Fundamentals, 1: 24–33.
Miyahara K., Adachi Y. and Nakaishi, K. (1998): The viscosity of a dilute suspension of sodium montmorillonite in an
alkaline state, Colloids and Surfaces A: Physicochemical
and Engeneering Aspects, 131: 69–75.
Miyahara, K., Ootsubo, M., Nakaishi, K. and Adachi, Y.

Acknowledgments(2001): Sedimentation rate of sodium montmorillonite
suspension under high ionic strength, Journal of the Clay

Thoughtful suggestions from Dr. Setsuo Ooi and Dr.
Katsuya Nakaishi are acknowledged. Appreciation to Kakenhi 22H00387 for providing the funding for this research
project is extended.

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