Paper No 7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
Experimental and Modeling Study of Breakage and Restructuring of Colloidal
Aggregates
Yogesh M. Harshe, Miroslav Soos, Marco Lattuada, Massimo Morbidelli
Department of Chemistry and Applied Biosciences, Institute for Chemical and Bioengineering, ETH Zurich, Zurich 8093,
Switzerland
massimo.morbidelli@cchem.ethz.ch
Keywords: colloidal aggregates, breakage, restructuring, elongational flow, Stokesian dynamics
Abstract
The study of response of colloidal aggregates to different flow fields is mostly carried out either by experimental means or
through particleparticle modeling, however, seldom together. Three different processes occur simultaneously namely,
aggregation, breakage, and restructuring. In this work we set out to provide further clarification to the phenomena, by
combining both experimental work and computer simulations. Aggregates of significantly different morphology produced
from primary particles of 90 and 810 nm under static and flow conditions and having fractal dimension d =1.7 and 2.5 were
exposed to elongational flow generated within a nozzle. Light scattering and image analysis were used to characterize
aggregate morphology and size. The dynamic evolution of aggregates was tracked and was qualitatively compared with the
Stokesian dynamics modeling results. From the obtained data, different scaling laws and governing mechanisms for different
operating conditions were defined. The modeling efforts helped to understand and distinguish between breakage and
restructuring. Systematic study of dependence of resulting aggregate geometries on different flow conditions and initial
aggregate properties helped to express lumped parameters which can be used in population balance breakage kernel.
Introduction
The size and size distribution of colloidal aggregates is
important in many chemical processes such as polymer
processing, coagulation processes, etc. The size of a
colloidal aggregate in such processes is decided by the
initial size and structure of the aggregate, size of primary
particle in the cluster, applied flow field, interparticle
forces, and so forth. The experimental and modeling efforts
provided so far still fail to predict the fate of a colloidal
aggregate, and do not provide summarizing scaling laws to
clarify our understanding on the interdependence of such
quantities. On one hand experimental efforts lack modeling
proofs and generalization of the observed phenomena while
on the other hand, theoretical modeling of such processes
still lacks experimental proofs. For example, when clusters
are subjected to shear, three phenomena occur
simultaneously, i.e. aggregation, breakage and restructuring.
The first mechanism increases the size, the second one
reduces the size of the aggregate whereas the last process
leads to the aggregate densification. The transition between
these processes, more importantly the later two processes,
which is a function of cluster geometry, is an untouched
subject of study.
The experimental works so far are either under turbulent
conditions or in laminar flows. Turbulent jets (Glasgow and
Hsu 1982) and stirred tanks with different impeller
geometries (Tambo and Hozumi 1979; Soos, et al. 2008;
Ehrl, et al. 2008) are typically used configurations for study
of colloidal aggregate breakage under turbulent flow
conditions. However, under these conditions the flow field
is not exactly defined. Moreover due to heterogeneous
distribution of the velocity field, even locally, the total
hydrodynamic force acting on the suspended aggregates is
difficult to define. On the other hand, the velocity fields in
the laminar flows can be easily defined and can be
expressed in simple forms. It is for the same reason that the
laminar flow conditions are more interesting. In the
literature different devices are used to generate different
types of laminar flows such as, rheometers are for simple
shear flow (Blaser 2000; Vassileva, et al. 2007; Kao and
Mason 1975), contracting nozzles (Sonntag and Russel
1987; Higashitani, et al. 1991; Kobayashi, et al. 1999; Soos,
et al. 2010) are used for extensional flow, while fourroll
mills (Blaser 2000) to generate twodimensional straining
flow. Since the time scale of the breakage and/or
restructuring event is very short in the present work the
elongational flow generated in nozzles was used to
experimentally study above mentioned processes.
The colloidal aggregates in suspensions experience different
forces. The morphology and size of the evolving aggregates
are strong function of these forces as the bonds between
different particles of an aggregate or different aggregates
form/break/reform which subsequently results in
aggregation/breakage/restructuring phenomena. The total
hydrodynamic force acting on each particle is a result of the
position of the particle in the flow and also its position with
respect to the other particles in the flow. To account for the
total hydrodynamic force both short and longrange
hydrodynamic interactions must be calculated correctly. In
Paper No
the present work we adopted the Stokesian dynamics
approach to estimate the hydrodynamic effects imposed by
the fluid. The usual DLVO theory is followed to describe
the interparticle forces, which mainly include the van der
Walls attractive forces and Born repulsion to prevent
particles from overlapping. Additionally, recent
experimental evidence by Pantina and Furst (2005) indicates
the presence of bending moments due to contact forces
between particles in clusters, but there are only a few
simulation studies where such tangential contact forces are
included. We used the methodology developed by Becker
and Briesen (2008) to implement the tangential forces
acting between the connecting particles.
Nomenclature
F force (N)
T torque (Nm)
S stresslet (Nm)
U translational velocity (m/s)
Q angular velocity (1/s)
E rate of strain (1/s)
K, coefficient of tangential moment ()
R, primary particle radius (m)
Ah Hammaker constant
P Density (kg/m3)
N, Born repulsion constant ()
Greek letters
S Minimum particle distance (m)
q] viscosity (Pas)
J Spring (m)
Subsripts
Co fluid conditions
n Particle number
i,j Particle counter
Experimental Facility
Two types of aggregates with very different internal
structure were produced by aggregation process using static
and flow conditions and characterized by df =1.7 + 0.05 and
df =2.5 + 0.1, respectively. To investigate the effect of
primary particle size polystyrene (PS) particles with
different diameter were used to generate the mentioned
aggregates. In particular, white sulphate polystyrene latex
(product no. 1800, coefficient of variation =2.0%, batch no.
642,4, solid % =8.1, and surface charge density = 5.2
gC/cm2) with primary particles diameter equal to 810 nm
and carboxyl polystyrene (product no. 780,coefficient of
variation =11.8%, batch no. BM603, solid % =4.3, and
surface charge density = 7.2 gC/cm2)with primary particles
diameter equal to 90 nm, both purchased from Interfacial
Dynamics Corp. (IDC), Portland, OR (USA).
The aggregates were produced as follows
a) Open aggregates DLCA
The aggregates were prepared under static conditions by
mixing latex solution with D20 containing appropriate
amount of salt (Al(NO3)3) leading to complete
destabilization of primary particles. The solid volume
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
fraction of the final dispersion was equal to 1x10 The
proportion of pure water and D20 was kept such to match
density of the suspending fluid with that of particles to
minimize sedimentation. The static aggregation was
performed inside the light scattering instrument Mastersizer
(Malvem, UK) over 12 hours or 72 hours for 90nm and 810
nm primary particles, respectively. Aggregate size and
structure was monitored over the whole period of time.
Aggregates prepared in this way have very open structure
characterized by the fractal dimension d,=1.7 + 0.05. To
prevent further aggregation the resulting aggregates were
diluted to the solid volume fraction 1.7 xl06 during first
pass through the nozzle. In particular, in the case of 810 nm
primary particles 20 mL of the aggregate suspension was
pumped out of the Mastersizer through a nozzle and it was
stabilized with 100 ml mixture of PVA (12 ml with
concentration 1 g/l) and pure water (88 ml). For aggregates
composed of 90nm primary particle, 20 ml of suspension
was pumped out into 100 ml of pure water to eliminate
further aggregation. Such diluted and stabilized aggregates
were consequently broken in the extensional flow generated
in the contracting nozzle positioned between two syringes.
b) Dense aggregates
Aggregates composed of 810 nm primary particles were
prepared as described in Moussa, et al. (2007), Waldner, et
al. (2005), and Soos, et al. (2010). The breakage experiment
was carried out as explained in Soos, et al. (2010). In
contrary, in the case of 90 nm primary particles the
aggregates were prepared in a 225 ml stirred tank equipped
with Rushton turbine using an initial solid volume fraction
of lxl05. Aggregation was initiated by injecting 2.8 ml of
20% Al(NO)3 salt solution into the completely filled stirred
tank. After the aggregate size reached the steadystate value,
which happened after 1 h at 200 rpm, samples were gently
withdrawn and consequently diluted with pure water to stop
further aggregation. Before each breakage experiment each
sample was characterized by light scattering measurements.
The breakage experiment was carried out by applying
converging flow through the nozzle mounted between two
syringes with the help of a syringe pump connected to one
of the syringes. With the pump repeated to and fro cycles
were performed which are referred as the number of passes
through the nozzle.
The sketch of the breakage equipment is shown in Figure 1.
S(a)
/entry /nozzle /exit
Figure 1: Sketch of the breakage equipment with
dimensions
entry
Paper No
Experimental Characterization of Aggregate
Structure
1] Light scattering measurements
The Cluster Mass Distribution (CMD) of the produced
aggregates was characterized by measuring the intensity of
scattered light I(q), which is function of the aggregate size,
structure, and the size of the primary particles constituting
the aggregate and can be expressed as Sorensen (2001)
I(q)=I(0)P(q)S(q)
where I(0) is the zeroangle intensity, P(q) is the form
factor (due to primary particles), S(q) is the structure
factor (due to the arrangement of primary particles within
the aggregates), and q is the scattering vector amplitude
defined as:
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
conditions (Ehrl, et al. 2008; Soos, et al. 2008). The former
indicates very open structure while the latter very compact
structure (Ehrl, et al. 2009; Lu, et al. 2006).
2] Confocal laser microscopy
Due to the large size of primary particles, which is well
outside the region of the validity of the
RayleighDebyeGans (RDG) theory (Kerker 1969; Jones
1999) combined with the compact structure of the
aggregates, approach described above cannot be used to
determine the aggregate fractal dimension for aggregates
composed of 810 nm primary particles. Therefore, for these
aggregates the structure was obtained from the analysis of
2D confocal laserscanning microscopy (CLSM) pictures of
aggregates taken with a Zeiss Axiovert 100 microscope. In
this way the structure of the aggregates can be characterized
by the perimeter fractal dimension, dpf, obtained from the
projected surface area, A and the perimeter, P of the
binary image of an aggregate (Mandelbrot, et al. 1984; Lee
and Kramer 2004)
A o P21
q = 4xsin(
Here 0 stands for the scattering angle, n is the refractive
index of the dispersing fluid and 2 is the laser wavelength
in vacuum.
Using the Guinier approximation of the S(q) which reads as
(S(q)) (q) =exp ( q(Rg), 2) < (3)
I(0)P(q) 3 q)
was used to evaluate the rootmean square radius of gyration
of a population of aggregates according to
R(R=) ,(q) +(Rp) using the radius of gyration of the
primary particles, Rg, = Rp It is worth to note that
contribution of primary particles is significant only for
aggregates of very small size.
Due to small size of primary particles, the other information
that can be extracted from the light scattering signal is the
cluster fractal dimension, d which characterizes the
internal structure of the formed aggregates. According to the
RayleighDebyeGans (RDG) theory (Kerker 1969; Jones
1999) the average structure factor (S(q)) scales with q
according to
S(q))c cq d, for 1/(R)
Therefore, in the given q range, plotting S(q) vs q in
a double logarithmic plot should give us a straight line with
slope equal to d, Depending on the experimental
conditions values of the fractal dimension as low as 1.8
were measured for clusters grown under fully destabilized
quiescent conditions (Lin, et al. 1990) while values as high
as 2.7 were obtained for aggregates formed under turbulent
The value of dpf for 2D projections of aggregates varies
between 1 (corresponding to an Euclidean aggregate), and 2
(corresponding to a linear aggregate). Typical values of
for aggregates at steady state produced under turbulent
conditions are in the range from 1.1 to 1.4 (Spicer, et al.
1996; Wang, et al. 2005; Soos, et al. 2007). Having
determined dpf the mass fractal dimension d, can be
estimated using a correlation, as proposed by Ehrl, et al.
(2009). All above mentioned quantities were obtained using
the image analysis software ImageJ v1.34s
(http://rsb.info.nih.gov/ij/).
Numerical Scheme
1] Hydrodynamic interactions
The Stokesian dynamics (SD) method was developed by
Brady and Bossis (1988). The method was formulated by
Durlofsky, et al. (1987) in two forms namely, the FT
approach, which accounts for the forcetorque acting on
particles when translationalangular velocity of particles is
known, and the FTS approach, which along with the
previous terms accounts for the stresslet acting on the
particles and rate of strain of the imposed fluid flow. The
latter approach is more accurate as the hydrodynamic
interactions are approximated with higher order terms, and
accounts for the effect of fluid flow on the motion of
suspended particles. The SD method is valid for very small
particle Reynolds numbers i.e. under laminar flow and
unique rate of strain of the flow. Moreover, it has been
proven that SD method is accurate for very high volume
fractions of the suspended particles and can be virtually
used for any number of suspended particles. So, we adopted
the Stokesian dynamics method for estimating the
hydrodynamic interactions between particles.
The FTS form of the Stokesian dynamics model can be
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
presented in matrix form as follows,
F, ~U,U"~
KT =R Z UQ (2)
S, E
where, R is called as the grand resistance matrix, which is
11NxllN positive symmetric matrix with N number of
particles in the simulation domain.
R=(M") +Rb R; (3)
Here, M" is the farfield mobility approximation, obtained
by pairwise additivity of mobility of individual particles,
RE represents the exact twobody lubrication interactions
when particles are nearly touching, and r is subtracted as
the twobody farfield interactions are already accounted for
in M". Although the mobility is expressed by pairwise
addition, its inverse, the mobility inverse, accounts for
manybody interactions. Thus, once the grand resistance
matrix is estimated and the force acting on each particle is
known, the velocity and hence the trajectory of the each
particle can be tracked.
2] Particleparticle interactions
Apart from the hydrodynamic interactions which are
transmitted through the fluid in which the particles are
suspended, the particles experience different attractive and
repulsive forces. These particleparticle interactions are
usually satisfactorily expressed with the DLVO theory. In
the present work we expressed the attractive forces through
van der Waals interactions whereas Born repulsion was
introduced to prevent overlap between close particles.
Recently, Pantina and Furst (2005) experimentally
demonstrated the presence of tangential interactions
between closely separated particles, which are responsible
for the restructuring and bending strength of the aggregate.
The tangential interactions were effectively modelled by
Becker and Briesen (2008). We adopted their approach to
introduce the tangential forces between particles when they
are separated by very small distance (6,mn). The schematic of
the tangential interactions is show in Figure 2.
Normal interactions Spring is initiated
Figure 2: Sketch of tangential interactions between closely
separated particles
The tangential force and critical bending moment are
estimated as follows.
F =K, (' J,) M =2RK,n 
J is spring initiated between the two connecting particles.
The spring is broken when the spring, J, exceeds certain
critical value m, estimated from the critical bending
moment, and then sliding occurs.
To estimate the tangential forces, however, the well
celebrated Discrete Element Method (DEM) of Cundall and
Strack (1980) was used. The use of very small time steps
ensured the accuracy of the numerical.
To integrate the motion equations, RungeKutta 4th order
method was used with very small timestep. For each time
step the particleparticle interactions were updated and
contacts were identified. The grand resistance matrix for the
hydrodynamic interactions was estimated at each time step,
however, the inverse of the farfield mobility, M" was
calculated only when the distance between any two particles
changed by an amount equal to the primary particle size.
Conversely the lubrication matrix Rb was estimated when
the particleparticle distance for any pair changed by more
than 0.01% of the primary particle size, as the lubrication
forces are short range and change very rapidly when the
particle distances change even slightly. At each time step the
number of aggregates from the contact dynamics and the
average rootmeansquare radius of gyration of each cluster
were estimated. The simulation parameters are listed in
Table 1.
Table 1: Model parameters
Ah = 1.33 x 1020 J p,= 1050 kg/m3
At= lx109 S f= 1000 kg/m3
q7f= 1x103 Pa.s mmn = 3 nm
Nb,= lx1023
Results and Discussion
For analyzing the aggregates structure different approaches
were used for aggregates generated with primary particles of
90 nm and 810 nm. For aggregates generated with 90 nm
primary particles light scattering measurements were used
directly to determine the morphology. On the other hand, for
aggregates composed of 810 nm primary particles a direct
characterization of their internal structure by light scattering
techniques is challenging due to the large size of primary
particles with respect to the used laser wavelength, In this
case confocal laser microscopy combined with image
analyses was used to determine cluster structure.
Figure 3a and b show the structure factor, S(q) measured for
aggregates composed of 90 nm primary particles for
different number of passes through nozzle. Figure 3a
represents data for aggregates generated under static
conditions while Figure 3b shows data for aggregates
produced under shear conditions. The slope of the structure
factor gives the estimation of the fractal dimension of the
aggregates. For each sample 12 measurements were
performed and averaged to yield the presented results.
Paper No
Paper No
10'1.11 103
10 0,
100 0
10 10, 10, 10, 101 104 101 101
q /(nm) q/(n)
(a) (b)
Figure 3: Structure factor for different passes through
nozzle (a) statically generated aggregates (b)
shearinduced aggregates
For aggregates with 810 nm primary particles images were
taken with the confocal laser microscope. The images were
taken at different number of passes through the nozzle. For
each pass approximately 50 to 70 images were taken to
collect good statistic of different structures of the aggregates
present in the sample. Figure 4 shows examples of such
aggregates obtained along the breakage process starting
from statically generated clusters. It can be seen that the
change in the aggregate size and morphology is very evident
from the pictures the aggregates were broken down to
smaller sizes and became dense. The images were used to
estimate the perimeter fractal dimension from which the
mass fractal dimension was obtained as described elsewhere
(Ehrl, et al. 2009).
/h\
(c) (d)
Figure 4: Image analysis pictures from confocal
laserscanning microscopy for 810 nm primary particle
statically generated aggregates for different nozzle passes
(a) 0 (b) 1 (c)5 (d) 110
The evolution of aggregates size characterized by the
rootmeansquare radius of gyration, (R ) was obtained for
defined selected number of passes through light scattering
measurements. The results of experiments using primary
particle of 90 and 810 nm for aggregates generated under
static and shear conditions are summarized in Figure 5. It
can be seen that (R) decreases with the number of passes
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
through the nozzle as the aggregates are exposed more
frequently to the shear. Nevertheless it is interesting to note
that the radius of gyration attains the steadystate and
remains unchanged afterwards. For different nozzle
diameters the steadystate values of the rootmeansquare
radius of gyration differ as the hydrodynamic stress exerted
is different. Additionally, it can be observed that for all
nozzle diameters the steadystate is achieved around the
same number of passes (100).
R = 90 nm
102
A A A 0
A 0
iAAA A A A
100
0 50 100 150 200
Number of passes / ()
(a)
10,
*.e .
S10 *
10
15
10o/15
0 50 100 150 200 250
Number ofpasse / ()
R,= 810nm
0*
(mm)
lOm 'm05
10 . .20
0 50 100 150 200 250 300
Number ofpass /()
(b)
* *
10 *
10 ,
0 50 100 150 200 250 300 350
Number of passes / ()
(c) (U)
Figure 5: Rootmeansquare radius of gyration (R) as a
function of the number of passes through different nozzle
diameters for DLCA aggregates [(a) and (b)] and dense
aggregates [(c) and (d)]
Along with the average aggregate size we were interested
in knowing the evolution of morphology of the resulting
aggregates and hence we estimated the evolution of fractal
dimension along the breakage process. For aggregates with
90 nm primary particles we used light scattering
measurements. In Figure 6 we show the structure factor as
function of q(R,) for various operating conditions. Figure
6 a and c show the evolution of the structure factors for
various number of passes, where data in Figure 6a
corresponds to the DLCA aggregates while Figure 6b
stands for the evolution of the structure factor for
aggregates generated under flow. It can be seen that change
of internal morphology of aggregates is very fast and
occurs only for DLCA aggregates. The slope of S(q) curve
changes from pass 0 to pass 50, after which, it remains
constant. Due to reduction of size as well as change of the
aggregate structure it is fair to conclude that both, breakage
and restructuring, processes are in action resulting in
reduction in size along with densification. On the other
hand, for flow generated aggregates (denser clusters
initially) the slope of the curve remains constant with very
small deviations (Figure 6b) indicating, further
densification of the aggregate was not possible under these
conditions, and only the mechanism of breakage is in play
 solitary breakage is prevalent. As we focused on the
steadystate aggregate size in Figure 5, we followed the
steadystate morphology of the aggregate for different flow
strengths. In Figure 6c and d we have plotted the steady
state S(q) for various nozzle diameters. It can be confirmed
Paper No
that in both cases the structure of the aggregates at the
steadystate is independent of the nozzle diameter (applied
stress).
tol
101
10*'
50o 1
103.1 ':. ..
10 110
01 1 10 100
qx(R) / ()
(a)
10
10 Oass
05m.
10 1
01 1 10 100
qx / ()
(b)
10,
10 0
Opai
10 0 Inn
10=m
l lO n
10
01 1 10 100 1000
qx(R ()
(d)
Figure 6: Structure factor as a function of the number
passes through nozzle (a and c) and nozzle diameter for
steadystate values (b and d) for DLCA (a and b) and
shearinduced (c and d) aggregates from 90 nm PS
particles.
A summary of the evolution of fractal dimension along the
breakage process is shown in Figure 7. It can be seen for
the initially open aggregates that the fractal dimension of
the aggregates immediately (after approximately 10
passes) increases from 1.7 to 2.4 +0.1 and remains at this
value till the end of the experiment. In contrary, for
aggregates generated under turbulent conditions there is no
significant change in d, with value around 2.6 +0.1 in
agreement with evolution of the S(q) presented in Figure
6c.
Together with the evolution of the aggregate size and
morphology, the scaling of the steadystate size on the
applied shear is important in understanding the aggregate
breakage process. The aggregate breaks when the applied
hydrodynamic force is higher than the interparticle forces
responsible for keeping the aggregate together. Hence for a
given applied stress there is critical aggregate size below
which the aggregate does not break and remains intact. The
critical aggregate size in the present work corresponds to
the steadystate aggregate size. The average stress in the
nozzle was determined by characterizing the flow by
Computational Fluid Dynamic (CFD) calculations the
details of which can be found in Soos, et al. (2010). The
scaling of the steadystate aggregate size with the applied
shear is plotted in Figure 8. It was found that for both
primary particle sizes and different initial aggregate
morphologies the scaling exponent was around 0.5 +0.05.
The scaling exponent lies well in the range reported by
Zaccone, et al. (2009), where they observed similar
powerlaw scaling of the steadystate aggregate size as a
function of applied hydrodynamic stress.
Obtained experimental data will be in the next step
compared with ongoing Stokesian dynamic simulations. As
the flow in the contracting nozzle varies from pure
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
elongational (nozzle axes) to the simple shear (nozzle wall)
three type of flow (3D elongation, 2D elongational, and
simple shear) will be used to model the breakage process.
Moreover, to mimic experimental data aggregates with
very open and compact structure with d, equal to 1.8 and
2.6 respectively, composed of various numbers of primary
particles are considered. The scaling from the model
simulation for the aggregates size vs. shear rate (or shear
stress) as well as the evolution of d, will be compared
with the experimental data presented here.
2.7
2.4
S2.1.
1.8
1.5
3.0
? AAA
A A A
0 50 100 150 200
Number of passes / ()
2.70 o0 o o
2.4
2 2.1
1.8
1.5
0
50 100 150 200
Number of passes / ()
Figure 7: Evolution of the fractal dimension as a
function of number of passes through the nozzle for (a)
statically generated aggregates for 90 nm primary
particles (filled triangles) and 810 nm primary particles
(empty squares) (b) shearinduced aggregates for 90
nm ) empty circles) and 810 primary particles (line)
from Soos et al. (2010)
102
10
10
101
/ (Pa)
Figure 8: Scaling of the steady state rootmeansquare
radius of gyration () as function of the applied stress
for different initial aggregates (a) 810 nm DLCA
aggregates (empty circles) (b) 810 nm shearinduced
aggregates (filled circles) (c) 90 nm DLCA aggregates
A A
A
0 AA
0
Paper No
(empty triangles) (d) 90 nm shearinduced aggregates
(filled triangles)
Conclusions
The process of breakage of very open and dense aggregates
was studied experimentally for aggregates composed of 90
nm and 810 nm polystyrene primary particles under
elongational flow generated using a nozzle between two
syringes. Different hydrodynamic stresses were generated
using various nozzle diameters and flow rates. The
evolution of aggregate size and structure was followed by
light scattering measurements and confocal laser microscopy,
wherever possible. It was found that the rootmeansquare
radius of gyration reduced with the number of passes
through nozzle and reached a steadystate value after about
100 passes for all cases.. In addition to the aggregate size,
morphology of the resulting aggregate showed evolution,
however, only for aggregates with initially open structures.
Starting with the open aggregates relatively dense structures
were formed at the end of the experiment for both 90 nm
and 810 nm primary particle aggregates. The mass fractal
dimension evolved from 1.7 to 2.4 0.1. So, it can be
concluded that the process involved both breakage and
restructuring. On the other hand, starting with dense clusters
the aggregate size reduced with the number of passes,
however, the aggregate morphology remain unchanged with
df=2.6 0.1, indicating only the breakage of aggregates was
driving the process. It can be concluded that the history of
the aggregates governed the evolution of the morphology.
The steadystate value of (R) when plotted against the
applied hydrodynamic stress showed scaling with the
exponent around 0.5 +0.05 for all types of aggregates,
which is in agreement with similar fractal dimension of
produced aggregates. Combination of presented
experimental methodology and Stokesian dynamics can be
used to determine appropriate particleparticle interactions
and their magnitude to better understand the breakage
process. This approach will help to improved and
generalized scaling laws under different operating
conditions for switching on or off one of the three basic
mechanisms involved in the breakage of aggregates.
Acknowledgements
This work was financially supported by the Swiss National
Foundation (Grant No. 200020126487/1).
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