7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 – June 4, 2010
Lagrangian Particle Tracking of Aggregate Breakage
D.Saha∗, B. Lüthi∗, M. Holzner∗, M. Soos†, A. Liberzon‡, A. Tsinober‡ and W. Kinzelbach∗
∗
Institute of Environmental Engineering, ETH Zurich, 8093 Zurich, Switzerland
†
Institute of Chemical and Bio Chemical Engineering, ETH Zurich, 8093 Zurich, Switzerland
‡ School of Mechanical Engineering, Tel Aviv University, Ramat Aviv 69978, Israel
debashish.saha@ifu.baug.ethz.ch
Keywords: Lagrangian particle tracking, strain, colloid, agglomerate, breakage
Abstract
An experimental investigation has been carried out of the breakup of statically grown polystyrene latex of arbitrary
shape and size subjected to a laminar extensional flow. Three dimensional particle tracking velocimetry (3D-PTV), a
non intrusive Lagrangian flow diagnostic technique, was employed to gain flow field characteristics but also to track
the motion of colloids and detect their breakup. Extensional flow was made to emerge from an axially symmetric test
section converging to an orifice of 3 × 3 mm2. It is found that flocs were broken apart in the high strain zone that
extends 2 mm from the outset of the orifice to approximately 35 mm inside the orifice. The feasibility of detecting
breakage events from the observed particle trajectories is tested.
Introduction
Colloids are constellations of tiny particles on the or-
der of micron scale. Aggregation and breakage of col-
loids are quite prevalent phenomena in a variety of flows
spanning from industrial processes such as crystalliza-
tion, separation and reaction in multi phase systems to
environmental flows like the bio geochemical cycle of
marine colloid and transport of toxic elements.
The coagulation mechanism of particles in solutions
has been studied to significant extent and clarified fairly
well by Hunter et al. (1987) while the breakup mecha-
nism of coagulated particles, especially large aggregates
of arbitrary shape remains poorly understood up to now
as reported by Soos et al. (2008). Detailed knowledge
of the turbulent flow field around a moving colloid dur-
ing its breakage is essential to understand the physical
mechanism of the underlying process. Therefore, it is
necessary to have complete access to the properties of
the turbulent flow around the colloid before, during and
after its breakage. In other words we need to know the
full Lagrangian history of the fluid flow field and of
the colloid motion. This means the experimental tool
has to be capable of tracking the colloid along its La-
grangian trajectory and at the same time to provide the
full information about velocity gradients in its proxim-
ity. Recently, Luethi et al. (2005) developed a technique
to measure all the nine components of the velocity gra-
dient tensor in a turbulent flow field via 3D-PTV. Our
aim is to apply this technique to analyze colloid breakup.
Before analyzing the effect of turbulence, the problem of
breakage is investigated in a simple flow, i.e. in a lami-
nar flow converging to an orifice of 3 × 3 mm2. This is
what we intend to do in this proposed work by using the
Lagrangian measurement technique of 3D-PTV.
Extensive efforts have been invested from both ex-
perimental and simulation side for in depth analysis of
breakage dynamics of a variety of flocs under various
flow conditions. Different theoretical propositions and
experimental tools were surfaced over the decades to
gain an unequivocal interpretation of aggregate break-
age. As for the experimental investigations, Sonntag
and Russel (1986), Higashitani et al. (1991) and Blaser
(2000) performed (theoretical and experimental) stud-
ies on breakup of latex flocs subjected to a contraction
flow. Sonntag and Russel and Higshitani et al. ob-
tained the size of the broken flocs as a function of exten-
sional rates in converging flows. Also, Higashitani and
Blaser conducted directly observed breakup and defor-
mation of flocs formed with polymeric and precipitated
coagulants. They found that flocs were disrupted at the
close vicinity of the inlet of an orifice because of the
extremely high elongation rate. Parker, Kaufman and
Jenkins (1972) investigated the breakup mechanism in
shear flows and clarified that aggregates exhibit not only
surface erosion of constituent particles from the parent
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7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 – June 4, 2010
aggregates but also splitting of a parent aggregate into
smaller fragments.
As for theoretical investigations, various methods
have been proposed to predict the floc behavior in flows.
Adler and Miles (1979) performed a calculation to ob-
tain the critical size of aggregates in shear flow, approx-
imating the spherical aggregate as a porous body. The
relative motion between a pair of spherical particles in
flows has been investigated extensively by Batchelor and
Green et al. (1972) but only few studies are performed
on the behavior of coagulated particles. Doi and Chen
(1989) proposed the sticky-sphere model for the motion
of coagulated particles. In this model the Stokes’ hy-
drodynamic drag force was assumed to act on all the
particles comprising the aggregate, even though in re-
ality they are not necessarily all exposed to the flow di-
rectly. Hence this model is applicable only to flocs com-
posed of a small number of particles in which almost
all particles are exposed directly to the fluid. Bossis and
Brady (1984) proposed the Stokesian dynamics in which
the hydrodynamic movement of individual particles in a
floc is calculated rigorously. But this method requires an
extremely long computational time to simulate the 3D
movement of a sufficiently large floc.
Measurements addressing breakage have been per-
formed in various types of flows. Sonntag and Russel
(1986) performed their experiment in simple shear flow,
Blaser (2000) employed 2D straining flow generated in
four roll mill apparatus, Kobayashi (1999) used exten-
sional flow generated by a sudden contraction of a pipe
exemplify the effort to get a comprehensive insight of
the dynamics. Glasgow et al. (1982) and Soos et al.
(2008) studied turbulent jets and a stirred tank equipped
with different types of impellers. Stirred tanks operated
under turbulent conditions are closest to the industrial
conditions. However, up to now there is no direct study
of the three dimensional breakage event because experi-
mental techniques were not developed sufficiently to of-
fer the required resolution allowing the observation of
the motion of the particles of small size and simultane-
ously accessing the details of the turbulent flow field car-
rying them.
Therefore the intricacy of the problem clearly pushes
the choice towards the units operating under laminar
conditions where a narrower distribution of the hydro-
dynamic stress exists, e.g., Blaser et al. (2000) con-
ducted an experiment in rheometers and four roll mills.
Kobayashi et al. (1999) made an experiment in contract-
ing nozzles. The contractile flow was found to be ef-
fective in the breakup of flocs. Contractions in flow
are typical situations where high velocity gradients oc-
cur and therefore contribute to the breakup of flocs. In
the contractile flow, flocs near the centerline and wall
will be broken by the elongational and shear stresses
respectively as concluded by Higashitani et al. (1991).
Moreover implementing high speed cameras enables the
detection of individual breakage events. Glasgow and
Hsu (1982) and Liu and Glasgow (1997) applied this
method to study the breakup of aggregates in turbulent
jet (600>Rejet>5400). The objective of their study was
to observe the disintegration of the individual flocs pho-
tographically and deduce the magnitude of the force re-
quired to produce the break up. It was attempted to mea-
sure the gradients of the flow field and track the colloid
as well as the broken fragments simultaneously.
In the present experimental effort we deal with stati-
cally grown polystyrene latex aggregates. However, due
to the technical limitations outlined in detail below, ag-
gregates and aggregate fragments have to be relatively
large (several tens of microns). The prime purpose of the
present work is to substantiate our notion of the break-
age behavior through a relatively simple experiment in
laminar flow by employing sophisticated imaging hard-
ware like high speed cameras, strong illumination source
(laser), as well as generic optical elements (lens, beam
expander, pi shaper etc.) alongside with the conventional
laboratory equipments like pumps. On this course, we
attempt to carefully orchestrate the existing 3D-PTV al-
gorithm in a way to enhance its ability i.e., to make the
code realize the breakage event visible in reality with
high accuracy. This will certainly advocate the compe-
tence and utility of 3D-PTV as a reliable tool not only
for tracking a lonely particle in a flow but also to track
detached particles from the original one. First we as-
sess the feasibility to track breakage. Flow field and gra-
dients are studied separately and thereafter we proceed
to extend our understanding of breakage based on a al-
ready well perceived laminar flow field which will pave
the way for further analysis in increasingly complicated
turbulent flow close to realistic environment.
Materials and Methods
3D-PTV
3D-PTV (Three dimensional particle tracking ve-
locimetry) is a non intrusive Lagrangian flow measure-
ment technique. 3D-PTV can be divided into two ma-
jor parts: determination of particle positions in space
coordinates and tracking of individual particles in time.
Through a stereoscopic principle and careful calibration
of the camera position and orientation, 3D positions are
computed from 2D images of the tracer particles . This
is very similar to what our eyes do in daily life to judge
distances and positions of objects and persons. Individ-
ual particles from the object space are recognized into
the image space of the camera. This is referred to as
detection phase. Then in the correspondence phase, 2D
particle coordinates of the species are linked in 3D carte-
2