2003_lin - sundararaj_erosion and breakup of polymer drops under simple shear
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E ros ion and B reakup of P o l y m e r D r o p s
Unde r S imp le S hear
in H igh V iscos i ty Ra t i o S ys tems *
BIN LIN a n d UTI’ANDARAMAN SUNDARARAJ**
Department of Chemical and Materials EngineeringUniversityof Alberta, Edmonton, Canada T6G 2G6
FREJ MIGHRI and MICHE L A. HUNEAULT
Industrial Materials Institute, National Research Council Canada
75 Boulevard de Mortagne, Boucherville, Canada J4B 6Y4
The deformation and breakup of a single polycarbonate (PC) drop in a polyethyl-
ene (PE) matrix were studied at high temperatures under simple shear flow using aspecially designed transparent Couette device. Two main breakup modes were ob-
served: (a) erosion from the surface of the drop in the form of thin r ibbons and
streams of droplets and (b)drop elongation and drop breakup along the axis per-
pendicular to the velocity direction. This is the first time drop breakup mechanism
(a),“erosion,” has been visualized in polymer systems. The breakup occurs even
when the viscosity ratio (q,.) s greater than 3.5, although it has been reported tha t
breakup is impossible at these high viscosity ratios in Newtonian systems. The
breakup of a polymer drop in a polymer matrix cannot be described by Capillary
number and viscosity ratio only; it is also controlled by shear rate, temperature,
elasticity and other polymer blending parameters. A pseudo first order decay modelwas used to describe the erosion phenomenon and it fits the experimental da ta well.
INTRODUCTION review papers of Rallison (5),Elmendorp and V a n der
olymer blends are attractive because they exhibitP etter properties than those expected from simple
mixing rules (11,yet are less expensive than synthesiz-
ing a new polymer (2).Most polymer pairs are immisci-
ble and must be blended in an intensive mixer. The
blending process controls the final morphology, which
in turn affects the properties of these blends (2).Study-
ing the deformation and breakup of a polymer drop in
a second polymer melt will help us to understand how
one polymer disperses into another, and will give
valuable insight into how the final drop distribution is
obtained.
The deformation and breakup of an solated drop in
a matrix has been studied extensively for the last
seven decades (1 8). Work in drop breakup experi-
ments and numerical simulations can be found in the
*Presented n part at: AIChEZG01 Annual Meeting 2001. Reno
* T owhom correspondence should be addressed:
electronic mail: [email protected].
Vegt (11, Stone (6),Utracki and Shi (2),and Briscoe
et al. (7),o name a few. However, most of the re-
search has concentrated on Newtonian systems. Drop
breakup in polymer-polymer systems is not well un-
ders ood.One of the first res earche rs in the ar ea of drop
breakup was Taylor. He established a small deforma-
tion theory based on Einstein’s theory for small solid
spheres suspended in a Newtonian fluid (3) .By bal-ancing the interfacial force and the shear force, he
predicted the maximum drop size that would be sta-
ble for small deformations in Newtonian fluids. He
also predicted that no drop breakup would occur
when viscosity ratio, the ratio of drop phase viscosity
to matrix phase viscosity (q,=qd/q, I , is greater than
2.5. Subsequent to Taylor’s work, special attention
was given to the drop configuration and orientation
during breakup and to the relationship between the
viscosity ratio and the critical Capillary number. The
Capillary number is a ratio of s hear force to interfacial
force (Ca=q,,,+R/T , where +is shear rate, R is drop
radius and r is interfacial tension). For Newtonian
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Bin Lin, Uttandaraman Sundararaj, Frej Mighri, and Michel A. Huneault
systems, the critical Capillary number, the flow condi-
tion where the drop deforms continuously, has been
found to correlate with the viscosity ratio of the two
phases. Grace (8)correlated critical Capillary number
with viscosity ratio and showed that a drop will not
break if the viscosity ratio is greater than 3.5 for New-
tonian systems subjected to a simple shear flow field.
In polymer systems, using twin-screw extruders orbatch mixers, it was found that drop breakup occurs
even when the viscosity ratio is higher than 3.5 (9 ,
10). The different critical breakup condition for poly-
mer systems is not surprising because polymers are
shear-thinning and viscoelastic. However, it should be
noted that twin-screw extruders and batch mixers (9 .
10) have a combination of shear and extensional flows.
Viscoelastic effects on drop breakup have also been
studied experimentally (11- 13) and using numerical
simulations (14). Other investigations studied the
effect of surfactants and the resulting change in inter-
facial tension on droplet deformation and breakup
(15)and the effect of the first normal s tress difference,N ,, for a viscoelastic drop (16-20). In most studies, it
was found that matrix elasticity helped to deform the
drops, whereas the drop elasticity resisted the drop
deformation. More recently, Mighri and Huneault (21)
visualized dispersion of viscoelastic (Boger fluid) drops
in a PDMS matrix through a transparent Couette flow
cell and found that the drops are elongated perpendic-
ular to flow direction: that is, in the vorticity direction.
They suggested that this kind of elongation is due to
the normal stresses acting along the streamlines in-
side the drop.
It should be emphasized that most of the research
work on viscoelastic systems was done at room tem-perature on polymer solutions. However, one of the
main difficulties in studying a polymer drop in a poly-
mer matrix has been viewing breakup at the high pro-
cessing temperatures and high deformation rates. Ad-
ditionally, molten polymer materials are different from
viscoelastic solutions like Boger fluids because poiy-
mer viscosity decreases with increasing shear rate.
There are a few studies on drop breakup in polymer
systems. For example, Sundararaj et al. (22, 23) stud -
ied initial blend morphology and showed that sheets
could easily be formed in a shear flow. k v i tt et al. (24)
traced polypropylene (PP) drops in a polystyrene (PSI
matrix with transparent counter-rotatingparallel platesand observed widening of drop along the vorticity di-
rection. They attributed the widening to the second
normal stress difference, N,. Hobbie and Migler (25)
and Migler et al. (26) built a pressure-driven optical
flow cell situated at the exit or die region of a twin-
screw extruder. They observed that PS drops are elon-
gated perpendicularly to the flow field in polyethylene
(PE) matrix. Mighri and Huneault (27) studied PS
drops in a PE matrix under simple shear . They found
that drop elasticity helped vorticity alignment.
It has been shown that the final morphology of poly-
mer blends develops rapidly during the blending pro-
cess: therefore, the initial morphology development of
blends is crucial in understanding the final morphol-
ogy. During the initial stages, minor phase sheets and
lamellar structures are formed followed by drop break-
up and coalescence processes (23, 28-31]. The final
morphology is developed in the first few seconds of res-
idence time in an extruder (29, 30),which is too fast to
observe the breakup process. Therefore, we visualized
breakup in a simple shear flow field for polymer-poly-mer systems to help us understand the morphoiogy
development in the initial blending stages. In this
study, we visualize a polycarbonate (PC) drop soften-
ing, deforming and then breaking up in PE matrix. The
polymer systems are subjected to simple shear flow
generated by a heated tran spa rent counter-rotating
Couette cell. Through the visualization, we saw at least
two distinctly different breakup mechanisms for poly-
mer-polymer systems under simple shear.
EXPERIMENT
Materials and Preparation
The polymer systems used were composed of drops
of PC inside a matrix of PE. All polymers were ob-
tained in pellet form. The source, commercial name,
abbreviation, average molecular weight, specific heat,
density and refractive index are given in Table 1. Two
kinds of PE of different viscosity were used: PE1 and
PE2. Three kinds of PC pellets were used: PC1, PC2
and PC3. Differential Scanning Calorimetry (DSC) was
performed using a DSC 2910 calorimeter from TA
lnstruments to obtain the specific heat capacity. The
refractive index difference between PC and PE is 0.09,
which is sufficient for visualizing PC drops in PE ma-
tri x.Dynamic rheological characterizations were per-
formed on a Rheometrics RMS800 Rheometer with a
25 mm parallel plate fucture at 10% strain. FTgure la
shows the complex viscosity of PC and PE at 220°C!;
Fig. 1b gives the elastic modulus of PC and PE at
220°C;w.c shows the viscosity ratio of the six sys-
tems a t 220°C; and Fig. I d gives the viscosity ratio for
PE2/PC2 system at 220°C and 230°C. For all the sys-
tems studied, the viscosity ratio ranged from 6 to 100
and varied slightly with frequency (or shear rate). The
interfacial tension between PC and PE is 3.18 mN/m
at 220°C and 2.56 mN/m at 230°C (32).
The PC spheres were specially prepared in DowComing 550 silicone oil heated to 210°C. Initially, one
PC pellet was c ut into about 200 small pieces with a
razor. A small PC piece was heated for 30 min in 100
mL of silicone oil. The PC softened and became spher-
ical due to interfacial forces. The temperature was
then slowly reduced below 100°C over a period of 20
minutes. During the heating a nd cooling processes, a
stirrer was used to suspend the PC particle in the
fluid. The PC drop was rinsed with heptane five times
to remove the silicone oil on the surface. The dimen-
sion s of th e s phere s were measure d using Visilog
image analysis software after imaging the spheres
using an Olympus BHSM optical microscope.
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Erosion and B reakup of PolymerDrops
Table 1. Propertiesof Polymers Used.
Polymer Commercial Molecular Specific Heat Densit y Refract ive
Name (Abbreviation) Source Weight (M,) (Cp, J/mol . K) (Pt ks/m3) Indexa
Lexan AP1300 (PC1) (25°C)b
Polycarbonate: GE Plastics 28,450 1775.6 (220°C) 1200 1.58Lexan 140 (PC2)
1794.2 (230°C) (25"C)b
Lexan 101 (PC3) (25°C)b
DMDA-8920 (PE1) (25"C)b
DMDB-8907 (PE2) (25°C)b
Scott C-24 (PS) (25Wb
Polycarbonate: GE Plastics 22,900 1200 1.58
Polycarbonate: GE Plastics 31,600 1200 1.58
Polyethylene: Petromont 53,400 2114.6 (190°C) 954 1.49
Polyethylene: Petromont 68,900 2558.3 (1 90°C) 952 1.49
Polystyrene: Styrochem 24,000 1040 1.59
aDW van Krevelen. Properties ofPolymers 2nd Ed , Elsevier Scientlflc C ompany, Amsterdam(1976)
bProvidedby supplier
Experimental Setup
The transparent Couette flow cell used consists of
two counter-rotating concentric cylinders (Fig.2).The
outer transparent cylinder is made of quartz (1.D. =
117 mm) and is heated by infrared heaters . The inner
cylinder is made of steel (O.D. = 109 mm) and is
heated by six cartridge heaters uniformly distributed
inside the cylinder. The Couette cell ha s a gap 4 mm
in width and 50 mm in height. A detailed description
of the setup can be found elsewhere (21).
The drop deformation and breakup processes were
recorded using two video camera systems: a high-reso-
lution digital camcorder [3CCD XL1, from Canon] with
a magnification macrolens and a digital chronometer;
and a h ln ix CCD camera [TMC-71 with mom attach-
ment. In the present Couette setup, the visualization
plane through the transparent quartz cylinder is the
plane containing the flow direction and the vorticity
axis. The observations were made close to the gap
center and at the mid portion of the tr ansparent cell
in order to minimize the wall and end effects.
Experimental Procedure
All polymers (PE pellets and PC drops) were dried
under vacuum at 80°C overnight before the experi-
ments . At the beginning of each run, the Couette cell
was preheate d to 125°C. The 4 mm gap was then
filled with PE pellets premixed with small amount of
thermal stabilizer, Irganox 1076 [octadecyl-3-(3,5-di-
tert-butyl-4-hydroxy-phenyl)-propionate],rom Ciba
Chemicals, and 4 to 6 PC spheres were inserted care-
fully into PE matrix. A vacuum pump was used to re-
move air from the polymer system. Then, the temper-
atu re of the Co uette device was increased to the
desired starting temperature and the matrix was al-
lowed to melt at low shear rates to achieve tempera-
ture uniformity. The drop deformation and breakup
processes were then recorded at a well-controlled
shear rate and temperature. Finally, the digital re-
cording was analyzed separately using Adobe Photo-
shop software. Drop images at well-known deforma-
tion times were grabbed, and their dimensions were
measured using SigmaScan ver. 4.01 software based
on prior calibration.
RESULTS AND DISCUSSION
Visualization
Experiments were performed by either increasing
shear rate stepwise at a constant temperature (Exper-
iment m e ) or increasing temperature stepwise at aconstant shear rate (Experiment Type 2). Figures 3-6
describe the experimental results for the tw o cases.
Fig. 3 illustrates the gap-average shea r rate profile for
Experiment 1 and Fig. 5 illustrates the tempera-
ture profile for Experiment Type 2. The average shear
rate, 9, is calculated for a power law fluid according to
the following equations (33):
Y i ++o+=-rwhere n is the power-law index in the high frequency
range: the subscript i and o are the inner cylinder and
outer cylinder, respectively; R i s the radius of the
cylinders; n ( t )=nJt) - Cl,(t) s the relative rotation
speed of the outer and inner cylinders. The marked
solid circles in Figs. 3 and 5 correspond to the experi-
mental conditions shown in the relevant photos in
Figs. 4 and 6, respectively.
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Bin Lin, Uttandaraman Sundararaj, Frej Mighri, and MichelA. Huneault
tn
an
Frequency (a), -’
(b )
Fg. . (a)Complex viscosity ofPC and PE a t 22OOC: b)Elastic modulus of F C and PE a t 220°C: c)Viscosity ratio of PEIPC systems
a t 220°C: d) Viscosity ratio ofPC2 drop in PE2 at 220°C and 230°C.
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Erosion and Breakup of PolymerDrops
(aFig. 1 . Continued.
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Bin Lin, Uttandaraman Su ndararaj , Frej Mighri, and Michel A. Huneault
Ftg. 2. Couette$ow cell setup (adapted rom ref.21).
Figure 4 shows typical images of a PC1 drop de-
forming in a PE1 matrix at 220°C for different shear
rates. The corresponding viscosity ratio, qClrs appro^-
mately constant at 15. Initially at a shear rate of 1.2
s-l , the drop looks fairly spherical (Fig. 4a), however,
it is slightly deformed to an oval shape even at the low
shear rate. I t is then deformed into a diamond-like
shape and spins like an old-fashioned top when shear
rate is increased to 8 s-l. I t maintains the diamond
LmQ)
c
u)
t
a
40
35
30
25
20
15
10
5
0
shape even at a shear rate of 23 s (Fig. 4b). Streams
of daughter droplets, cylinders and sheets coming 011
the mother drop are seen when the shear rate is in-
creased to 27 s- . The drop then becomes irregular in
shape with small daughter droplets and ribbons peel-
ing off the mother drop. When the drop softens, acloud of daughter droplets envelop the mother drop,
and the mother drop looks like a burning su n, releas-
ing thin ribbons and small streams of droplets into PI3E# 1
---1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 -
0 500 1000 1500
Time, s
Fg. . Experiment Type 1-Plot of shear rate versus timefor stepwise shear rate increase at constant temperature (T= 220°C).Thesolid circles shown on the plot correspond to the times at which the micrographs in Fg. were taken
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E r o si o n a n d B r e a k u p of Polymer Drops
Fg. . Drop deformationand erosion of a PCl drop in a PEl
matrix at 220°C with stepwise shear rate increase show n inFg. . Time and conditions or eachfiure: [a) = 0 , i.= 1.2
s - ~ ,r= 15.1: @ t =I030 , 9 = 22.6 s-’, 9,= 14.8: [c) =
1456 s . if = 28.9 s-l. r= 14.6. Note scale bar. For the mitregraphs, theflow direction is horizontal and the vorticity direc-tion is vertical
melt (Fg. c). We describe this phenomenon as “ero-
sion.” All six systems tested exhibit this erosion phe-
nomenon. This is the first time the erosion phenome-
non ha s been visualized for polymer systems.
I s erosion a kind of drop breakup? Tests done with
stepwise increase of temperature clarified this ques-
tion. Figure 6 shows a PC2 drop of 0.83 mm in diame-
ter (Fig. 6a) that deformed and eroded in a PE2 ma-tri x. Temperature was stepwise increased from 160°C
to 230”C, while the shear rate was maintained at
around 17 ssl. As temperature was increased, the
drop remained rigid with little change in shape be-
cause of the high viscosity ratio of the system (q r=
151) at 180°C. Essentially, the drop behaved like a
solid sphere in a fluid. At 210°C (q, == 30), the drop
started to deform into a diamond-like shape and at
223°C (q, = 18), he drop became more diamond-like
in shape, as shown in Fg. 6b. When the temperature
was raised to 233°C (q, = 8.81, ribbons formed and
encircled the mother drop, and the entire drop began
to soften. F‘igure 6c shows a cloud of daughter dropletsand cylinders around the mother drop with thin rib-
bons stretching out from the mother drop. Figure 6d
shows the completely softened drop with thin ribbons
and streams of daughter droplets being taken away in
the melt flow stream. The drop size is larger in Fig. 6 d
than in Fig.6a This is due to thermal expansion and
to the cloud of droplets around the mother drop that
makes the drop in Fig. 6 d appear larger. The mother
drop becomes smaller and smaller because of the loss
of mass as thin ribbons and streams are eroded from
the surface of the mother drop (Figs.6 d - 6J). Frgure 6 fshows that almost 90% of the initial drop volume has
been eroded as the drop breaks up by this mechan-ism. This new mechanism describes how a polymer
drop can be deformed and dispersed into a polymer
melt during polymer blending. It also explains how a
millimeter-sized polymer pellet breaks into micron
sized droplets.
In order to visualize more details on surface erosion,
a high magnification h ln i x CCD camera was used to
follow a PC2 drop deformation and erosion in a PE2
matrix for a stepwise increasing shear rate profile at
230°C. Typical pictures showing the evolution of drop
erosion are shown in FQ. 7. At shear rate of 13 s-l,
we observed thin layers or sheets peeling off the dia-
mond shaped mother drop, as shown in Fig. 7 a Thesesheets are broken into small dropletswithin a minute
after their formation. A cloud of small droplets and
ribbons is formed around the mother drop 5 min later
at a slightly higher shear rate of 14 s-I (Fig. 7b).These
droplets and ribbons continue to peel off the mother
drop as the latter is continuously sheared. The mother
drop decreases in volume as it erodes, or as ribbons
and small droplets peel off the mother drop.
Images of the small droplets breaking up a t even
higher magnification are displayed in Fig. 8 for a PC2
drop in a PE1 matrix. Figure 8a and Fig. 8b show
many droplets elongated in the vorticity direction
(white sausage shapes) suspended in the PE melt. The
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Bin Lin, Uttandaraman Sundararaj,Rej Mighri, and M i c he l A. Huneault
Time, s
Fig.5. Experiment Type 2 -Temperature prof& of PE meltfor stepwise temperature increase at constant shear rate (9 = 17 s- I ) . 7Xesolid circles shown on the plot correspond to the times at which the micrographs in Fig. 6 were taken.
sizes of these small droplets are in the range of 5-20pm. These droplets are much smaller than those leav-
ing the mother drop and are the result of the subse-
quent breakup of the daughter droplets. Figure 8c il-
lustrates the small threads surrounding the mother
drop schematically. The schematic is shown because
though the image (i.e. the threads surrounding the
drop) could be seen clearly in the analog video record-
ing, it was difficult to obtain clear still pictures via
digital frame grabbing. Since the micron level particles
are aligned perpendicularly to the flow direction, this
suggests that this breakup is along the vorticity axi s
and results from normal stress development inside
the PC droplets (25-27). Mighri and Huneault (27)
observed similar vorticity alignment for polyethyl-
ene/polystyrene (PE/PS)ystems. Elongated drops
and drop breakup in the vorticity direction for the
PE/PS ystem are illustrated in Figs. 9a and 9b.
Mechanisms
We have shown two kinds of breakup modes for PCdrops in a PE matrix under simple shear. The major
mechanism is erosion from the surface of the mother
drop in the form of thin ribbons and streams of small
droplets. The secondary mode is the elongation of the
daughter droplets and subsequent drop breakup
along the vorticity axis. Drop breakup occurs over the
full range of viscosity ratio studied from 6 to 60, con-
trary to empirical correlations and theoretical predic-
tions of drop breakup in Newtonian systems (3, 4, 8).
In the literature, these correlations have been extended
to polymer systems: however, it is clear from our re-
sults that the Newtonian results are not appropriate
for polymer blends.
The different breakup phenomena observed for poly-
mer systems may be due to several reasons including
the shear-thinning characteristic of polymer melts,
the existence of normal stresses in the drop and in
the matrix, and the extremely high stresses in poly-
mer systems due to the very high melt viscosity. At
low shear rates, the shear stress stretches the drop in
the flow direction and the normal stress elongates the
drop in the direction perpendicular to the flow, i.e.,
the vorticity axis. As a result, the spherical drop is de-
formed into a diamond-like shape and resembles an
old-fashioned spinning top.
When the shear rate is increased further, both forces
are increased because shear stress is proportional to
9 and normal stress is proportional to q 2 . A new com-
petition between the forces results in more irregularity
of drop shape. According to recent numerical simula-
tion work on PC2 drop breakup in a PE2melt done in
our group, the shear stress acting on the surface of
the drop is an order of magnitude more than that in-
side the drop (34).From the simulation, it was found
that the maximum shear stress of the drop surface
could reach 10 times that in the matrix phase. This
work will be elaborated upon in a future paper. If the
shear stress at the surface is much greater than that
inside the drop, and the surface of the drop is much
less viscous than in the center of the drop (due to
shear thinning), then it is reasonable that the surface
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Erosion and B re ak up of Polymer D r o p s
Ftg. 6. Drop deformation an d erosion of a PC2 drop in a PE2 matrixfor stepwise temperature increase as shown in Fg.5. Time andconditionsfor eachfigure: (a) = 0 s. T= 163"C,q r= 15.1 (9 = 1.2 S- ' t beginning of run):(b) t = 1351 s , T= 223"C, q = 17.8: ( c )t = 1632 S, T= 233"C, q r=8.8; (d) t = 1747 s. T= 233°C. q r =8.8; [e) =2075 s . T = 233"C, q r=8.8: If., t = 2356 s. T= 233"C,qr =8.8. Note scale bar.For the micrographs, theBow direction is horizontaland the uorticity direction is uertical.
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Bin Lin, Uttandaram an Sundararaj , Frej Mighri, and Michel A. Huneault
FUJ. 7. A PC2 drop deformation and erosion in a PE2 mtrix
at 230°C with stepwise shear rate increase. Time and condi-tions or each qure: [a) = 753 s, y = 12.8 s-l, q r= 8.8 and(b) t = 1006 s. y = 13.7 l . q = 8.8. Not e scale bar. For themicrographs. they ow direction is horizontal and the vorticitydirectionis vertical.
can be easily peeled off. Therefore, when the shear
rate reaches a critical value, the drop can no longer
sustain the material at the surface, and surface ero-sion begins as the drop releases ribbons and droplets
into the matrix.
We observed that the Capillary num ber decreases
when the drop size decreases as the drop continu-
ously releases streams of droplets and ribbons into
the matrix via erosion phenomenon. Therefore, the
Capillary number may not be the critical parameter to
characterize erosion: rather, a critical shea r rate may
be more relevant. Figure 10 shows the critical shear
rate for the onset of a PC drop erosion in a PE matrix
as a function of viscosity ratio (the initial drop sizes
were in the range of 0.68 to 1.10mm). The critical
shear rate increases with viscosity ratio when viscosity
ratio is less than 24 , but is almost constant a t higher
viscosity ratios. An increase of shear rate with viscos-
ity ratio is expected at lower viscosity ratios because a
critical shear stress is required to deform a fluid-like
drop. However, when the viscosity ratio is high, the
PC drop behaves even more like a solid particle inside
and ratio of the surface shear stress to the stress in-
side the drop may be even greater than 10. Therefore,the shear force needed to peel off the droplets may not
increase as greatly a t the higher viscosity ratios.
Sheets are formed at the beginning of surface ero-
sion of the mother drop. Breakup via sheets and sub-
sequent sheet breakup are effective ways to achieve
quick reduction in particle dimension (23, 35). Rib-
bons and daughte r droplets leave the mother drop
within a minute or so after the sheets are stretched
along the flow direction. These ribbons and small drop-
lets break up further to micron-size domains. This
subsequent breakup is achieved by drop elongation
and breakup in the vorticity axis. This secondary
breakup mode is also observed for PS drops in a PEmatrix (27), and is attributed to the normal stress ex-
isting in both the drops and matrix.
Erosion Kinetics
The erosion breakup phenomenon is new for poly-
mer drops in a polymer matrix, but it has already
been studied in many other fields, such as agglomer-
ate dispersion (36, 37), drug delivery (38).and rock
erosion. There are a few studies on modeling the ero-
sion process. Kao and Mason (39)proposed that the
number of spherical particles pulled off the periphery
of the agglomerate was proportional to the shear rate
in the matrix a t a given point on the surface of the ag-glomerate:
(2)
where R, is the initial agglomerate radius, R , is the
agglomerate radius at time t , k is a rate constant and
9 is the shear rate. Powell and Mason (40)presented a
second dispersion rate model for agglomerates with-
out surface tension in the form of:
R: - R: = kj+t
(3)
Both models are developed for use at short times of
agglomerate breakup, i.e., the strain, * t , is small-
less than 1000.A third model, a pseudo-first order ki -netic model, is proposed by Kenley et d. (38).based
on the degradation rate of copolymer (d,l-latidelgly-
colide) in drug delivery:
(4)
where rn, (= rn,/rn,)s the remaining mass of the co-
polymer, rn, is the initial mass, rn , is the mass a t time
t , ton s the onset time and kapps a rate constant.
The erosion of the PC drop is slow at the beginning
and some softening time is needed before a distinct
“peeling off occurs. Once the erosion starts, it lasts
fora
long period of time (20-30 min) and then after
Wm,) =- kapp x ( t - oll)
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Erosion and Breakup of Polymer Drops
Rg. 8. A P C 2 drop in a PEl matrix a t 220°C with stepw ise she ar rate increase. [a] t = 2412 s, 9 = 36.5 s-'. q r= 35.5. Smalldroplets aligned along vorticity axis; circles drawn a round af ew extended droplets; (b)Schematic illustration of small droplets in la):[c) Schematic illustration o small threads aro und the upper par t of mother drop. Note scale ba rs. For the micrographs, thejlow direc-tion is horizontal and the vorticity direction is uerticaL
Fig. 9. A PS drop in a P E 2 mabiv a t 193"C,9 =10.3 s-l. -qr= 5.2. [a) t i me = 446 s. Drop elongation dong the uorticity axis: &) time
= 476 s. Drop breakup along the vorticity axis. Note scale bar. For the micrographs, theflow direction is horizontal and the vorticity
direction is vertical.
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Bin Lin, Uttandaraman Sundararaj,Rej Mighri, and Michel A. Huneault
45
40
35
5
0
0 10 20 30 40 50 60
Viscosity Ratio (qr)
Flg. 10 Critical shear rate or PC drop erosion in PE matrix at dflerent viscosity ratios.
0.0
-0.5
-1 on
1"> -1.5Lt-
-2.0
-2.5
-3.00 200 400 600 800 1000 1200
time, s
Q. 1 1 . PE2/PC2 rosion pro$le-Semilogarithmic plot of volume remaining versus time or determination of the erosion rate.
this time, we are unable to visualize the drop since it
has become very small due to the erosion.
Rgure 1 1 plots the erosion profile of PE2/PC2 ys-
tem at 230°C.The remaining volume, which is propor-
tional to the remaining mass, is used in our case. Zero
time corresponds to the time when the temperature of
the matrix phase is 230°C and the average shear rate
is 17 s-l. We analyzed pictures taken when the drop
begins to soften and set the volume at tha t point as
the initial volume for the following calculations. For
each data point in Fig. 1 1 , we use the average size ob-
tained from 30 frames of pictures. The procedure for
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Erosionand Breakup of Polymer Drops
Table 2. Experimental Condit ions or Calculation of PE2/PC2 Erosion Rate.
Stepwise temperature increase at
Time drop was kept at dif ferent temperatures (s)
Stepwise shear rate i ncrease at
Time drop was kept at di fferent shear rates (s)
9 ~ 1 7 s - l T =230°C
Exp. No. 160°C 180°C 200°C 220°C 230°C 13 s-l 14 S- l 17 - 18 S-'
#I 232 189 288 98 828.8 - - -#2 230 200 246 276 1050
- 159 400 7503
- - -- - -Table 3. Kineti c Constants or PEUPC2 Erosion at 230°C.
Exp. No. kaDD SD (s-l) to n2 SD(s) R e
#1
#2#3
Mean t SD
0.0040% 0.00010.00392 0.00010.00392 0.00010.0039? 0.0001
366 5 7363 i 12373 t 3368 5 7
0.9920.9860.994
=From east-square inear regression01 In(V,) =- kapp(t-ton)
volume determination is as follows: (a) measure the
drop area using image analysis; (b)calculate the equiv-
alent diameter of a circle with the same area; and (c)
calcula te the remaining volume of the drop by assum-
ing the drop is spherical. Three se ts of experimental
data: Exp. #1 , #2 and #3 , are presented and the exper-
imental conditions are shown in Table 2.
We fit the experimental data to the first two models
an d found significant deviations pe rhaps because of
our long shearing time and thus, large strains. How-
ever, the erosion rate of PC drop can be described by
the two parameters model proposed by Kenley et al.
(38).We modified E q 4 with the volume remaining (Vr,
defined as V,/V,, where V, is the volume at time t and
V is the initial volume) by assuming the density is
constant a t the test temperature. The kappwas calcu-
lated using least square regression of the decay of the
relative volume:
In(Vr) =- kWpx ( t- on) (5)
The solid line in Fig. 1 1 is the model fit to the data,
and T a b l e 3 lists the determined model parameters for
the three sets of experiments. The result s suggest the
model fits the PC drop erosion well. The apparent
decay rate for the experiments are the same (kwp =0.0039 ? 0.0001) for the three different runs of PE2/
PC2 performed at T = 230°C and +F= 17 s-l. The
onset time is also found to be similar for the three ex-
periments ( ton= 368 i 7 s ) , uggesting that a partic-
ular softening time is needed to initiate the surface
erosion phenomenon.
CONCLUSIONS
Two modes of breakup were visualized for PC drops
in PE matrix undergoing simple shear flow generated
by a transparent Couette device: (a) surface erosion
from the drop in the form of thin ribbons an d streams
of droplets and (b)drop elongation and drop breakup
along the axis perpendicular to the velocity direction,
i.e., in the vorticity direction. This is th e first time that
drop breakup mechanism (a) has been visualized in
polymer systems. Despite the fact there is an abun-
dance of literature indicating that there is no drop
breakup above qr >3.5, we viewed drop breakup at
viscosity ratios higher than 6 up to viscosity ratio of
60. The rule that no drop breakup occurs in simple
shear flow at qr >3.5 does not hold for polymer sys-
tems.
I t was also observed that sheets form at the begin-
ning of the drop surface erosion. Sheet breakup pro-
vides an efficient and rapid reduction in the dimen-
sion of the drop size since the sheets ar e on the order
of 1 pm thick, and when they break up, they create
drops 1.000 times smaller than the initial drop size.
Surface erosion is the primary breakup mode for the
present systems: the mother drop slowly shrinks by
giving off streams of sheets, cylinders a nd daughter
droplets. The daughter droplets are able to break up
again until a drop size on the order of microns is
achieved. This secondary breakup takes place by drop
stretching perpendicular to the flow direction as a re-
sul t of the normal stre ss.
A pseudo-first order decay kinetics was applied to
describe the drop erosion phenomenon. The onset
time and the apparent decay rate for PE2/PC2 system
at 230°C show that the kinetic model is appropriate
for PC drop erosion in PE matrix.
ACKNOWLEDGMENTS
We would like to thank the Natural Sciences and
Engineering Research Council of Canada for support-
ing this research.
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