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

POLYMER ENGINEERING AND SCIENCE, APRIL 2003, Vol. 43, No. 4 891



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.

892 POLYMER ENGINEERING AND SCIENCE, APRIL 2003, Vol. 43, No. 4



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.




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.

a94 POLYMER ENGINEERING AND SCIENCE, APRIL 2003, Vol. 43, No. 4



Erosion and Breakup of PolymerDrops

(aFig. 1 . Continued.

POLYMER ENGINEERING AND SCIENCE, APRIL 2003, Vol.43,No. 4 895



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

896 POLYM ER ENGINEERING AND SCIENCE, APRIL 2003, Vol. 43, No . 4



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

POLYMER ENGINEERING AND SCIENCE, APRIL 2003, Vo l. 43, No. 4 897



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

898 POLYMER ENGINEERING AND SCIENCE, APRIL 2003, Vol. 43, No. 4



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.




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)

900 POLYMER ENGINEERING A ND SCIENCE, APRlL 2003, Vol.43, No. 4



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.




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

902 POLYMER ENGIN€ERING AND SCE NC €, APRIL 2003, Vol. 43, No . 4



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.

POLYMERENGINEERING AND SCIENCE, APRIL 2003, Vol. 43, No . 4 903



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