Chemical Engineering Science 57 (2002) 3415–3426www.elsevier.com/locate/ces

Degassing of molten polymersI. Gestring ∗, D. Mewes

Institute for Process Engineering, University of Hannover, Callinstr. 36, 30167 Hannover, Germany

Received 6 August 2001; received in revised form 5 November 2001; accepted 5 November 2001

Abstract

Degassing is a key-step in polymer processing. Low-molecular-weight components are removed from a polymeric system. The transportof these components takes place by di3usion to the polymer–vapour interface. This interface can be formed by free surfaces of single-phasepolymer melts or by bubbles. In this study, the transport with and without bubble nucleation is investigated independently from each otherin a special designed apparatus similar to a degassing extruder.The mass transport in thin 5lms and in rotating pools with surface renewal is measured. High surface renewal rates and thick 5lms

enhance the mass transfer for single phase 7ow and bubbly 7ow. Dimensionless mass transfer coe8cients are given as a function ofthe surface renewal rate, the area of the free surface and the total mass of the polymer. The conditions for bubble nucleation and foamformation are investigated. The bubble nucleation is observed in the rotating pool in the area of high shear velocity. ? 2002 ElsevierScience Ltd. All rights reserved.

Keywords: Di3usion; Foam; Mass transfer; Multiphase 7ow; Polymer processing; Extruder

1. Introduction

If the polymerisation reaction is stopped unreactedmonomers, solvents or impurities still remain in the poly-mer. These components must be removed in order to obtainspeci5c material properties with very low monomer con-centrations. The degassing step during polymer processingoften requires expensive equipment. Therefore, it is nec-essary to have a detailed knowledge about the degassingprocess in order to reduce costs.The concentration range of the volatiles, which have to

be removed, is from several ppm to several tens of percent.For the degassing step a large variety of equipment is usedwhich can be classi5ed into two main categories: rotatingdegassers, like vented extruders or thin 5lm evaporators andstill degasser like 7ash evaporators.Two dominant mass transfer mechanisms exist. On the

one hand a mass transfer process takes place due to a con-centration gradient close to the exposed polymer surface. Inrotating degassers the mass transfer occurs at the polymer–vapour interface of rotating pools in front of scrapers orwipes and in thin 5lms. The surface of pool and 5lm ispermanently renewed. The result of the convective

∗ Corresponding author. Tel: +49-511-762-3820;fax: +49-511-762-3031.

E-mail address: gestring@ifv.uni-hannover.de (I. Gestring).

transport in pool and 5lm is an increase in the concentrationgradient, this enhances the mass transfer and so the processe8ciency. On the other hand bubbles of the volatile compo-nent are nucleated under speci5c conditions in the polymer.The bubbles grow, coalesce and reach the polymer–vapourinterface, where they rupture and release the volatiles to thegas phase. This process is known as foam degassing. Be-cause of the large internal surface area of the foam, this kindof degassing process is more e8cient than single-phase 7ow.The polymer melt is heated by energy dissipation. The

mechanical energy of the rotating equipment is dissipated inviscous heating of the polymer. The highest shear rate andso the highest energy dissipation is in the gap between theblade and the barrel of the extruder. The rise in temperatureof the polymer can destroy the polymer chains. The lowmolecular component evaporates out of the free surfaces ofthe polymer melt. This results in a decrease in temperature.In order to obtain a temperature pro5le along the screwchannel, which ensures a good degassing process, the barrelis heated or cooled. The rate of evaporation cooling andviscous heating depends on the 7ow regime.Bubble free mass transfer in vented one- or twin-screw

extruders has been studied by several researchers (Latinen,1962; Coughlin & Canevari, 1969; Roberts, 1970; Collins,Denson, & Astarita, 1985; Secor, 1986). Bubble free masstransfer occurs if the pressure of the gas phase exceeds the

0009-2509/02/$ - see front matter ? 2002 Elsevier Science Ltd. All rights reserved.PII: S 0009 -2509(02)00207 -5

3416 I. Gestring, D. Mewes / Chemical Engineering Science 57 (2002) 3415–3426

vapour pressure of the volatile component. In front of thescrew a pool is formed. At the barrel wall a thin 5lm ex-ists. The volatile component di3uses through the polymergas–interface into the continuous gas phase. This gas phasecan be formed by the volatile component itself or by a gasmixture. The free surfaces are permanently renewed, poly-mer from the inside of the pool reaches the free surface. Themass transfer during this surface renewal can be describedby the penetration model. In this model it is assumed thatthe concentration of the volatile component is homogenouswithin the polymer. A concentration gradient exists only atthe free surface. Latinen (1962) studied the degassing pro-cess in a single-screw extruder. He calculates the degassinge8ciency with the penetration model. For longer screws thecalculated mass transfer exceeds the experimentally inves-tigated mass transfer. He concludes that the mixing of thepolymer melt in the single-screw extruder is insu8cient toachieve a homogeneous concentration 5eld of the volatilecomponent in the polymer. This results in smaller concen-tration gradients at the free surface and so in a smaller masstransfer. Collins et al. (1985) calculate and investigate ex-perimentally mass transfer coe8cients in vented twin-screwextruders. The predicted rates of mass transfer are higherthan measured ones. They conclude that the surface area formass transfer is smaller than the value calculated on the ba-sis that continuous 5lms are formed on the surfaces of thescrews and the barrel wall. The free surfaces are di8cultto predict. They depend on the screw geometry, the degreeof 5lling, the screw speed and the viscosity of the polymer.Wang, Sakai, and Hashimoto (1995) present a model withwhich the interface areas and their surface renewal timescan be calculated.Another mechanism with higher mass transfer rates is the

degassing during bubbly or foaming 7ow. This mechanismconsists of the step bubble nucleation, grow, coalesce andrupture. The degassing with foam formation is done undervacuum. Due to bubbles the internal surface of the foamis large. This increases the mass transfer rates. For bubblenucleation the vapour pressure of the volatile component ina binary mixture with the polymer must exceed the pressureof the gas phase. In addition stripping agents can be used.These agents also form bubbles and enlarge the surface of thefoam. These components reduce the partial vapour pressureof the volatile component in the gas phase and increase thethermodynamic driving force for mass transfer. As strippingagents water, nitrogen or carbondioxide can be used.Bubble nucleation in polymers di3ers from bubble nu-

cleation in low-molecular liquids. In order to achieve bub-ble nucleation of toluene in stagnant polystyrene the vapourpressure of toluene must exceed the gas pressure about10 times depending on the polystyrene concentration (Han& Han, 1990a,b). This high degree of supersaturation canbe lowered by the deformation of the polymer. Han andHan (1988) observe bubble nucleation of refrigerants inpolystyrene even at unsaturated conditions in a shear 7ow5eld. Biesenberger and Lee (1986b) assume that gas is avail-

able in pre-existing heterogeneous cavities of particles in thepolymer. If the pressure is reduced the nuclei swell in sizebut remain in stable equilibrium with the polymer, althoughthe polymer might be supersaturated. The gas is detachedfrom the particle by shear. A free unstable bubble is pro-duced. The in7uence of shear stress and acoustic 5elds whichcause high frequency stretch-compression stresses within inthe polymer is studied by Albalak, Tadmor, and Talmon(1987, 1990) and Tukachinsky, Talmon, and Tadmor (1993,1994). They observe vigorous foaming when the polymeris deformed by ultrasound or shear stress. The size and theform of the bubbles in the polymer is studied. Near visi-ble bubbles of 100 �m blisters of smaller size are found.Favelukis, Tadmor, and Semiat (1999) studied the bubblenucleation in a Couette apparatus. They postulate a criticalshear rate at which the nucleation process starts.The mass transfer of the volatile component from the

polymer to the gas phase is completed when the bub-bles burst at the interface to the gas phase. This kind ofmass transfer is studied by Biesenberger and Lee (1986a,1987, 1989) in a special designed apparatus. The changein concentration of a refrigerant in polydimethylsiloxane ismeasured for foam degassing for di3erent parameters. Highrotation speeds and so high shear stress result in intensivefoaming. This increases the mass transfer. Biesenbergerand Kessidis (1982) made experiment in a single-screwextruder with and without bubble nucleation. They foundthat devolatilisation with bubble nucleation is much moree8cient than without. Foster and Lindt (1989, 1990) ob-serve the foaming of ethylbenzene in polystyrene in acounter-rotating non-intermeshing twin-screw extruder. Thepolystyrene foams in the 5rst part of the degassing zone.The mass transfer is controlled by bubble growth. The chan-nels of the partially 5lled degassing zone have a restrictedvolume. Bubbles compete with polymer for that volume.If bubbles are constrained in their growth because of thelimiting volume the mass transfer decreases. High masstransfer rates are achieved for unconstrained foam expan-sion. Yang, Smith, Bigio, and Anolick (1997a,b) develop amodel to calculate the mass transfer during foam-enhanceddegassing. In contrast to Chella and Lindt (1986) they donot need the initial number and size of bubbles to calcu-late the mass transfer. Instead they use the foam-volumeexpansion and the time of degassing for their model.

2. Experimental set-up

The object of the experimental study is to measure themass transfer during the degassing with and without bubbleformation. The mass transfer out of a rotating pool and thin5lms can be measured independently from each other. Thisis not possible in industrial used equipment. Therefore aspecial designed apparatus is used.In Fig. 1 a schematic sketch of the apparatus is given.

A drum rotates coaxially around a 5xed inner barrel. In

I. Gestring, D. Mewes / Chemical Engineering Science 57 (2002) 3415–3426 3417

Fig. 1. Schematic sketch of the special designed equipment.

Fig. 2. Photo of the drum.

front of a blade, a circulating pool is created. Due to asmall gap between the blade and the drum a thin 5lm isformed at the inner surface of the drum. The ratio of thediameters of the inner and the outer cylinders is 1.7, whichis similar to that of barrel and screw of a degassing extruder.The drum is made of transparent polymethylmethacrylateto make visual observations possible. A photograph of thedrum is given in Fig. 2. The bubble-free degassing is studiedunder atmospheric conditions by pumping nitrogen throughthe drum. Because of the atmospheric pressure in the drumbubble nucleation is not possible. The volatile componentdi3uses into the nitrogen because of the low partial pressureof that component in the gas phase. Nitrogen enters thedrum through a drilled hole in the 5xed shaft and leavesit through another hole. The mass transfer of the 5lm andthe pool can be measured independently from each other bycovering the 5lm or the pool with a seal. Nitrogen is then7owing just over the 5lm or the pool. The mass 7ow ofnitrogen and the concentration of the volatile component innitrogen are measured. With this information the mass 7owof the volatile component out of the polymer and so the

Fig. 3. Photo of the drum with foam formation.

degree of separation can be calculated. The melt temperatureis measured with a Pt100 element at the inner cylinder nearthe blade.The bubble nucleation and foam formation experiments

are done under vacuum. The drum is connected via a valveto a tank. This tank is evacuated, its volume is 80 timeslarger than that of the drum. After the valve is opened and sovacuum applied to the drum, the rotation of the drum starts.The mass 7ow of the volatile component out of the polymermelt is measured by the increase in pressure of the tank.The bubble nucleation and foam heights are videotaped. Aphotograph of the foaming polymer in the drum is given inFig. 3.The experimental investigations are carried out for room

temperature. Therefore polydimethylsiloxane is used as thepolymer. Polydimethylsiloxane is liquid for room tempera-ture and available in di3erent viscosities. N -pentane is usedas the volatile component. The varied parameters of the ex-perimental investigations are given in Table 1.The temperature is for all experiments 22:0◦C and the

vacuum pressure was set constant to 20 mbar.

3. Bubble free mass transfer

The mass transfer rate out of a stagnant free surface dueto di3usion can be calculated by

M =

√D�t(c − ceq)A: (1)

A is the free surface,D the di3usion coe8cient of the volatilecomponent, t the total time, c the concentration and ceqthe equilibrium concentration. Eq. (1) is only valid for anin5nite depth and a constant concentration within the liquid.The time interval a 7uid element spends at the free surfaceis called surface renewal time. Integrating Eq. (1) over thistime yields to

Mf =1tf

∫ tf

0M dt = 2

√D� tf

(c − ceq)A: (2)

3418 I. Gestring, D. Mewes / Chemical Engineering Science 57 (2002) 3415–3426

Table 1Parameters of the experimental investigations

Name Value 1 Value 2 Value 3

Rotation speed 0:167 rounds=s 0:50 rounds=s 1:00 rounds=sViscosity at 25◦C 10 Pas 50 Pas 100 PasFilm heights 0:2 mm 1:0 mm 2:0 mmDegree of 5lling 5.5% 16.7% 25.0%Mass fraction pentane 0.01 0.04 0.07

0 20 40 60 80 1000.5

0.6

0.7

0.8

0.9

1.0

n=1.0 s−1

n=0.5 s−1

n=0.167 s−1

η0= 50.0 Pas

ξ0 = 0.04

h = 1.0 mm

M0 =125.0 10−3 kg

m2/kg s0.5

dim

ensi

onle

ss

conc

entr

atio

nξ* =

ξ(t)

-ξeq

/ξ0-

ξ eq

EK=(AFilm

/tFilm

0.5+APool

/tPool

0.5)/M0 t

Fig. 4. Change in dimensionless concentration as a function of the degassing number for di3erent rotation speeds.

This equation is only valid if the polymer is homogeneousmixed after every rotation. It is known as the penetrationmodel for a one-dimensional case. Sometimes 5lms are onlytens of a millimetre thick. The concentration of the 5lm atthe other side of the free surface may not decrease duringthe surface renewal time. This can be expressed by

c(tf; h)− ceqc0 − ceq

= erf

[h

2√Dtf

]¿ 0:99: (3)

c(tf; h) is the concentration at the inside of the 5lm at thesurface renewal time, c0 is the uniform concentration of the5lm when the degassing of the 5lm starts. Solving Eq. (3)to the Fourier-number yields to

Fo =tfh2=D

¡ 0:1: (4)

The penetration model is only valid for Fo¡ 0:1. The masstransfer coe8cient of Eq. (2) is

� = 2

√D�tf

: (5)

A dimensionless version of the mass transfer coe8cient canbe given by the Sherwood-number. Together with the length

of the free surface L the Sherwood-number is given by

Sh=�LD= 2

√L2

�Dtf=

2√�

√wL�

�D=

2√�

√Re Sc: (6)

In this equation w is the velocity of the 5lm, � the kine-matic viscosity, Re the Reynolds-number and Sc theSchmidt-number. The product of the Reynolds-number andthe Schmidt-number is also known as the Peclet-number Pe.The change in the dimensionless mass fraction of the pen-

tane

�∗ =�(t)− �eq�0 − �eq

(7)

is presented as a function of the degassing number

EK =

Af√tf+ Ap√

tp

M0t: (8)

Af and Ap are the free surfaces of the 5lm and the pool andtf and tp the surface renewal times, M0 is the total massof the polymer and t the total time. The free surface of thepool depends on the viscosity and the rotation speed of thedrum. For high rotation speeds and high viscosities the freesurface of the pool becomes more curved which results inan increase in area of the surface.In Fig. 4 the change in concentration is given for di3erent

rotation speeds of the drum as a function of the degassing

I. Gestring, D. Mewes / Chemical Engineering Science 57 (2002) 3415–3426 3419

h=0.2 mm h=1.0 mm h=2.0 mm

η0=50.0 Pas

ξ0=0.04

m0=130.0 10−3 kg

n=0.5 s−1

m2/kg s0.5

dim

ensi

onle

ssco

ncen

trat

ion

ξ* =ξ(

t)-ξ

e/ξ 0-

ξ e

EK=(AFilm

/tFilm

0.5)/m t

1.0

0.9

0.8

0.7

0.6

0.50 20 40 60 80

Fig. 5. Change in dimensionless concentration as a function of the degassing number for di3erent 5lm heights.

Fig. 6. Concentration 5eld of the pool for mass transfer out of the 5lm.

number. The experiments with the di3erent rotation speedslast 400 s each. With higher rotation speeds the time of a7uid element at the free surface decreases. That means ahigher mass transfer as indicated in Eq. (2). So the concen-tration is lowest for the highest rotation speed after 400 s.All curves have the same shape. So the concentration is in-verse proportional to the surface renewal time as indicatedby the penetration theory.In Fig. 5 the change in concentration is given for dif-

ferent 5lm heights for mass transfer out of the 5lm. Thepool is covered with a seal. For each experiment Fo¡ 0:1is valid. The concentration of the 5lm at the inside of thedrum should not decrease during the surface renewal time.

After 400 s the concentration is lowest for the thickest 5lm.One prerequisite for the penetration model is that the 5lm iscompletely mixed after every rotation with the pool. In Fig.6 the numerically calculated concentration 5eld is shown formass transfer out of the 5lm. The calculation is done by thecomputational 7uid dynamics program CFX 4.4. The high-est concentration is in the inside of the pool, the 5lm hasthe lowest concentration. Film and pool are not completelymixed. The concentration gradient at the free surface is lowand so is the mass transfer. Thicker 5lms are better mixedwith the pool and so the mass transfer is higher.The degassing process in this special designed appara-

tus is instationary. In order to compare the experimentally

3420 I. Gestring, D. Mewes / Chemical Engineering Science 57 (2002) 3415–3426

Table 2Calculated and experimentally investigated Sherwood-numbers

Penetration theory Experiment

� �theo = 2

√D�tf

�exp =M ar

�(�− �eq)ln(Af + Ap)

Sh Shtheo =�LD =

√4�D

[√L2ftf+

√L2ptp

]Shexp =

�exp(LF + Lp)D

investigated results with stationary working machines, ex-perimentally investigated Sherwood-numbers are comparedto calculated ones. This is given in Table 2.M ar is the arithmetic mean mass 7ow of pentane out of

the drum. The di3usion coe8cient is calculated with the freevolume theory from Duda, Vrentas, Ju, and Liu (1982) to4:20 × 10−10 m2=s for a temperature of 22:0◦C. This valuecoincides with the experimentally investigated value fromBarrer, Barrie, and Raman (1962). They measure the dif-fusion coe8cient to 4:35 × 10−10 m2=s for a temperatureof 25◦C. In Fig. 7 the Sherwood-numbers are plotted as afunction of the Reynolds–Schmidt numbers. In Eq. (6) theSherwood-number calculated by the penetration theory isgiven by

Shtheo = 1:128√Re Sc: (9)

The measured values are given by

Shexp = 0:38√Re Sc: (10)

The factor of 0.38 characterises the incomplete mixing of5lm and pool. The measured values are three times smallerthan by the penetration theory predicted. If mass transferoccurs only out of the pool the penetration theory is valid.Then the 5lm is sealed, the mixing of pool and 5lm is

0.0 0.2 0.4 0.6 0.8 1.0-6

-5

-4

-3

-2

-1

0

1

2

.

shear velocity

supersaturation

x*=1

x*=0

s−1104 Pa

n=0.16 s−1

n=0.50 s−1

n=1.00 s−1

ηo=50 Pas

pvac

=2,000 Paξ=0.04, h=1 mm

she

ar

velo

city

γ

dimensionless lenght x*

supe

rsa

tura

tion

∆ p=

p S-p

gas

0

100

200

300

400

500

600

Fig. 7. Supersaturation and shear velocity along a streamline near the drum.

not important. Mass transfer out of the pool takes place for

√Re Sc¡ 5000: (11)

Collins et al. (1985) calculate and measure mass transfercoe8cient in vented extruders. The measured values alsodi3er from the values obtained by the penetration theory bya factor of 3.

4. Bubble formation

One necessary condition for bubble nucleation is thesupersaturation of the polydimethylsiloxane. The poly-dimethylsiloxane is supersaturated if the vapour pressure ofn-pentane pS exceeds the pressure of the gas phase pgas

Pp= pS − pgas: (12)

With the Flory–Huggins equation (Flory, 1953) the vapourpressure of pentane can be calculated in a binary mixturewith polydimethylsiloxane by

lnpSp0S

= ln S + (1− S) + !(1− S)2: (13)

p0S is the vapour pressure of pure pentane, S is the volumefraction of pentane and ! is the Flory–Huggins parame-ter. This parameter is given by Chahal, Kao, and Patter-son (1973) to ! = 0:40 for a temperature of 20◦C. TheFlory–Huggins parameter is a function of temperature andconcentration. These changes are small during the experi-ments, so the parameter is set constant. With Eq. (13) theequilibrium concentration of pentane in polydimethylsilox-ane can be calculated as a function of the pressure of thegas phase.

I. Gestring, D. Mewes / Chemical Engineering Science 57 (2002) 3415–3426 3421

Fig. 8. Pressure 5eld of the pool.

0 5 10 15 20 25 30 350

10

20

30

40

50

penetrationtheory

experiment

103

103

film+pool

n=1.0 s−1film+pool

n=0.5 s−1

film+pool

n=0.167 s−1

pool

n=0.5 s−1

film

n=0.5 s−1

Sh=

β L/

D

(Re Sc)0.5=(L2/tf,p

D)0.5

Fig. 9. Sherwood-numbers as a function of Re Sc.

For a mass fraction of pentane of 0.04 and a temperatureof 22◦C the vapour pressure of pentane in polydimethyl-siloxane is 132 mbar. So the pressure of the gas phasemust be smaller than this pressure. For degassing withbubble nucleation the drum is evacuated with a vacuumpump.For studying the bubble nucleation and the foam forma-

tion process of the pool, polydimethylsiloxane is carefully5lled into the drum, avoiding any air bubbles in the melt.These bubbles are potential nucleation sites. By varying theconcentration of pentane and the pressure level, di3erent de-grees of supersaturation can be applied. If vacuum pressuresare applied to the drum without rotation no bubbles can beobserved, although the supersaturation is varied between20 and 500 mbar. After the rotation has started bubblesare nucleated immediately at the inside of the drum. Thisis even valid for viscosities of the polydimethylsiloxaneof 100 Pas.

In Fig. 8 the numerically calculated pressure 5eld andthe stream lines are shown. The calculation is done bythe computational 7uid dynamics program CFX 4.4. Thepressure increases from the free surface to the blade. Anincrease in pressure results in a decrease in supersaturation.The supersaturation is highest next to the free surface. Theshear velocity and the supersaturation are given in Fig.9 for di3erent rotation speeds along a stream line. Thehighest shear velocity is observed in front of the blade butthere is also the lowest supersaturation. Therefore, bubblenucleation only can take place in the area of the drum nextto the free surface. This coincides with the visual observa-tions as shown in Fig. 10. After the bubble nucleation hastaken place, the bubbles are transported to the blade into aregion of higher pressure where they shrink. The bubblesare transported by the rotational movement to a regionof lower pressure, the bubbles grow, coalesce and forma foam.

3422 I. Gestring, D. Mewes / Chemical Engineering Science 57 (2002) 3415–3426

Fig. 10. Photo of the bubble nucleation in the apparatus.

The initial bubble nucleation and foam formation are rapidpassing processes. The maximum foam expansion is reachedseveral seconds after the rotation has started. High rotationspeeds and high concentrations of the volatile componentaccelerate the foam formation. The foam expansion is shownin Fig. 11. After the foam has reached its maximum volumeit depends mainly on the viscosity and the rotation speedhow long the polydimethylsiloxane foams. High viscositiesand high rotation speeds suppress the grow of bubbles. If theinitial foam formation is followed by a decreasing rotationspeed the bubbles stay longer in the polymer melt. Thesebubbles are transported with the motion of the pool from

0 20 40 60 80 1001

2

3

4

5

6

n, η

m0 =130 10−3kgξ

0=0.04

n=0.167 s−1, η= 50 Pas

n=0.5 s−1, η= 50 Pas

n=1.0 s−1, η= 50 Pas

n=1.0 s−1, η=100 Pas

s

dim

ensi

onle

ss v

olum

e V

*=V

/Vm

in

time t

Fig. 11. Foam heights as a function of time.

the outer cylinder via the blade and the inner cylinder to thesurface of the pool. The center of the pool volume is nota3ected by these bubbles.

5. Mass transfer during foaming

Due to a sudden pressure release the mixture of poly-dimethylsiloxane and pentane is supersaturated. The masstransfer of pentane out of the polydimethylsiloxane into thegas phase and the expanding air results in an increase inpressure. The change in pressure is measured. The partialpressure of pentane is

pS = p− pair : (14)

The air pressure is measured by running the apparatus with-out pentane. If the same amount of polydimethylsiloxane isused the increase in air pressure is the same for every ex-periment. With the ideal gas law the mass 7ow of pentanecan be calculated. In addition the mass fraction of pentane ismeasured gravimetrically. The degassing process is stoppedfor time intervals between 10 and 60 s. A probe of poly-dimethylsiloxane is taken and the mass fraction of pentaneis measured.In Fig. 12 the change in concentration is shown for mass

transfer with and without bubble formation. The change inconcentration is signi5cantly higher for foaming 7ow thanfor bubble free mass transfer. The mass transfer during thefoaming 7ow is highest during the 5rst 20 s. During thistime the foam expands as shown in Fig. 11. After 40 s thefoam has collapsed. Most of the pentane is degassed. Themass transfer takes place through the surfaces of 5lm andpool. During the expansion of the foam bubble break-upoccurs at the interface between foam and gas phase. This

I. Gestring, D. Mewes / Chemical Engineering Science 57 (2002) 3415–3426 3423

0 20 40 60 80 1000.0

0.2

0.4

0.6

0.8

1.0

−

bubble free mass transfer mass transfer with bubbles η

0=50.0 Pas

ξ0=0.04

n=0.5 s−1

h=1.0 mm

m0=130 10−3

kg

s

dim

ensi

onle

ssco

ncen

trat

ion

ξ* =ξ(

t)-ξ

eq/ξ

0-ξeq

time t

Fig. 12. Change in concentration for mass transfer with and without bubbles.

0 10 20 30 40 50 600.0

0.2

0.4

0.6

0.8

1.0

n=0.16 s−1

n=0.5 s−1

n=1.0 s−1

η0=100 Pas

ξ0=0.035

h=0.2 mm

M0=140,0 10−3 kg

s

dim

ensi

onle

ssco

ncen

trat

ion

ξ* =ξ (

t)-ξ

eq/ξ

0-ξ eq

time t

Fig. 13. Change in concentration for di3erent rotation speeds.

break-up occurs due to the expansion of bubbles. Mass istransferred out of a lamella of the 5lm into the bubble andthe bubble grows. If the growth of the bubble is fast, thelamella is stretched and bursts. The break-up occurs alsodue to the deformation of bubbles. Bubbles are transportedto the rotating drum. There they are sheared and the lamellabursts. The deformation of the bubble is higher for higherrotation speeds of the drum.In Fig. 13 the change in concentration is shown for dif-

ferent rotation speeds as a function of the time. The concen-tration is determined gravimetrically. After 10 s the concen-tration is lowest for the highest rotation speed. The bubblesbreak easier due to the higher deformation of the lamella.For low rotation speeds the foam collapses later, the masstransfer is not as high as for higher rotation speeds but lastslonger. After 60 s when all foam is destroyed the concen-trations are equal.

In rotating degassing equipment like vented extruders thetime for degassing is limited by the geometry, the mass 7owof the polymer and the rotation speed of the screw. High rota-tion speeds decrease the time for degassing. By multiplyingthe time with the rotation speed a dimensionless dwell timeis obtained. In Fig. 14 the change in concentration is shownas a function of this dimensionless time. The change in con-centration is higher for lower rotation speeds. The foamingprocess itself is more important for the mass transfer thanan improved bubble break-up by high deformation.If the pool is covered with a seal, mass transfer takes

place solely out of the 5lm. Vigorous foaming of the 5lmis observed for thick 5lms. Bubbles out of the pool aretransported through the small gap between blade and druminto the 5lm. There they grow, burst and release their contentto the gas phase. If the gap is small the bubbles stay in thepool and do not reach the 5lm. The degassing is better for

3424 I. Gestring, D. Mewes / Chemical Engineering Science 57 (2002) 3415–3426

0 10 20 30 40 50 600.0

0.2

0.4

0.6

0.8

1.0

n=0.16 s−1

n=0.5 s−1

n=1.0 s−1

η0=100 Pas

ξ0=0.035

h=0.2 mm

M0=140.0 10−3 kg

s

dim

ensi

onle

ssco

ncen

trat

ion

ξ* =ξ(

t)- ξ

eq/ ξ

0- ξeq

dimensionless time τ =n t

Fig. 14. Change in concentration as a function of the dimensionless time.

0 10 20 30 40 50 600.01

0.1

1

10

min−1

m/s10−4

foaming flowbubble free mass transfer

mas

s tr

ansf

er c

oeffi

cien

t β

rotation speed n

Fig. 15. Mass transfer coe8cients for foaming 7ow and bubble free mass transfer.

thicker 5lms, although the main mass transfer occurs out ofthe pool. Mehta, Valsamis, and Tadmor (1984) make similarobservations. They measure the mass transfer of a volatilecomponent out of a polymer 5lm. The volume of the 5lm isconstant but the area and the 5lm thickness are varied. Thebetter degassing e8ciency of thicker 5lm is due to bubbles,which can grow in thick 5lms. The volatile component candi3use into the bubbles until they burst. The thicker the 5lmthe higher is the mass transfer.In order to compare the foaming and bubble free mass

transfer integral mass transfer coe8cients are calculated asshown in Table 2. The internal surface of the foam is notknown. Therefore the free surfaces for bubbly free masstransfer are taken. The coe8cients are given in Fig. 15 as afunction of the rotation speed. They are in general 40 times

higher than those one for bubble free mass transfer. Withvalues from 3.1 to 4:0×10−4 m=s they are similar to valuesreported by Curry and Brauer (1996) for degassing of styrolfrom polystyrol in a vented double screw-extruder. With thiscoe8cients the mass transfer during foaming 7ow can becalculated.

6. Conclusions

The degassing of polydimethylsiloxane is studied in a spe-cial designed rotating apparatus. It is made of transparentpolymer so that the foaming process can be observed. Pen-tane is used as the volatile component. The mass transfer isstudied with and without bubble nucleation. The mass trans-

I. Gestring, D. Mewes / Chemical Engineering Science 57 (2002) 3415–3426 3425

fer without bubble nucleation is studied under atmosphericpressure by pumping nitrogen through the drum. The foamformation experiments and the involved mass transfer arestudied for vacuum pressure. The partial pressure of pen-tane in the gas phase is the same for the two di3erent masstransfer mechanisms.The bubble free mass transfer takes place by mass trans-

fer through the free surfaces of 5lm and pool into the gasphase. To achieve high mass transfer rates the 5lm must becompletely mixed with the pool after every rotation. This isvalid for every rotating degassing equipment like thin-5lmevaporators and vented extruders. A better degassing canbe obtained by using di3erent 5lm heights in the degassingzone. The polymer in the pool should also have a homoge-nous concentration. A homogenous concentration is easierobtained in double screw extruders because of the mixingsection between the two screws. In thin-5lm evaporators andsingle screw extruders additional mixing elements could benecessary.The mass transfer with bubble nucleation is higher than

the mass transfer process to contiguous surfaces. The initialbubble nucleation is a rapid process. If no stripping agentsare used the bubble nucleation is a function of supersatu-ration and deformation. In spite of supersaturations of over500 mbar, bubble nucleation does not take place in the stag-nant polydimethylsiloxane. If shear is applied to the poly-dimethylsiloxane bubbles are nucleated immediately. Highsupersaturation and high shear velocities improve the bub-ble nucleation. In rotating degassing equipment both factorsact opposed. In the region of high shear velocity is a low su-persaturation and the other way round. Therefore, it is nec-essary to design screw elements which promote the bubblenucleation.The mass transfer during foaming 7ow is highest during

the expansion of the foam. This happens in the designedapparatus during the 5rst 10 s. After the foam has collapsedthe mass transfer is low. Thus more short degassing sectionsare more e3ective than one long section.

Notation

A surface, m2

c concentration, mol=m3

D di3usion coe8cient, m2=sh 5lm height, mL length, mM mass, kgM mass 7ow, kg=sp pressure, Pap0S vapour pressure of pure pentane, PapS vapour pressure of pentane in a mixture, PaT temperature, Kt time, sw velocity, m=sx coordinate

Greek letters

� mass transfer coe8cient, m=s� mass fraction, dimensionless� density, kg=m3

volume fraction, dimensionless! Flory–Huggins parameter, dimensionless

Dimensionless key 0gures

Pe Peclet-numberRe Reynolds-numberSc Schmidt-number$ dimensionless time

Acknowledgements

The authors would like to gratefully acknowledgethe 5nancial support from the AiF (Arbeitskreis in-dustrieller Forschungsvereinigungen e.V) and the GVT(Forschungs-Gesellschaft Verfahrenstechnik e.V.).

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