Modeling of pneumatic melt spinning processesbluebox.ippt.pan.pl/~tlipnia/docs/Jarecki2012.pdf ·...

Modeling of Pneumatic Melt Spinning Processes

Leszek Jarecki, Slawomir Blonski, Anna Blim, Andrzej Zachara

Institute of Fundamental Technological Research, Polish Academy of Sciences, Pawinskiego 5B,Warsaw 02-106, Poland

Received 30 November 2011; accepted 30 November 2011DOI 10.1002/app.36575Published online 29 February 2012 in Wiley Online Library (wileyonlinelibrary.com).

ABSTRACT: Computer simulation of the pneumaticprocesses of fiber formation from the polymer melts is dis-cussed. The dynamics of air-drawing of thin polymerstreams in supersonic air jets formed in the Laval nozzle ispresented versus the melt blowing process. In the Lavalnozzle process, the air flow takes place with high Reyn-olds number and the k–x model is used which considerskinetic energy of the air flow and the specific dissipationrate of the kinetic energy. For melt blowing, the air fieldsare simulated with the use of the k–e turbulent model. Theair velocity, temperature, and pressure distributions alongthe centerline of the air jets are considered in the modelingof both pneumatic processes. The air fields are predeter-mined at the absence of the polymer streams for severalair compression values in the Laval nozzle inlet and sev-eral initial air velocities in the melt blowing process. Eachpolymer stream in a usual configuration of a single row ofthe filaments in the process is considered as non-interact-ing aerodynamically with other streams, and the air jet isassumed to be undisturbed by the polymer streams. Air-

drawing of the polymer filaments is simulated as con-trolled by the distribution of air velocity, temperature, andpressure on the air jet centerline with the use of a station-ary model of melt spinning in a single-, thin-filamentapproximation. Effects of non-linear viscoelasticity of thepolymer melt subjected to fast uniaxial elongation areaccounted for in the modeling. Strong influence of the airjet velocity, the melt viscosity which controls response ofthe polymer melt on the air-drawing forces, and the die-to-collector distance has been predicted. Influence of initialair temperature, geometry of the air die, initial velocityand temperature of the melt, extrusion orifice diametercan be also predicted from the model. The example com-putations concern air-drawing of isotactic polypropylenewith the use of the Laval nozzle are compared with thepredictions for the melt blowing process. VC 2012 WileyPeriodicals, Inc. J Appl Polym Sci 125: 4402–4415, 2012

Key words: computer modeling; fibers; melt blowing;supersonic melt spinning; polypropylene

INTRODUCTION

Pneumatic methods of melt spinning, i.e., melt blow-ing and air-drawing with the use of Laval nozzle,provide an efficient way of obtaining super-thinfibers from a variety of thermoplastic fiber-formingpolymers in which web structure is obtained in aone-step process. Nowadays, the interest in the labo-ratory research and technology of fabrication ofultra-fine fibers results from an increasing demandof high-surface-activity fabrics designed for techni-cal, biotechnological, and medical applications, suchas filtration and germicide mats, medical implants,tissue engineering scaffolds, non-wovens with sur-face catalyzers, enzymes etc. Such products takeadvantage of high specific surface of ultra-finefibers, inversely proportional to their diameter.Ultra-fine fibers with high molecular orientation

could find application also in the reinforcement ofcomposites.Super-thin fibers are defined as fibers with the di-

ameter in the range 10–0.1 lm, with the specific sur-face in the range 0.4–40 m2/cm3 (Fig. 1). They arethinner than those obtained in high-speed melt spin-ning. Higher specific fiber surface of the order of100 m2/cm3 is obtained by electrospinning. Themethod allows to obtain filaments with the diameteras small as 50 nm, but it usually involves solventsand the output is by orders of magnitude lower.Commercial non-wovens of fibers with the diame-

ter as small as 1–2 lm are now produced by a num-ber of companies with the use of melt blowingtechnology. In melt blowing, two convergent high-velocity jets of hot air are blown from rectangularair slots on both sides of a longitudinal spinningbeam onto the polymer filaments. Due to frequentonline brakes of the air-drawn filaments taking placein melt blowing under stochastic coiling and entan-glements, finite length fibers, often very short, areproduced by this method.1–4 Besides, melt blowinginvolves high volumes of hot air resulting in highenergy consumption and requires manufacturing ofhigh precision die assembly.5

Correspondence to: L. Jarecki ([email protected]).Contract grant sponsor: Ministry of Science and Higher

Education of the Republic of Poland; contract grantnumber: N N507 448437.

Journal of Applied Polymer Science, Vol. 125, 4402–4415 (2012)VC 2012 Wiley Periodicals, Inc.

A new and efficient pneumatic process has beeninvented in this decade in the Nanoval Company inBerlin with the application of Laval nozzle wherethe streams of fiber-forming polymers are meltdrawn in the supersonic air jet.6–8 In this process,cold air is used to generate supersonic air jet, andthe polymer streams extruded coaxially with the airjet undergo very rapid pneumatic drawing to super-thin fibers. Air velocity in the supersonic Laval noz-zle process is not decelerating away from the nozzle,as it is in melt blowing, and continuous fibers aresuccessfully obtained. Also the design and use of thedie assembly is simpler due to not so fine diesneeded in the process.6,9 Gerking6–8 claims that thepolymer melt monofilaments are attenuated in theLaval nozzle by the supersonic air jet until they dis-integrate into a number of sub-filaments by a longi-tudinal burst splitting. However, observation of thesplitting is controversial and some other authors donot observe the fiber splitting phenomena in the pro-cess. Mechanism involved in the burst opening ofthe filaments, as well as dynamics of the supersonicair-drawing of the melt are not clear.

Experimental tests on melt drawing of polypropyl-ene in the Laval nozzle indicate that higher air pres-sure used in the nozzle inlet leads to finer filamentsin the non-wovens’ structure due to higher air jetvelocity along the spinline. It is confirmed that thesupersonic process is effective for production of con-tinuous fine fibers at the compression of the air inthe nozzle inlet around one bar, or more. Neverthe-less, the scanning electron microscope (SEM) obser-vations of the polypropylene non-wovens do notindicate burst splitting of the air-drawn monofila-ments.10,11 The SEM images show polypropylenefibers with smooth surface and uniform diameter,without irregularities in the shapes, cracks, or split-ting. Burst splitting is a random process and one

should expect the irregularities, as well as broad dis-tribution of the fibers’ diameter. Also model consid-erations are still lacking in the literature whichwould describe dynamics of the Laval nozzleprocess.Pneumatic processes of melt spinning are compli-

cated by the influence of relatively high number ofthe process parameters, coupled with the influenceof material parameters of the polymer. In this article,we compare influence of important process and ma-terial parameters on the dynamics of the melt air-drawing in the supersonic Laval nozzle process withthat in melt blowing. The comparison bases on theresults obtained from computations performed usingfundamental equations of mathematical model ofmelt spinning adopted for air-drawing of the melt ina coaxial air jet. The aerodynamic model of the airjet will be applied for the Laval nozzle process tak-ing into account supersonic air velocities, as well asthe latest model of rapid extension of a thin streamof the melt in a coaxial air jet.12,13

MODEL APPROXIMATIONS

In both pneumatic processes, melt blowing and theLaval nozzle process, the die assembly is usuallylongitudinal and consists of a longitudinal spinneretwith a single row of melt extrusion orifices with cir-cular cross-section and a longitudinal air die sym-metrically on both sides of the orifices. The curtainof thin polymer streams extruded from the orificesin the symmetry plane of the air jet is subjected torapid drawing by the air flowing along thestreams.2,6 The fibers fall down freely onto a collec-tor at a fixed distance from the spinneret forming aweb of statistically distributed fibers.In the Laval nozzle process, velocity of the air jet

achieves supersonic level within the nozzle andremains at such level over a considerable range ofthe process axis what results in continuous filamentsdeposited into the web. In melt blowing, decelera-tion of the air jet along the process axis leads tointensive coiling, entanglements, and breaks of thefilaments before they achieve the collector, startingform the point where the filament and the air veloc-ities coincide. Differences in the dynamics of the airjets in the melt blowing and Laval nozzle processesis reflected in the dynamics of air-drawing of themelt, as well as in the non-wovens’ structure. Com-puter modeling is used in this article to illustrate dif-ferences in the character of both processes and showinfluence of important processing and materialparameters on the main features of the processes.For longitudinal die assemblies, with the aspect

ratio exceeding 50, modeling of the process dynam-ics reduces to two dimensions in the cross-sectionplane normal to the long dimension of the die

Figure 1 Specific surface of fibers versus fiber diameterand the thickness ranges of fibers obtained by differentmethods.

PNEUMATIC MELT SPINNING PROCESSES 4403

Journal of Applied Polymer Science DOI 10.1002/app

assembly. In both pneumatic processes, thin polymerfilaments are extruded along the symmetry axis ofthe air jet in the plane, z, and the problem reducesto two-dimensional air jet blown symmetrically onboth sides of each filament. The melt extrusion ve-locity, V0, is constant for stationary processes andthe filaments attenuated by the aerodynamic forcesalong the z-axis fall down onto the collector at afixed distance from the extrusion point, L. In meltblowing, initial velocity of hot air at the exit of theair slots is in the range 30–500 m/s, and fixed forstationary processes. Initial air temperature in meltblowing of polypropylene non-wovens is usuallyfixed near the level of 300�C.

In the Laval nozzle processes, the pressure of cold(room temperature) air at the nozzle inlet is elevatedto the values exceeding a critical value for genera-tion of supersonic air jet and fixed to maintain sta-tionary conditions. The air jet accelerates in the con-verging entrance of the nozzle to sonic velocity atthe nozzle throat, and next continues acceleration toa supersonic level in the diverging part of the noz-zle. We consider air-drawing of the polypropylenemelt extruded to the supersonic air jet in the single-filament approximation.

In general, pneumatic melt spinning processes aretwo-phase processes involving polymer streams andthe air jets blown along the streams as the phases. Inthe modeling, dynamic fields of the velocity, temper-ature, stresses, and/or pressure distributions areconsidered in each phase. We assume that thedynamic fields of the air, being the working mediumin the pneumatic processes, are not affected by thesingle row of thin polymer filaments and the fila-ments are considered in thin-, single-filamentapproximation.12,13 Experimental investigations indi-cate negligible influence of single row of the fila-ments on the dynamic air fields in the pneumaticprocesses.14

In thin-filament approximation, the velocity, tem-perature, and pressure fields of the air at the fila-ment surface are approximated by the predeter-mined values along the filament paths at thecenterline axis z. Pneumatic melt spinning is drivenby air friction forces cumulating along the filamentsurface and resulting in flow deformation of themelt with the elongational flow dominating over theshear flow. Dominating contribution of the elonga-tional flow results from high aspect ratio of the fila-ment in the process and accumulation of the air fric-tion forces tangential to the filament surface. Radialgradients of the polymer velocity V, temperature T,and components of the stress tensor r inside the fila-ment are neglected in thin-filament approximation,and the dynamic fields in the polymer bulk areapproximated by their average values on the radialfilament cross-section, V(z), T(z), r(z).

With the assumptions of longitudinal die assemblyand single row of polymer extrusion orifices, model-ing of the filament attenuation in both pneumaticprocesses, melt blowing and Laval nozzle process,separates into two steps. In the first step, predeter-mined two-dimensional air velocity, temperature,and pressure fields are computed in the cross-sec-tion plane normal to the die assembly at the absenceof the polymer filament. The second step concernsthe dynamics of stationary air-drawing of an indi-vidual polymer stream considered with the use ofthe mathematical model of melt spinning in the sin-gle-, thin-filament approximation.

AIR JET FIELDS

The air jet fields in the Laval nozzle process betweenthe polymer extrusion head and the collector arepre-determined based on the mathematical k–xmethod.15–17 High air velocities considered in thisprocess generate high Reynolds numbers in the jetafter exiting from the nozzle and the air flow is con-sidered as turbulent.18 To solve the turbulent phe-nomena, the average turbulent kinetic energy k ¼huiuii/2 and specific dissipation rate of the kineticenergy x ¼ e/k are chosen in this model where the

average dissipation rate e ¼ m ouioxj

� oujoxi

D E, m is kinematic

air viscosity, and Einstein’s summation conventionis used. Compressible and steady-state two-dimen-sional air flow is considered in the (y,z) plane nor-mal to the die assembly. It is considered that no airflow in the x-direction along the assembly takesplace due to the symmetry. The coordinate systemwith z-axis identical with the symmetry axis of thenozzle in the cross-section normal to the die assem-bly is considered. Origin of the z-axis is fixed at theextrusion point of the melt at the center of the orificeexit.The continuity equation for the two-dimensional

air flow with the velocity components Uy, Uz, andthe local air density q reads

ooy

ðqUyÞ þ ooz

ðqUzÞ ¼ 0: (1)

The momentum conservation equations for thez- and y-direction.

qUyoUz

oyþ qUz

oUy

oz¼ � oP

ozþ 2

3

ooz

� ½q:ðmþ mTÞ�2oUz

oz� oUy

oy

�� qk

�

þ ooy

�q:ðmþ mTÞ

�oUz

oyþ oUy

oz

��; ð2Þ

4404 JARECKI ET AL.


qUy

oUy

oyþ qUz

oUy

oz¼ � oP

oyþ 2

3

ooy

��q:ðmþ mTÞ

�2oUy

oy� oUz

oz

�� qk

�

þ ooz

�q:ðmþ mTÞ

�oUz

oyþ oUy

oz

��; ð3Þ

where m, mT ¼ k/x are kinematic viscosity and kine-matic viscosity of the turbulent motion, respectively,P is air pressure.

The energy conservation equation

qUyoHoy

þ qUzoHoz

¼ 2

3

ooy

�q:ðmþ mTÞUy

�2oUy

oy� oUz

oz

�

� qk

�þ ooy

�q � ðmþ mTÞUz

�oUz

oyþ oUy

oz

��

þ ooz

�q � ðmþ mTÞUy

�oUz

oyþ oUy

oz

��

þ 2

3

ooz

�qðmþ mTÞUz

�2:oUz

oz� oUy

oy

�� qk

�

þ ooy

�qðmþ rmTÞ okoy

�þ ooz

�qðmþ rmTÞ okoz

�

þ ooy

�q

�mPrL

þ mTPrT

�ooy

�cvTa þ P

q

��

þ ooz

�q

�mPrL

þ mTPrT

�ooz

�cvTa þ P

q

��; ð4Þ

where H ¼ cVTa þ Pq þ kþ 1

2 U2y þU2

z

� �is total en-

thalpy, cV is specific heat of the air at constant vol-ume, Ta is absolute air temperature, and PrL, PrT islaminar and turbulent Prandtl numbers.

The equations of turbulent kinetic energy k andspecific dissipation rate x read

qUyokoy

þ qUzokoz

¼ 2

3

�q:mT

�2oUy

oy� oUz

oz

�� qk

�

� oUy

oyþ qmT

�oUz

oyþ oUy

oz

�2

þ 2

3

�q:mT

�2oUz

oz� oUy

oy

�� qk

�

� oUz

oz� b�qxkþ o

oy

�qðmþ r�mTÞ okoy

�

þ ooy

�qðmþ r�mTÞ okoy

�; ð5Þ

qUyoxoy

þ qUzoxoz

¼ 4

3cxkqmT

��oUy

oy� oUz

oz

�2

þ oUz

oz:oUoy

�� bqx2 þ o

oy

�qðmþ r � mTÞ oxoy

�

þ ooy

�qðmþ r:mTÞ oxoz

�ð6Þ

where c ¼ 0.8, b ¼ 0.075, r ¼ 0.5, b* ¼ 0.09, r* ¼0.5. The equation of state of ideal gas is applied, P ¼qRTa, where R is the gas constant.Due to symmetry of the flow fields, the numerical

domain in the simulations reduces to the half of thetwo-dimensional field, with the symmetry axis ofthe fields at the edge. For the Laval nozzle geometryand the computational domain presented in Figure2, the boundary conditions for the equations read:

-inlet to the nozzle, z ¼ �10 mm: P ¼ PambþDP,k ¼ x ¼ 0, Ta ¼ T0,

-the wall of nozzle: Uy ¼ Uz ¼ k ¼ x ¼ 0, Ta ¼Tamb,

-the symmetry axis y ¼ 0: oUz

oy ¼oTa

oy ¼ oPoy ¼ ok

oy ¼ oxoy ¼ 0; Uy ¼ 0,

-outlet of the domain, z ¼ 240 mm and y ¼ 100mm: ok

oy ¼ oxoz ¼ 0

where DP is air compression at the nozzle inlet, Tamb

and Pamb is ambient temperature and pressure.The air fields has been computed based on the

eqs. (1)–(6), the state equation of ideal gas, and theboundary conditions using the finite volume ele-ments method of the computational fluid dynamicsand the Fluent 12 package. Several mesh resolutiontests were performed to evaluate the grid conver-gence index (GCI)19 and to identify the optimalmesh resolution, being compromise of the computa-tional time and the numerical accuracy. The mostcritical flow region of the domain is located within

Figure 2 Geometry of the Laval nozzle and the air jetcomputational domain with the symmetry axis y ¼ 0.



the narrowing of the Laval nozzle. Based on the testsimulations in this region, the optimal mesh soughtusing GCI was found for the model to consist of143,795 grid cells, with the distance between gridnodes of about 0.4 mm and the error of the compu-tations <1%.

The computations of the air fields have been per-formed for the inlet air temperature of 20�C and sev-eral air compression values DP at the nozzle inletbetween 1 and 10 bars. Figures 3(a) and 4(a) presentthe computed air velocity and temperature distribu-tions along the symmetry axis z of the jet, since thisregion controls dynamics of air-drawing of the fila-ment. For comparison, axial distributions of the airvelocity and temperature computed for melt blowingat several initial air velocities U0 in the range 50–300m/s in a separate publication20 with the aid of theFluent package are presented in Figures 3(b) and4(b) (line plots). The computations were performedfor the initial air temperature fixed to 300�C usingthe k–e model of turbulent flow which consists of a

system of differential equations in the (y,z) plane forthe mass continuity, momentum and energy conser-vation, turbulent kinetic energy k, the turbulent dis-sipation rate e, and the state equation of idealgas.15,20,21 The die assembly with the blunt noserecessed by 0.3 mm, the width of the slots of0.5 mm, the air slots inclination angle 28.25� to thez-axis was assumed in that computations. Zero ofthe z-axis is fixed at the exit of the polymer extru-sion orifice.The experimental points presented in Figures 3(b)

and 4(b) provide satisfactory verification of the sim-ulation results obtained for melt blowing and con-firm general character of the computed axial profilesof air velocity and temperature, as well as the influ-ence of the initial air velocity on the profiles. In thevicinity of the air slots, the axial air velocity rapidlyincreases to a maximum within a few millimeters.The maximum is followed by a monotonic decay ofthe air velocity along the z-axis. Such a decayingcharacter show also axial profiles of the airtemperature.No experimental data are available in the litera-

ture for verification of the air fields simulated for

Figure 4 Axial air temperature profiles versus distance zcomputed for: (a), (b) as in Figures 3(a,b).

Figure 3 Axial air velocity profiles versus distance zcomputed for: (a) Laval nozzle process with room temper-ature air at the nozzle inlet and air compressions DP, (b)melt blowing with the initial air temperature 300�C andinitial air velocities U0 (lines20) and the experimentaldata.22,23

4406 JARECKI ET AL.


the supersonic Laval nozzle processes. Validation ofthe computations performed for the supersonic airjets bases on the numerical criteria of convergence atthe mesh resolution and the number of computationcycles adjustment. The air velocity and temperatureprofiles presented in Figures 3(a,b) and 4(a,b) illus-trate fundamental differences in the dynamics of theair jets in the Laval nozzle and melt blowing proc-esses. In the Laval nozzle process, the air acceleratesrapidly in the convergent inlet of the nozzle to thevelocity of sound at the nozzle throat point. In thedivergent outlet of the nozzle, the velocity increasesfurther to supersonic values and remains at highlevel over a considerable range of the axis withoutdecaying. The computed Mach number achieves thevalues between unity and three in the nozzle range,depending upon the air compression at the inlet.Behind the nozzle, the Mach number decreases butit is still relatively high.

The air temperature is predicted to decrease alongthe z-axis for every air compression value at the noz-zle inlet, from room temperature at the inlet to aminimum in the diverging part of the nozzle wherethe air decompresses. Next, the air temperatureincreases after the nozzle exit, with some waving, tovalues still remaining much below the ambient roomtemperature. The computed air pressure (not shownin the figures) rapidly drops down to the ambientvalue at the nozzle outlet and remains at this levelin the whole area outside the nozzle. The air decom-pression in the nozzle is accompanied by rapiddecrease in the air temperature. In melt blowing, thesimulated air pressure shows a slight increase withina few millimeters of the jet axis followed by rapiddecay to the ambient value. The axial distributionsof the air velocity, temperature, and pressureobtained for the Laval nozzle air jet are used in thecomputations of the dynamic profiles of air-drawingof the polymer melt in the Laval nozzle process, forcomparison with the dynamics of melt blowing.

DYNAMICS OF AIR-DRAWING

Air-drawing of the polymer filament and its attenua-tion in the pneumatic processes take place withinthe range of the process axis where the air velocityexceeds velocity of the polymer. The supersonicLaval nozzle process differs from melt blowing byapplication of cold air and much higher air velocity,non-decaying over a significant range of the processaxis. Such an air jet allows air-drawing of the poly-mer filament over a much longer range of the axiswithout coiling. To discuss dynamics of air-drawingin both pneumatic processes, mathematical model ofstationary fiber melt spinning in single-, thin-fila-ment approximation is applied.24,25 Relatively lowvolume concentration of the filaments in the spin-

ning space allows to neglect inter-filament aero-dynamic interactions. In the model, attenuation ofan individual thin polymer stream extruded alongthe symmetry axis of the planar air fields from a cir-cular cross-section orifice is considered. Dynamics ofair-drawing of the filament is calculated using thepredetermined axial distribution of the air fields.The model of melt air-drawing consists of a set of

first order ordinary differential equations for thelocal polymer velocity V(z), temperature T(z), tensilestress Dp(z), and rheological extra-pressure prh(z).The equations result from the mass, force, energyconservation equations, and the constitutive equa-tion of viscoelasticity. Preliminary computations per-formed for air-drawing of isotactic polypropylene(iPP) in the Laval nozzle process indicate no onlinecrystallization of the polymer because temperatureof the polymer does not fall below the critical tem-perature of crystallization enough early before reach-ing the collector, similarly as it was predicted formelt blowing of iPP.13,26

The mass conservation equation of stationarypolymer stream

pD2ðzÞ4

qðzÞVðzÞ ¼ W ¼ const (7)

provides relation between the polymer velocity V(z)and local filament diameter D(z), valid in the rangeof z-axis where the air velocity is higher than the ve-locity of the filament, U(z) > V(z). The temperaturedependence of the polypropylene melt densityreads27

qa½TðzÞ� ¼103

1:145þ 9:03� 10�4½TðzÞ � 273� ðin kg=m3Þ(8)

where T(z) is the polymer absolute temperature.The axial gradient of the tensile force F(z) results

from the force balance equation of the filament andaccounts for the inertia, air friction, and gravityforces, respectively.

dF

dz¼ W

dV

dzþ dFa

dz� pD2ðzÞ

4qðzÞg: (9)

Axial gradient of the air friction forces

dFadz

¼ �pDðzÞ2

qaðzÞCf ðzÞ½UðzÞ � VðzÞ�2 (10)

is negative in the air-drawing range and depends onthe difference of the air and the filament axial veloc-ities, U(z)�V(z). The air friction coefficient Cf(z) isassumed with the numerical parameters for the



turbulent boundary layer suggested for pneumaticprocesses by Majumdar and Shambaugh28

Cf ðzÞ ¼ 0:78DðzÞjUðzÞ � VðzÞj

maðzÞ� ��0:61

: (11)

Local air density qa(z) ¼ const P(z)/Ta(z) dependson the air pressure and temperature along the z-axisand is determined for dry air assuming qa(z) ¼352.32/Ta(z) (in kg/m3) for the air under atmos-pheric pressure. Local kinematic viscosity of dry airunder pressure Pa reads

25

maðzÞ ¼ 4:1618� 10�9 T5=2a ðzÞ

TaðzÞ þ 114

Pamb

PaðzÞ ðin m2=sÞ:(12)

The air friction on the filament surface providesdriving force of pneumatic melt spinning processes,with negative gradient of the air friction forces in theair-drawing range, U(z) � V(z) > 0, which cumulatesthe tensile force nearby the extrusion point. The cumu-lated tensile force leads to sharp attenuation of the fila-ment diameter observed in the range of a few centi-meters next to the spinneret and fast increase of thefilament elongation rate in the pneumatic processes.29

Axial gradient of the filament temperature, dT/dz,expresses by the equation

qðzÞCpðzÞVðzÞ dTdz

¼ � 4a�ðzÞDðzÞ ½TðzÞ � TaðzÞ�

þ 4FðzÞpD2ðzÞ

dV

dz(13)

which accounts for convective heat exchangebetween the filament and the air dependent on thelocal difference of the filament and air temperatures,T(z) � Ta(z), as well as for viscous friction heat gen-erated in the polymer bulk under high-velocity gra-dient, dV/dz.13 Cp(z) is the specific heat of the meltdependent on its local temperature.

CpðzÞ ¼ Cp0 þ Cp1½TðzÞ � 273� (14)

with Cp0 ¼ 1.5358�103 J/(kg�K), Cp1 ¼ 10.13 J/(kg�K2) for polypropylene.27 The convective heatexchange coefficient a*(z) determined from the corre-lation between the Nusselt and Reynolds numbers,Nu ¼ 0.42 Re1/3, and confirmed for melt blowing ofpolypropylene by Bansal and Shambaugh29 is used.

a�ðzÞ ¼ 0:42kaðzÞDðzÞ2=3

jUðzÞ � VðzÞjmaðzÞ

� �1=3: (15)

The air fields computed for the Laval nozzle andmelt blowing20 processes indicate that the air flow is

coaxial with the jet’s centerline and normal compo-nent of the air velocity vanishes. Sutherland formulais used for the temperature dependence of the airconductivity coefficient.25

kaðzÞ ¼ 2:0848� 10�3 T3=2a ðzÞ

TaðzÞ þ 114ðin J=ðm � s � KÞÞ:

(16)

For uniaxial elongational flow of the polymermelt, the axial and radial stress components, pzz, prr,determine tensile stress Dp ¼ pzz � prr and the rheo-logical pressure p ¼ �(pzz þ 2prr)/3. The local stresstensor p(z) in the polymer bulk expresses by thelocal air pressure P(z) and the extra-stress tensorr(z), p(z) ¼ �P(z)I þ r(z), where I is a unit tensor.In steady-state air-drawing of the melt and thin-fila-ment approximation, the local tensile stress Dp(z) isassociated with the local tensile force F(z) acting onthe filament cross-section

DpðzÞ ¼ pzz � prr ¼ rzzðzÞ � rrrðzÞ ¼ 4FðzÞpD2ðzÞ : (17)

The local pressure in the filament

pðzÞ ¼ � 1

3ðpzz þ 2prrÞ ¼ PðzÞ � 1

3ðrzz þ 2rrrÞ (18)

where the second term is the rheological extra-pres-sure determined by the extra-stress components.

prhðzÞ ¼ � 1

3ðrzz þ 2rrrÞ: (19)

Phan-Thien/Tanner constitutive equation of non-linear viscoelasticity30,31 is used to determine thetensile stress and rheological extra-pressure. The fol-lowing differential equations are obtained12 for thetensile stress, Dp(z), and rheological extra-pressure,prh(z), for steady-state uniaxial air-drawing of thepolymer melt in thin-filament approximation.

sðzÞVðzÞ d

dzDpþ DpðzÞexp �3 2 sðzÞ

gðzÞ prhðzÞ� �

¼ 3gðzÞ dVdz

þ sðzÞð1� nÞ½Dp� 3prhðzÞ� dVdz

ð20Þ

sðzÞVðzÞ d

dzprh þ prhðzÞexp �3 2 sðzÞ

gðzÞ prhðzÞ� �

¼ � 2

3sðzÞð1� nÞDpðzÞ dV

dzð21Þ

where g(z) is local Newtonian viscosity, s(z) is relax-ation time dependent on local temperature T(z). Theparameters [ ¼ 0.015 and n ¼ 0.6 responsible for

4408 JARECKI ET AL.


non-linear elasticity and shear thinning effects areassumed for iPP melt.32

The temperature dependence of the Newtonianviscosity of the amorphous polymer is assumed inthe Arrhenius form, with the front factor g0 depend-ent on the weight-average molecular weight Mw.

gðTÞ ¼ g0ðMwÞexp ED

kT

� �T > Tg

1 T � Tg

(22)

where ED is activation energy of viscous motion, Tg

is glass transition temperature, k is the Boltzmannconstant, g0ðMwÞ ¼ Const �M3;4

w .33 For iPP, we haveED/k ¼ 5292K and Tg ¼ 253K.24,34 With a referenceshear viscosity gref at a reference molecular weightMw,ref and temperature Tref we have

g0ðMwÞ ¼ grefðTref;Mw;refÞ Mw

Mw;ref

� �3:4

exp � ED

kTref

� �:

(23)

gref ¼ 3000 Pa s is chosen as the reference viscos-ity of iPP melt at 220�C and Mw,ref ¼ 300,000.33

The relaxation time s(z) of the melt is determinedfrom the ratio s(z) ¼ g(z)/G(z) of shear viscosity andthe modulus of elasticity proportional to the localpolymer temperature, G(z) ¼ BT(z). The constantB ¼ k(1 � n)2l is proportional to the volume concen-tration of sub-chains between the entanglements, l,independent of the polymer molecular weight31, andthe molecular weight dependence of s(z) resultsfrom the melt viscosity.

For local modulus of elasticity of the melt at T(z)expressed by a reference modulus at Tref, G(z) ¼Gref(Tref)T(z)/Tref, the relaxation time s(z) reads,

sðzÞ ¼ srefMw

Mw;ref

� �3:4

expED

k

1

TðzÞ �1

Tref

� �� Tref

Tz

(24)

where sref ¼ gref(Tref, Mw,ref)/Gref(Tref) is a referencerelaxation time of the polymer melt at the referencetemperature and reference molecular weight. Thereference relaxation time 0.035 s is used, estimatedfor 220�C and Mw,ref ¼ 300,000 from the relaxationtime of 0.040 s reported for the iPP grade of shearviscosity 3420 Pa�s at 210�C.32

The mathematic model of melt air-drawing pre-sented by eqs. (7,9,13,17,20,21) leads to four ordinarydifferential equations of first order for the axial pro-files V(z), T(z), F(z), and prh(z). Runge-Kutta numeri-cal integration procedure has been used to computethe profiles with the stationary conditions for initialmelt velocity Vðz ¼ 0Þ ¼ V0 ¼ 4W= pD2

0qðT0Þ �

, tem-perature T(z ¼ 0) ¼ T0, and the rheological extra-pressure prh (z ¼ 0) ¼ 0 at the melt extrusion point,

z ¼ 0, from a circular orifice of a diameter D0. Theinitial condition for the tensile force, F(z ¼ 0) ¼ F0,is adjusted by an inverse method to the zero tensileforce at the free end of the filament deposited ontothe collector, F(z ¼ L) ¼ 0, in the non-wovens forma-tion processes.

RESULTS AND DISCUSSION

In the computations for air-drawing of iPP melt inthe Laval nozzle process we assume initial tempera-ture 300�C of the polymer at the extrusion point. Itis reported in the literature6 that the diameter D0 ofthe extrusion orifices in the Laval nozzle processes islarger by a factor of 2–3 than that used in melt blow-ing. This leads to higher mass outputs W of thepolymer melt by a factor of 4–9, respectively, at thesame polymer extrusion velocity. We assume D0 ¼0.7 mm and W ¼ 0.04 g/s per single orifice for theLaval nozzle process. At these values, the initialmelt velocity V0 in the Laval nozzle process is thesame as in the computations performed for meltblowing with D0 ¼ 0.35 mm and W ¼ 0.01 g/s.13

Figure 5(a) show profiles of the iPP filament veloc-ity V(z) between the extrusion point z ¼ 0 and thecollector located at z ¼ 20 cm (solid lines), obtainedfrom the computations for the Laval nozzle processand different values of the melt extrusion viscosityat 300�C. The viscosities are in the range 64–671 Pa sand corresponds to the melt flow rate index in therange 65–6 [g/10 min], calculated from the formulaMFR ¼ Const/g(230�C) at Const ¼ 15,000 Pa�s,33and to molecular weight Mw between 150,000 and300,000 with a step of 50,000, respectively. The com-putations have been performed from the modelequations for air-drawing of the melt by the super-sonic air jet with the air velocity distribution (dashedline) obtained for the air compression of two bars inthe nozzle inlet. In this process, air velocity domi-nates along the entire processing axis over the fila-ment velocity predicted for each melt extrusion vis-cosity, and the polymer is subjected to air-drawingbetween the extrusion point and the collector.The filament velocity increases along the process

axis to the highest values at the collector, which arehigher for lower melt viscosities. For the extrusionviscosity of 169 Pa s (MFR ¼ 24), the filament veloc-ity is predicted to be as high as 10,000 m/min at thecollector. At 64 Pa s (MFR ¼ 65), the filament veloc-ity profile discontinues before the collector due to aninstability which results from a divergence of the fil-ament velocity in the computations. The divergencemay indicate a failure of the steady-state model ofair-drawing for the lower polymer extrusionviscosities.For comparison with the Laval nozzle process,

Figure 5(b) illustrates filament velocity distribution



in melt blowing (solid lines) computed for the samevalues of the melt extrusion viscosity at 300�C, thesame collector location at z ¼ 20 cm, and the air ve-locity distribution (dashed line) fitting to the experi-mental data (points).1 The decaying air jet in meltblowing causes that the range of air-drawing is lim-ited at lower extrusion viscosities by the point wherethe air velocity approaches velocity of the filament.Such a character of the air jet is confirmed by experi-mental data1 presented in Figure 5(b) which showlimited range of the process axis where the air veloc-ity exceeds velocity of the filament. The air-drawingzone extends from the melt extrusion point to theposition on the z-axis at which both velocities coin-cide. Extent of the air-drawing zone in melt blowingis determined by the decaying character of the air jetand by the dynamics of the filament air-drawing.Beyond that zone the filaments decelerate andundergo intensive coiling observed in the experi-

ments before achieving the collector.1 The transitionfrom the air-drawing to the deceleration & coilingzone takes place in the range of the process axiswhere the maximum of the filament velocity is seenin the experimental data. The computations indicatethat the coiling zone appears earlier on the z-axis forlower melt extrusion viscosities, at which higher ve-locity and stronger attenuation of the filament ispredicted.Figures 6(a)–9(a) illustrate influence of the air jet

velocity on the filament velocity, diameter, tempera-ture, and tensile stress in the Laval nozzle processpredicted for several values of the air compressionDP from the range 1–10 bars, fixed melt extrusionviscosity of 360 Pa s (MFR ¼ 12) in the nozzle inlet,and the collector distance of 20 cm from the extru-sion point. For comparison, Figures 6(b)–9(b) showthe profiles computed for melt blowing for severalvalues of the initial air velocity from the range 50–300 m/s, at the same collector position z ¼ 20 cmand melt extrusion viscosity of 360 Pa s.

Figure 6 Filament velocity V versus distance z computedfor iPP. (a) Laval nozzle process for several DP values; (b)melt blowing for several U0 values and T0 ¼ 300�C. Meltextrusion viscosity of 360 Pa s at 300�C (MFR ¼ 12) andthe collector located at z ¼ 20 cm.

Figure 5 Filament velocity versus distance z computedfor several extrusion viscosities of the iPP melt (solidlines). (a) Laval nozzle process with the air velocity distri-bution computed for DP ¼ 2 bars (dashed line); (b) meltblowing with the air velocity distribution (dashed line)adjusted to experimental data1 (open symbols) with initialair temperature 300�C, solid symbols—filament velocityexperimental data1 for MFR ¼ 1259 (melt extrusion viscos-ity of 3.3 Pa s at 300�C).

4410 JARECKI ET AL.


The filament velocity predicted for the highest ini-tial air velocity in melt blowing [Fig. 6(b)]approaches at the collector the values known fromhigh-speed melt spinning. But the values in meltblowing are achieved within much shorter range ofthe process axis due to much higher elongation ratepredicted for about 300 s�1 at its maximum. In theLaval nozzle process, under the supersonic air jetcomputed for DP ¼ 2 bars, the filament velocity atthe collector [Fig. 6(a)] achieves twice higher levelthan in high-speed melt spinning and the melt elon-gation rate is as high as 1000 s�1 at the maximum.Higher air compressions in the Laval nozzle inletlead to higher elongation rates, higher filamentvelocities, and attenuation.

Majority of the filament diameter attenuation inboth pneumatic processes is predicted to takes placenext to the extrusion point within the range of 4–5cm [Fig. 7(a,b)]. In melt blowing, the attenuation isvery sensitive to the initial air velocity, from a rela-tively weak at low initial air velocities to very high

for the fastest air jets. For the Laval nozzle process,attenuation of the filament diameter is predicted tobe similar for each air compression leading to super-sonic air jet and very high.The predicted filament temperature versus dis-

tance z remains above the equilibrium melting pointT0m of iPP in both pneumatic processes [Fig. 8(a,b)]

and the polymer should not crystallize online beforeachieving the collector. In the computations, temper-ature of the filament approaching the collector isclose to Tm

0, with a deviation not exceeding 30�C.Influence of the air compression in the Laval nozzleinlet, or of the initial air velocity in melt blowing, onthe axial profile of the filament temperature is notsignificant in both pneumatic processes, but with theopposite effects. In the Laval nozzle process athigher DP, the filament temperature predicted at thecollector is in general lower, while at higher initialair velocities U0 in melt blowing it is higher.The air temperature predicted for the supersonic

Laval nozzle process remains at a level of �50�C

Figure 7 Filament diameter D versus distance z com-puted for iPP. (a) Laval nozzle process for several DP val-ues; (b) melt blowing for several U0 values and T0 ¼300�C. Melt extrusion viscosity of 360 Pa s at 300�C (MFR¼ 12) and the collector located at z ¼ 20 cm.

Figure 8 Filament temperature T versus distance z com-puted for iPP. (a) Laval nozzle process for several DP val-ues; (b) melt blowing for several U0 values and T0 ¼300�C. Melt extrusion viscosity of 360 Pa s at 300�C (MFR¼ 12) and the collector located at z ¼ 20 cm.



down to �100�C along the majority of the processaxis, depending upon the inlet air compression DP,while in melt blowing it is higher by the order of100–200�C [Fig. 4(a,b)]. It is surprising that tempera-ture of the filaments computed for the supersonicprocesses at various DP values remains generallyhigher along the axis than in melt blowing despitemuch lower air temperature in the supersonic pro-cess and does not fall below Tm

0 [Fig. 8(a,b)]. This isan effect of higher mass output of the polymer melt,W ¼ 0.04 g/s per orifice, assumed in this computa-tions for the Laval nozzle process versus W ¼ 0.01g/s per orifice assumed for melt blowing. In thesecomputations, the orifice diameter is twice higher inthe Laval nozzle process to preserve the same valueof the melt extrusion velocity in both pneumaticprocesses. In the literature, the Laval nozzle proc-esses are characterized by the mass outputs severaltimes higher than in melt blowing, with the diameterof the melt extrusion orifice twice higher or more.6

Higher mass output W reduces contribution of theconvective heat exchange between the filament and

the air, �bcon (z)[T(z) � Ta(z)], to the axial gradientof the filament temperature dT/dz where,

bconðzÞ ¼ � 0:42pkaðzÞWCpðzÞ

DðzÞjUðzÞ � VðzÞjmaðzÞ

� �1=3(25)

is a coefficient which represents intensity of axialcooling by the convective heat exchange per onedegree of the difference in the polymer and air tem-peratures at the point z. In melt bowing, the com-puted values of bcon(z) vary from about 9–10 m�1

near the extrusion point for all initial air velocitiesU0 considered to nearly fixed value of about 5 m�1

in the range of the process axis from the middle(z ¼ 10 cm), down to the collector (z ¼ 20 cm) forU0 ¼ 100 m/s. For U0 ¼ 200 m/s and 300 m/s, thebcon(z) values in the middle are of about 4.3 m�1

and 3.3 m�1, respectively, and next they continu-ously diminish to about 2.1 m�1 for both initial airvelocities at approaching the collector. Values ofbcon(z) obtained in the computations for the Lavalnozzle process vary from about 3 m�1 near theextrusion point down to nearly fixed values of about1.6 m�1 at the middle and the rest of the processaxis for all of the air compressions DP considered.The computations indicate about three times lower

axial cooling intensity near the melt extrusion point(per one degree of the difference in the filament andair temperatures) in the Laval nozzle process than inmelt blowing, about 3–2 times lower in the middleand about 3–1.3 lower at the end of the process axis,depending upon the initial air velocity U0. This pro-vides an explanation for the axial distributions ofthe filament temperature predicted for the Lavalnozzle processes on the level comparable with thosepredicted for melt blowing, despite 2–3 times higherdifferences in the filament and air temperatures inthe Laval nozzle processes. This is a consequence ofthe mass output W considered in the Laval nozzleprocess four times higher than in melt blowing,which reduces coefficient bcon(z) by a factor of 4.Smaller reduction of the coefficient than expectedfrom the W value results from higher differencesbetween the filament and air velocities in the Lavalnozzle processes than in melt blowing [eq. (25)].Local cooling rate of the polymer via the convective

heat exchange, dT/dt ¼ �bcon (z)[T(z) � Ta(z)]V(z),estimated in the computations for the Laval nozzleprocesses for DP ¼ 1, 3, and 5 bars is of about 1.4 �104, 4.0 � 104, and 6.2 � 104�C/s in the middle of theprocess axis (z ¼ 10 cm), respectively, and furtherincrease of the cooling rate by about 40% at the ulti-mate part of the axis is predicted. In melt blowing,the estimated values of the cooling rate are of about1.0 � 103, 6.2 � 103, and 2.8 � 104�C/s for the initialair velocities U0 ¼ 100, 200, and 300 m/s, respec-tively. Higher cooling rates of the polymer, dT/dt, at

Figure 9 Tensile stress Dp versus distance z computedfor iPP. (a) Laval nozzle process for several DP values; (b)melt blowing for several U0 values and T0 ¼ 300�C. Meltextrusion viscosity of 360 Pa s at 300�C (MFR ¼ 12) andthe collector located at z ¼ 20 cm.

4412 JARECKI ET AL.


higher filament velocities V(z) in the Laval nozzleprocesses result in axial gradients of the filament tem-perature dT/dz similar to those obtained in the com-putations for melt blowing, as well as in similar axialtemperature profiles remaining generally above Tm

0

in both pneumatic processes. Such a feature of meltcooling along the process axis in the Laval nozzleprocess allows for melt bonding of the non-wovensduring cooling on the collector, similarly as in meltblowing with the application of hot air.

Total contribution of the viscous friction heat gen-erated in the polymer bulk under high-velocity gra-dient dV/dz in eq. (13) elevates the predicted fila-ment temperature by about 1.2, 3.6, and 4.7�C at theend of the process axis in the Laval nozzle case forthe discussed air compressions, respectively, and ismuch lower than the contribution of the convectiveheat exchange. In melt blowing, the viscous frictiongenerates lower elevation of the polymer tempera-ture, by 1.1�C at the end of the process axis for theinitial air velocity U0 ¼ 300 m/s and lower for lowerU0 values.

Axial profiles of the tensile stresses presented inFigures 9(a,b) for both pneumatic processes indicatetensile stresses higher by an order of magnitude forthe Laval nozzle process, with a maximum of thestress at a higher distance from the extrusion point.The tensile stress increases significantly with DP. Itpredicts higher stream birefringence in the super-sonic Laval nozzle process than in melt blowing. Inmelt blowing, maximum of the tensile stress locatescloser to the extrusion point, in the range where ma-jority of the filament attenuation is predicted. Inboth processes, the tensile stress vanishes at the freeend of the filament on the non-woven surface.Nevertheless, the tensile stress vanishes ratherabruptly in the Laval nozzle case because the stressremains at much higher level over wider range ofthe processing axis due to non-decaying character ofthe air jet in this range, in comparison with decayingair jet in melt blowing [Fig. 3(a,b)]. One could expectthat the tensile stress in the Laval nozzle processshould vanish more softly at higher distances fromthe extrusion point, but at higher distances betweendie and the collector.

Negative rheological extra-pressure is predicted tobe created inside the iPP filament at fast elongationunder supersonic jets in Laval nozzle process. Thenegative pressure appears inside the Laval nozzlethroat in a narrow range of about 20–25 mm of theair-drawing axis, next to the extrusion point. Maxi-mum of the absolute extra-pressure value increasessignificantly with the air compression DP and is pre-dicted very close to the extrusion point, at a distanceof 7–10 mm for each DP (Fig. 10). The negative pres-sure results from non-linear viscoelasticity of thepolymer subjected to high elongation rates in the

pneumatic process. It may cause cavitation in thepolymer bulk which under uniaxial molecular orien-tation could lead to longitudinal burst splitting ofthe filament into a number of sub-filaments.The cavitation under the influence of negative

pressure (hydrostatic tension) is a usual cause instandard Newtonian fluids, but much less is knownabout this phenomenon in the case of polymer meltssubjected to fast elongational flow such as in pneu-matic drawing of melt filaments. Negative pressureinduced cavitation in the polymer melts has beenobserved in the pockets of polyethylene, polypropyl-ene, and poly(methylene oxide) melts occluded byimpinging spherulites during polymer crystalliza-tion.35,36 In this case, the negative pressure isbuildup in the occluded melt due to change in den-sity. Spontaneous formation of longitudinal cavitieswas observed by the real-time high-speed video mi-croscopy at the exit of capillary die during extrusionof a linear polyethylene melt when the extensionalstress at the die entrance exceeds a critical condi-tion.37 Numerical simulation of the stress fields in acapillary die predicted large negative pressure in alinear poly(dimethyl siloxane) melt near the exitregion of the die.38 It is postulated in Ref. 38 that thenegative pressure cavitates polymer melt dependingon the cohesion of the polymer bulk. Experimentalobservation of cavitation in polypropylene duringtensile drawing led to the conclusion that initiationof the cavitation process in the amorphous phasehas a homogeneous nature39 and should depend onthe cohesive forces in the melt.With the assumption that the extra-pressure

energy converts in total into the surface energy ofsub-filaments during the hypothetical splitting at apoint zs of the axis, an average diameter of the sub-

Figure 10 Extra-pressure prh in the iPP filament versusdistance z predicted for the Laval nozzle process at severalDP. Melt extrusion viscosity of 360 Pa s at 300�C (MFR ¼12) and the collector located at z ¼ 20 cm.



filament created in the splitting should approxi-mately read13

dðzsÞ ffi � 4cðzsÞprhðzsÞ (25)

where c is the surface free energy density of thepolymer, and the extra-pressure is high enough, i.e.,�prh(zs) 4c(zs)/D(zs). Equation (25) is valid for themaximum absolute value of the extra-pressure pre-dicted at the air compression DP > 1 bar in theLaval nozzle, and the average diameter of the sub-filaments is controlled by the ratio of the surfacefree energy density and the negative extra-pressure.With this prediction, the sub-filament diameter inthe supersonic process is controlled by the polymersurface tension. We assume temperature dependenceof the surface free energy density of iPP melt c(zs) ¼2.94 � 10�2 � 5.6 � 10�5 [T(zs) � 296] (in J/m2).34

Average number of the sub-filaments predictedfrom such hypothetical splitting at zs of an individ-ual filament of diameter D(zs) reads,

NðzsÞ ¼ DðzsÞdðzsÞ

� �2ffi 1

16

DðzsÞprhðzsÞcðzsÞ

� �2(26)

The predicted number of sub-filaments from thesplitting under the extra-pressure taken at its maxi-mum absolute value versus the air compression DPis shown in Figure 11 for iPP with the extrusionviscosity of 360 Pa s. Average diameter of the sub-filaments are indicated for the particular levels ofsplitting, from about 10 lm with splitting into 1000sub-filaments at the air compression DP of 1 bardown to about 2 lm with spitting into 3000 sub-fila-ments above three bars. Saturation of the highest

number and the lowest diameter of the sub-filamentsis predicted above three bars of the air compression.Splitting of air drawn filaments into super-thin

sub-filaments in the supersonic Laval nozzle processwas reported by Gerking6 in the Nanoval process.Gerking claims that the photo in Figure 12 (re-printfrom Ref. 6) shows splitting of individual filamentsinto a bundle of sub-filaments taking place withinthe Laval nozzle range. In this range, we predicthighest cavitation extra-pressure in the polymerbulk. Average diameter of the sub-filaments afterthe spitting measured in the Nanoval process6 wasin the range between 15 lm at the lowest splitting toabout 2 lm at the highest number of sub-filamentsin the splitting. Nevertheless, such a phenomena iscontroversial and has not been observed by otherauthors in the supersonic process where the finestfilaments with a diameter of 10–20 lm and smoothsurface were obtained without any evidence of fila-ment splitting.10,11

CONCLUSIONS

Computer modeling of air-drawing of polymer meltsin pneumatic melt spinning reduces to modeling ofthe predetermined two-dimensional fields of the airvelocity, temperature, and pressure and one-dimen-sional stationary melt spinning by the coaxial air jetalong its centerline. The model allows analysis of theair-drawing dynamics in the Laval nozzle processversus melt blowing and the role of individual proc-essing and material parameters. Significant differen-ces in the dynamics of both pneumatic processesresult from the differences in the character of the airjets—supersonic and high-velocity jet over relativelylong range of the process axis in the Laval nozzlemethod and fast decaying air jet in melt blowing,which results in highly coiled and entangled fibers

Figure 11 Average number N of iPP sub-filaments in thesplitting versus air compression DP predicted for the Lavalnozzle process. Melt extrusion viscosity of 360 Pa s at300�C (MFR ¼ 12) and the collector located at z ¼ 20 cm.Average diameter of the sub-filaments indicated.

Figure 12 Splitting of polypropylene melt monofilamentsin a Laval nozzle process registered by a photo at 1/8000 s.Re-printed from Ref. 6 by the courtesy of the ChemicalFibers International.

4414 JARECKI ET AL.


in the non-wovens. Contrary to melt blowing, air-drawing in the Laval nozzle extends over a longrange of the process axis and allows to obtain con-tinuous fibers by depositing them onto a collector asa non-woven, or winding-up by a drum. This featureopens possibilities of modifications of the supersonicprocess for obtaining high strength continuous fila-ments with high molecular orientation on thewinder.

Strong influence of the air jet velocity, the die-to-collector distance, and the melt extrusion viscosity(MFR index) which controls response of the polymermelt on the air-drawing forces has been predictedfrom the modeling. Melt blowing is particularly sen-sitive to the collector position where the air-drawingzone is limited by the coiling. Influence of otherprocessing parameters, such as initial air tempera-ture, geometry of the air die, initial temperature ofthe polymer melt, extrusion velocity of the polymer,extrusion orifice diameter, can be also predicted.

The model predicts negative rheological extra-pressure which results from non-linear viscoelastic-ity of the polymer melt subjected to fast elongationin the pneumatic process. The pressure activates inthe polymer bulk in a narrow range of the air-draw-ing axis inside the Laval nozzle and can lead to lon-gitudinal cavitation under the orienting tensilestresses. Hypothetical burst splitting of the filamentinto a high number of sub-filaments is consideredfollowing an energetic criterion of transformation ofthe pressure energy into surface energy of the sub-filaments. The splitting is controversial nevertheless,and lack of the experimental data in the literature onthe Laval nozzle process melt spinning process doesnot allow for verification of the model predictions.Validation of the modeling of the pneumatic air-drawing processes is given by comparison of themodel predictions with the experimental data pro-vided in the literature for melt blowing.

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