Effect of perturbation on the whipping motion in electrospinning

Effect of Perturbation on the Whipping Motionin Electrospinning

J. P. Yang, Y. C. Zeng, Z. G. Pei, X. H. Wang

College of Textiles, Donghua University, Songjiang, Shanghai 201620, People’s Republic of China

Received 29 April 2009; accepted 18 July 2009DOI 10.1002/app.31140Published online 15 October 2009 in Wiley InterScience (www.interscience.wiley.com).

ABSTRACT: Recent studies have demonstrated that theessential electrospinning mechanism is a rapidly whippingjet in an electric field. Perturbation growth is responsiblefor the observed whipping motion in electrospinning. Inthis study, we focused on the effect of perturbation on thewhipping motion in electrospinning. Experimental andmodeling studies were performed. Experimental observa-tions by electrospinning under normal and vacuum condi-tions showed that perturbations caused by the ambient air

influenced the whipping motion and fiber diameter. Mod-eling predictions also showed the effect of the initial per-turbation on the whipping instability, and qualitativetrends in the model predictions were in accordance withthe experimental investigation. VC 2009 Wiley Periodicals, Inc. JAppl Polym Sci 115: 2508–2513, 2010

Key words: drawing; extrusion; fibers; modeling;processing

INTRODUCTION

The physical mechanism of the electrospinning pro-cess has been explained and described by severalresearchers.1–7 It has been shown that the longitudi-nal stress caused by the electric field acting on thecharge carried by the jet stabilizes the straight jet forsome distance. Then, a lateral perturbation grows inresponse to the repulsive forces between the adja-cent elements of charge carried by the jet. The per-turbation grows to become observed as whippingmotion, which is the key physical element of theelectrospinning process responsible for the enor-mously strong stretching and the formation of nano-fibers. The authors of these works have explainedthe reasons for the observed bending instability ofjets in electrospinning. Lateral perturbation seems toplay an important role in the whipping instability,whereas no researchers have explored the relation-ship between perturbations and the whippingmotion.

In this study, we adopted the electrospinningmodel described in our previous article8 to predictthe effect of perturbation on the whipping instabilityand to compare the prediction results to experimen-

tal results on poly(ethylene oxide) (PEO) and poly(vinyl alcohol) (PVA). To study the effect of pertur-bation on the whipping motion experimentally, weperformed electrospinning experiments under nor-mal and vacuum conditions and investigated theresulting fiber diameters under different conditions.Here, we focused on the perturbation caused byambient air during the electrospinning process. Infact, in the vacuum condition, the rare air led to aweaker perturbation in the electrospinning process.

EXPERIMENTAL

Experimental procedure

PEO and PVA were chosen for the electrospinningexperiments. PEO (number-average molecularweight ¼ 1,000,000) was dissolved in deionizedwater to make a 5% (g/mL) solution for the experi-ments. The viscosity of the 5% PEO solution was695 mPa s. PVA (number-average molecularweight ¼ 10,000) was dissolved in deionized water tomake an 8% (g/mL) solution for the experiments.The viscosity of the 8% PVA solution was 355 mPa s.The experimental setup is shown in Figure 1. In

this setup, the syringe needle and the collector ofthe electrospinning apparatus were installed inside a40 � 40 cm2 chamber. A 20 � 20 cm2 lid was in oneof the faces of the chamber. The solution was forcedthrough the syringe needle via a Cole-Parmersyringe pump (Cole-Parmer Instrument Co., VernonHills, IL). When the solution was electrospun undervacuum conditions, the chamber was sealed andvacuumed via a vacuum pump before electrospin-ning. Although the solution was electrospun under

Correspondence to: Y. C. Zeng ([email protected]).Contract grant sponsor: Foundation for the Author of

National Excellent Doctoral Dissertation of the People’sRepublic of China; contract grant number: 2007B54.

Contract grant sponsor: The National Natural ScienceFoundation of China; contract grant number: 10972052.

Journal ofAppliedPolymerScience,Vol. 115, 2508–2513 (2010)VC 2009 Wiley Periodicals, Inc.

normal conditions, the lid was taken away, and theelectrospinning was performed at atmospheric pres-sure. In the electrospinning experiments, the proc-essing parameters were set as applied voltage (V) ¼15 kV, solution flow rate (Q) ¼ 0.5 mL/h, tip-to-col-lector distance (H) ¼ 20 cm, needle inner diameter(d) ¼ 1 mm, and period for collecting ¼ 10 min.

The collected electrospun fibers were observed byscanning electron microscopy (SEM; DXS-10ACKT,Shanghai, China). Image processing and the analysisof the fiber diameter were performed with Image Jimage analysis software.

Characterizing whipping motion is not a simpletask, either by experimental or theoretical methods.Recently, Yang et al.9 used the initial angle of thelooping envelop (X), the bending frequency of thefirst few loops (x), and the helical pitch to character-ize whipping instability. However, the measure-ments of these parameters were very difficult. Inthis analysis, the effect of perturbation on the whip-ping motion was evaluated by an indirect parame-ter: the area of the collected mat (S). S was definedas the deposited area of the fibers on the collector.

An image of the collected mat was obtained with ascanner. Image processing and the measurement ofS was performed with Image J software. As shownin Figure 2, the fiber mat collected on the collectorcovered an almost round area. When the period offiber collecting was constant, say, 10 min, a largerS indicated a stronger whipping motion.

Experimental results

The electrospinning experiments were performedunder normal and vacuum conditions, with theprocessing parameters unvaried. To evaluate theeffects of different vacuums on the whippingmotion, two vacuum conditions, �0.02 and�0.03 MPa, were used. In these experiments, thehigher vacuum was difficult to obtain because of thelow strength of the vacuum chamber.The resulting diameters and the S values of the

PEO fibers spun under normal and vacuum condi-tions are shown in Table I. Figure 3 shows the SEMmicrographs of the fibers that were electrospun fromPEO. The results of the experiments on PVA areshown in Table II and Figure 4. As shown by theseresults, the fibers obtained under vacuum conditionswere coarser than those obtained under normal con-ditions, and the higher vacuum of �0.03 MPa gavethe largest fiber diameter. The fiber diameter range(i.e., the range of the maximum and minimum fiberdiameters) under normal conditions was a bitsmaller than those under vacuum conditions. For thePEO fibers, the maximum diameter spun under nor-mal conditions was 143 nm, whereas the maximumdiameters spun under �0.02 and �0.03 MPa were180 and 228 nm, respectively. For the PVA fibers,the maximum diameter spun under normal condi-tions was 134 nm, whereas the maximum diametersspun under �0.02 and �0.03 MPa were 173 and197 nm, respectively. With regard to S, the valuesobtained under vacuum conditions were smallerthan that obtained under normal conditions, and the

Figure 1 Schematic diagram of the electrospinningin vacuo.

Figure 2 Measurement of S: (a) image obtained by a scanner, (b) image processed by Image J software, and (c) finalprocessed image.

WHIPPING MOTION IN ELECTROSPINNING 2509

Journal of Applied Polymer Science DOI 10.1002/app

higher vacuum of �0.03 MPa led to the smallest S.As mentioned previously, a larger S indicates astronger whipping motion. The smaller S obtainedunder vacuum conditions may have been due therare air in the vacuum. The rare air gave rise to aweaker perturbation in the electrospinning processand, therefore, suppressed the whipping motion.The weaker whipping motion in a vacuum led tosmaller stretching during electrospinning, whichresulted in coarser fibers. As one can see, a weakerperturbation in the process caused slightly weakerwhipping and a slightly larger fiber diameter.Although the differences were small, the directionsof change were as expected.

MODELING STUDY

The linear and nonlinear models of the dynamics ofbending instability in electrospinning were devel-oped by Rutledge and coworkers,1–4 and Renekerand Yarin and coworkers5–7 However, the relation-ship between the amplitude of the whipping insta-bility and the final fiber diameter was not exploredin these articles. Recently, Fridrikh et al.10 modeledthe nonlinear whipping behavior of an electrospin-ning jet. Their model predicts the amplitude ofthe whipping instability causing the formation of

nanofibers to saturate and the jet to reach a terminaldiameter controlled by the surface tension, surfacecharge repulsion, and solvent evaporation. In theirmodel, one can determine the terminal jet radius bybalancing the charge repulsion and the surfacetensions.In our previous study,9 the whipping motion of

electrospinning was simulated. In the this study, weadopted a developed mathematical model to studythe effect of perturbation on the whipping motionand final fiber diameter.The electrospun jet (fiber) was modeled as a bead-

viscoelastic element chain. The total number ofbeads (N) increased over time as new electricallycharged beads were inserted at the top to representthe flow of the solution into the jet. The three-dimensional equation of the dynamics of the electro-spun jets is

md2ridt2

¼ FCi þ FEi þ Fvei þ FBi (1)

where m is the mass of bead i, ri ¼ ixi þ jyi þ kzi isthe position of bead i, and i, j, and k are the unitvectors along the x, y, and z axes, respectively. FCi isthe net Coulomb force acting on bead i from all ofthe other beads and is expressed as

TABLE IPEO Fiber Diameters and S Values for Fibers Spun

Under Normal and Vacuum Conditions

Condition Normal �0.02 MPa �0.03 MPa

S (cm2) 51.4 40.5 35.1Average fiber diameter (nm) 120 146 164Fiber diameter range (nm) 85 91 97

Processing parameters: solution concentration ¼ 5%,V ¼ 15 kV, Q ¼ 0.5 mL/h, H ¼ 20 cm, and d ¼ 1 mm.

Figure 3 SEM images of the PEO fibers electrospun under (a) normal conditions, (b) at �0.02 MPa, and (c) at �0.03 MPa(processing parameters: solution concentration ¼ 5%, V ¼ 15 kV, Q ¼ 0.5 mL/h, H ¼ 20 cm, and d ¼ 1 mm).

TABLE IIPVA Fiber Diameters and S Values of Fibers Spun

Under Normal and Vacuum Conditions

Condition Normal �0.02 MPa �0.03 MPa

S (cm2) 48.1 36.6 31.7Average fiber diameter (nm) 116 131 140Fiber diameter range (nm) 67 75 76

Processing parameters: solution concentration ¼ 8%,V ¼ 15 kV, Q ¼ 0.5 mL/h, H ¼ 20 cm, and d ¼ 1 mm.

2510 YANG ET AL.


FCi ¼XNj¼1j 6¼i

e2

R2ij

ri � rj

Rij

� �(2)

where e is the charge each bead possesses and Rij isthe distance between bead i and bead j. FEi is theelectric force imposed on bead i by the electric fieldand is expressed as

FEi ¼ �eV0

hk (3)

where V0 is the applied voltage and h is the distancefrom the spinneret to the collector. Fvei is the netviscoelastic force acting on bead i and is expressedas

Fvei ¼pd2i;iþ1

4ri;iþ1

riþ1 � rili;iþ1

� �� pd2i�1;i

4ri�1;i

ri � ri�1

li�1;i

� �

(4)

where di�1,i, ri�1,i, and li�1,i are the diameter, stress,and length of the fiber segment (i � 1, i), respec-tively. FBi is the surface tension force exerting onbead i, tends to restore the rectilinear shape of thebending part of the jet, and is given as

FBi ¼ap di;iþ1þdi�1;i

2

� �2ki

4ðx2i þ y2i Þ1=2ixi þ jyi½ � (5)

where a is the surface tension coefficient and ki isthe curvature of the jet segment (i � 1, i, i þ 1).

To model the way a spatial perturbation develops,an initial perturbation is added:

xi ¼ aL sinðxtÞ (6:a)

yi ¼ aL cosðxtÞ (6:b)

where xi and yi are the positions of bead i at x and ycoordinates; x is the perturbation frequency; a is aconstant; and L ¼ (4e2/pd20G)

1/2 and is defined asthe length scale, where d0 is the initial jet diameterand G is the elastic modulus of the polymersolution.When a is changed, the amplitude of the initial

perturbation aL is changed. Therefore, when a and xare changed during calculation, the effects of theamplitude and frequency of the initial perturbationon the development of whipping instability can beinvestigated. To characterize whipping motion, theamplitude of the whipping is introduced. Whippingamplitude is defined as the maximum lateraldisplacement at position z and is calculated as (x2imax

Figure 4 SEM images of the PVA fibers electrospun under (a) normal conditions, (b) at �0.02 MPa, and (c) at �0.03 MPa(processing parameters: solution concentration ¼ 8%, V ¼ 15 kV, Q ¼ 0.5 mL/h, H ¼ 20 cm, and d ¼ 1 mm).

Figure 5 Effect of the amplitude of the initial perturba-tion on the whipping amplitude. [Color figure can beviewed in the online issue, which is available atwww.interscience.wiley.com.]



þ y2imax)1/2; where ximax is the maximum displace-

ment of x at position z and yimax is the maximumdisplacement of y at position z. In this study, wechanged a from 10�3 to 5 � 10�3 to 10�2 to 5 � 10�2

and changed x from 10 to 50 by steps of 10. Theseparameters are dimensionless.

RESULTS AND DISCUSSION

Figure 5 shows the effect of the amplitude of the ini-tial perturbation on the whipping amplitude. Thecalculations showed the whipping amplitude growthas the jet moved downward from the spinneret tothe collector during the electrospinning process. Fora 10�3L initial perturbation amplitude, the whippingamplitude was very small. However, the whippingamplitude increased substantially as the amplitudeof the initial perturbation increased.

Figure 6 shows the effect of the initial perturbationfrequency on the whipping amplitude. The whippingamplitude decreased as the initial perturbation fre-quency increased. With increasing perturbation fre-quency, the period for the jet motion remainedunvaried; whereas the whipping amplitude decreased,and the number of the loops of whipping increased.

Our experimental results show that a weaker per-turbation under vacuum conditions led to a smallerS, which indicated a weaker whipping motion. Qual-itative trends in the model predictions were inaccordance with the experimental investigation.

The experimental results show that a weaker per-turbation in the process caused slightly weaker whip-ping and slightly larger fiber diameters. Unfortu-nately, our modeling predictions showed that theamplitude and frequency of the initial perturbationhad little influence on the fiber diameters. Figure 7shows the effect of the perturbation frequency on the

fiber diameter. In fact, it was not easy to obtain arealistic set of dimensionless perturbation amplitudeand frequency for calculation. The discussion in thisarticle is an initial exploration in this area, and wehave focused on the effect of perturbations on thewhipping motion for the first step of the study.

CONCLUSIONS

The effect of perturbations on the whipping motionin electrospinning was studied with experimentaland modeling methods. The experimental observa-tions of electrospinning under normal and vacuumconditions showed that perturbations of ambient airinfluenced the whipping motion and the resultingfiber diameter to some extent. A weaker perturba-tion in the process caused slightly weaker whippingand slightly larger fiber diameters. An electrospin-ning model was adopted to predict the effect of ini-tial perturbation on the whipping instability and thefinal fiber diameter. The predictions showed that theamplitude and frequency of the initial perturbationdramatically influenced the whipping amplitude.Qualitative trends in the model predictions were inaccordance with the experimental investigation.However, the initial perturbation predicted littleinfluence on the final fiber diameter.

The authors express their appreciation to W. Oxenham forhis valuable discussion concerning this article.

References

1. Shin, Y. M.; Hohman, M. M.; Brenner, M. P.; Rutlege, G. C.Appl Phys Lett 2001, 78, 1149.

2. Shin, Y. M.; Hohman, M. M.; Brenner, M. P.; Rutlege, G. C.Polymer 2001, 42, 9955.

Figure 6 Effect of the initial perturbation frequency onthe whipping amplitude. [Color figure can be viewed in theonline issue, which is available at www.interscience.wiley.com.]

Figure 7 Effect of the initial perturbation frequency onthe fiber diameter. [Color figure can be viewed in theonline issue, which is available at www.interscience.wiley.com.]


2512 YANG ET AL.

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4. Hohman, M. M.; Shin, Y. M.; Rutledge, G. C.; Brenner, M. P.Phys Fluids 2001, 13, 2221.

5. Reneker, D. H.; Yarin, A. L.; Fong, H.; Koombhongse, S.J Appl Phys 2000, 87, 4531.

6. Yarin, A. L.; Koombhongse, S.; Reneker, D. H. J Appl Phys2001, 89, 3018.

7. Yarin, A. L.; Koombhongse, S.; Reneker, D. H. J Appl Phys2001, 90, 4836.

8. Zeng, Y. C.; Wu, Y.; Pei, Z. G.; Yu, C. W. Int J Nonlinear SciNumer Simul 2006, 7, 385.

9. Yang, Y.; Jia, Z. D.; Liu, J. N.; Li, Q.; Hou, L.; Wang, L. M.;Guan, Z. C. J Appl Phys 2008, 103, 104307.

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Effect of perturbation on the whipping motion in electrospinning