The stretching of an electrified non-Newtonian jet: A model for electrospinning

Electrospinning uses an external electrostatic field to accelerate and stretch a charged polymer jet, and may produce ultrafine “nanofibers.” Many polymers have been successfully electrospun in the laboratory. Recently Hohman et al. [Phys. Fluids, 13, 2201 (2001)] proposed an electrohydrodynamic model for electrospinning Newtonian jets. A problem arises, however, with the boundary condition at the nozzle. Unless the initial surface charge density is zero or very small, the jet bulges out upon exiting the nozzle in a “ballooning instability,” which never occurs in reality. In this paper, we will first describe a slightly different Newtonian model that avoids the instability. Well-behaved solutions are produced that are insensitive to the initial charge density, except inside a tiny “boundary layer” at the nozzle. Then a non-Newtonian viscosity function is introduced into the model and the effects of extension thinning and thickening are explored. Results show two distinct regimes of stretching. For a “mild...

[1]  T. Sridhar,et al.  A filament stretching device for measurement of extensional viscosity , 1993 .

[2]  W. M. Haynes.  CRC Handbook of Chemistry and Physics , 1990 .

[3]  David C. Martin,et al.  Processing and microstructural characterization of porous biocompatible protein polymer thin films , 1999 .

[4]  Alfonso M. Gañán-Calvo,et al.  On the theory of electrohydrodynamically driven capillary jets , 1997, Journal of Fluid Mechanics.

[5]  H. Laun,et al.  Elongational behaviour of a low density polyethylene melt , 1978 .

[6]  Alfonso M. Gañán-Calvo,et al.  Cone-Jet Analytical Extension of Taylor's Electrostatic Solution and the Asymptotic Universal Scaling Laws in Electrospraying , 1997 .

[7]  J. Deitzel,et al.  The effect of processing variables on the morphology of electrospun nanofibers and textiles , 2001 .

[8]  Vimal Singh,et al.  Perturbation methods , 1991 .

[9]  Michael P. Brenner,et al.  Electrospinning: A whipping fluid jet generates submicron polymer fibers , 2001 .

[10]  Robert C. Armstrong,et al.  Dynamics of polymeric liquids: Fluid mechanics , 1987 .

[11]  William H. Press,et al.  Numerical Recipes: FORTRAN , 1988 .

[12]  A. Gañán-Calvo.  THE SURFACE CHARGE IN ELECTROSPRAYING: ITS NATURE AND ITS UNIVERSAL SCALING LAWS , 1999 .

[13]  R. Bird.  Dynamics of Polymeric Liquids , 1977 .

[14]  Darrell H. Reneker,et al.  Bending instability in electrospinning of nanofibers , 2001 .

[15]  J. R. A. Pearson,et al.  Computational Analysis of Polymer Processing , 1983 .

[16]  D. J. Brunner,et al.  ELECTROHYDRODYNAMIC ATOMIZATION IN THE CONE–JET MODE PHYSICAL MODELING OF THE LIQUID CONE AND JET , 1997 .

[17]  W. N. Song,et al.  A phenomenological viscosity model for polymeric fluid , 1994 .

[18]  J. Karger‐Kocsis.  Techniques in rheological measurements: A. A. Collyer (Editor) Chapman and Hall, London, 1993, 343 pp., ISBN 0-412-53490-8, £69 , 1995 .

[19]  T. Dupont,et al.  Drop Formation in a One-Dimensional Approximation of the Navier-Stokes Equation , 1992, physics/0110081.

[20]  Morton M. Denn,et al.  Mechanics of steady spinning of a viscoelastic liquid , 1975 .

[21]  D. Reneker,et al.  Nanometre diameter fibres of polymer, produced by electrospinning , 1996 .

[22]  J. O'm. Bockris,et al.  Textbook of electrochemistry , 1951 .

[23]  Darrell H. Reneker,et al.  Bending instability of electrically charged liquid jets of polymer solutions in electrospinning , 2000 .

[24]  Gyula J. Vancso,et al.  Transparent Nanocomposites with Ultrathin, Electrospun Nylon-4,6 Fiber Reinforcement , 1999 .

[25]  M. Brenner,et al.  Electrospinning and electrically forced jets. I. Stability theory , 2001 .

[26]  D. Saville.  ELECTROHYDRODYNAMICS:The Taylor-Melcher Leaky Dielectric Model , 1997 .

[27]  Y. Dzenis,et al.  Asymptotic decay of radius of a weakly conductive viscous jet , 1998 .

[28]  J. Eggers.  Nonlinear dynamics and breakup of free-surface flows , 1997 .

[29]  Darrell H. Reneker,et al.  Electrospinning process and applications of electrospun fibers , 1995 .

[30]  D. F. James,et al.  A Critical Appraisal of Available Methods for the Measurement of Extensional Properties of Mobile Systems , 1993 .

[31]  Michael P. Brenner,et al.  Electrospinning and electrically forced jets. II. Applications , 2001 .

[32]  R. Jaeger,et al.  Electrospinning of ultra-thin polymer fibers , 1998 .

[33]  S. Bechtel,et al.  Recovery of the Rayleigh capillary instability from slender 1‐D inviscid and viscous models , 1995 .

[34]  John Aurie Dean,et al.  Lange's Handbook of Chemistry , 1978 .

[35]  M. Denn,et al.  A theory of isothermal melt spinning and draw resonance , 1976 .

[36]  R. Keunings,et al.  Profile development in continuous drawing of viscoelastic liquids , 1983 .

[37]  I. Sokolov,et al.  Asymptotic radius of a slightly conducting liquid jet in an electric field , 1986 .

[38]  O. Basaran,et al.  Nonlinear deformation and breakup of stretching liquid bridges , 1996, Journal of Fluid Mechanics.