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Instabilities of Electrically Forced Jets

Instabilities of Electrically Forced Jets. Moses Hohman (Univ. of Chicago Thoughtworks) Michael Shin (Materials Science, MIT) Greg Rutledge (Chemical Engineering, MIT). I hate Computers David Quere IMA Workshop January, 2001. Electrospinning is complicated. The Product:.

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Instabilities of Electrically Forced Jets

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  1. Instabilities of Electrically Forced Jets Moses Hohman (Univ. of Chicago Thoughtworks) Michael Shin (Materials Science, MIT) Greg Rutledge (Chemical Engineering, MIT)

  2. I hate Computers David Quere IMA Workshop January, 2001

  3. Electrospinning is complicated The Product: The Physics: Electrohydrodynamics, evaporation, rheology, air drag, electrostatics wetting, solid-liquid charge transfer, temperature gradients, etc. Which factors influence the final product?

  4. Approaches: • Experimental: Try to control various processes, in hope that • something jumps out. • (2) Numerical simulations. Include all physical factors and try to • understand which dominate. • (3) “Theory”. Understand a single effect quantitatively. Do not • “curve fit” results to experiments but instead try to • assess how much of the physics stems from this effect. • Caveats: • Free parameters are absolutely unacceptable. • Numerical simulations of parts of the system always necessary.

  5. A principle advantage of “theory” as opposed to numerical simulations and experiments is that one also studies what does not happen.

  6. Procedure for calculating instability thresholds • (flavor) • Difficulties • Applications. Electrospinning, etc.

  7. “Strange” effects in Fluid Conductors: (1) Surface Charge Density s + Tangential Electric field Tangential Electrical Stress. In a fluid, this must be balanced by viscous stress (flow). Both viscosity and conductivity are singular parameters. (2) A Non-Ohmic mechanism for conduction: G.I. Taylor, 1964 (78 years old) h(z) K

  8. Stability of a thinning Jet: . (1) Locally jet is a cylinder (constant radius h, surface charge s) Find w(h,s) (2) Find global shape: (h(z),s(z),E(z)) (3) Piece together stability properties along the jet

  9. K 0 1 n Nayyar and Murty, 1960 Saville (1972) 0 Saville (1970) Nayyar and Murty, 1960 1 Saville (1970) Saville (1972) Nayyar and Murty, 1960 Previous Work on Linear Stability of uncharged cylinders Experiments (Mestel JFM 1994,1996) Experiments: Must Include Surface Charge

  10. - + E - + Electrostatics P(z) l(z) dielectric dielectric free charge sD free charges Line Dipole + Line Charge

  11. Long wavelength Instabilities h l whipping varicose h<<l

  12. Whipping Mode: the electrostatics Field from a line dipole Field from a line charge l determined by matching outside field to field inside the jet. (and using Gauss’ Law) P E.G: dielectric polarization dipolar free charge density

  13. Whipping Mode: the fluid mechanics External Forces: Surface Tension+ Electrical Stress Local Couple: Electrical Stresses Force Balance acceleration Torque Balance Bending Moment: viscous (Maha) dielectric

  14. Perfect Conductor: Waves - + - + spring

  15. Finite K:Tangential Stresses Drive Whipping Instability - + - + torque-producing instability

  16. -1 10 -2 10 -3 10 -4 10 -5 10 -6 10 -2 -1 0 1 10 10 10 10 Comparison with Saville (1972) 0 10 E Re w k • inviscid • K=0.7 • no charge density

  17. Varicose There is also an unstable varicose mode. The mechanism is not the Rayleigh instability, but is electrically driven.

  18. Have 2 Unstable (Electrically Driven) Modes: Who wins at high field?

  19. Phase Diagrams 0 -0.5 Whipping 0.2 -1 -1.5 0.1 -2 (h / cm) 0 -2.5 Varicose 10 log -3 -0.1 -3.5 -4 -0.2 -4.5 -0.3 -5 -1 -0.5 0 0.5 1 1.5 2 2.5 2 log ( s / (esu / cm )) 10 2% solution of PEO in water E=2 kV/cm

  20. Phase Diagrams 0 -0.5 Whipping 0.2 -1 -1.5 0.1 -2 (h / cm) 0 -2.5 Varicose 10 log -3 -0.1 -3.5 -4 -0.2 -4.5 -0.3 -5 -1 -0.5 0 0.5 1 1.5 2 2.5 2 log ( s / (esu / cm )) 10 2% solution of PEO in water E=2 kV/cm

  21. Phase Diagrams Whipping Varicose 2% solution of PEO in water E=2 kV/cm

  22. Whipping Varicose Phase Diagrams 2% solution of PEO in water

  23. Whipping Mode

  24. 3.5 BENDING + VARICOSE 3 2.5 BENDING E (kV/cm) 2 1.5 1 STEADY JET 0.5 VARICOSE 2 4 6 8 10 12 14 16 18 Q (ml/min) Viscosity Viscosity/10

  25. Conclusions The procedure quantitatively capture aspects of electrospinning. Honest comparisons with experiments allow us to hone in on subtle details. The Ideas are fairly general. Should have applicibility to many other Problems.

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