Instabilities of Electrically Forced Jets

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

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A principle advantage of theory as opposed to
numerical simulations and experiments is that
one also studies what does not happen.
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• Procedure for calculating instability thresholds
• (flavor)
• Difficulties
• Applications. Electrospinning, etc.

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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
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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
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Previous Work on Linear Stability of
uncharged cylinders
Experiments
(Mestel JFM 1994,1996)
Experiments Must Include Surface Charge
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Electrostatics
P(z) l(z) dielectric
dielectric free charge sD free charge s
Line Dipole Line Charge

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Long wavelength Instabilities
h
l
whipping
varicose
hltltl
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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
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Whipping Mode the fluid mechanics
Force Balance
acceleration
Torque Balance
Bending Moment viscous
(Maha) dielectric
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Perfect Conductor Waves
spring

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Finite KTangential Stresses Drive Whipping
Instability

torque-producing instability
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Comparison with Saville (1972)
0
10
E

Re w
k

• inviscid
• K0.7
• no charge density

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Varicose
There is also an unstable varicose mode. The
mechanism is not the Rayleigh instability, but
is electrically driven.
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Have 2 Unstable (Electrically Driven)
Modes Who wins at high field?
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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 E2 kV/cm
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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 E2 kV/cm
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Phase Diagrams

Whipping
Varicose
2 solution of PEO in water E2 kV/cm
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Phase Diagrams

2 solution of PEO in water
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Calculating the Jet Shape
(h(z),s(z),E(z)) F( ,Q)
Momentum Balance
external field
field from jet images
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What sets the current?
Mathematical Fact There is unique solution of
equations given surface charge density at nozzle
s(0)

Our procedure Iterate calculations for jet shape
w/ experiments. Result Can only find
theoretical steady state profiles at the (Df,
Q) observed experimentally only if s(0) 0
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A Comparison
E 5kV/cm Solid Line
Image processed experiment Q 1ml/min Dashed
Line Calculation.
A Disaster...
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Agreement much improved when Including Nozzle
Fringe Fields Shape of nozzle is important for
quantitative thresholds
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Lessons (1) s(0)0 gives best theoretical
description of experiments. Why? (2) Nozzle
fringe fields strongly affect (h(z), s(z),
I). (3) Whipping versus Dripping depends
strongly on (h(z), s(z)).
Dirty Details are very significant in
determining properties of Spinning (and hence
the fabric)
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Whipping Mode
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Viscosity Viscosity/10
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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.