STREAMER INITIATION AND
PROPAGATION IN WATER WITH THE
ASSISTANCE OF BUBBLES AND
ELECTRIC FIELD INITIATED
RAREFACTION
Wei Tiana) and Mark J. Kushnerb)
a)Department
of Nuclear Engineering and Radiological Sciences
University of Michigan, Ann Arbor, MI 48109, USA
bucktian@umich.edu
b)Department
of Electrical Engineering and Computer Science
University of Michigan, Ann Arbor, MI 48109, USA
mjkush@umich.edu
November 2011 GEC
* Work supported by Department of Energy Office of Fusion Energy Science
AGENDA
 Introduction to plasma discharges in liquids
 Breakdown mechanism: Initiation and propagation
 Initiation: avalanche inside the bubble
 Propagation: electric field rarefaction
Electric field emission
Dielectric constant reduction
 Description of the model
 Concluding Remarks
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University of Michigan
Institute for Plasma Science & Engr.
DISCHARGES IN LIQUIDS
 Plasmas sustained in liquids and bubbles in liquids are efficient
sources of chemically reactive radicals, such as O, H, OH and H2O2.
 Applications include pollution removal, sterilization and medical
treatment.
 The mechanisms for initiation of plasmas in liquids are poorly
known.
 K. Schoenbach et al, Plasma Sources Sci. Technol. 17 (2008) 024010
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 K. Shih et al, Plasma Process. Polym. 6 (2009), 729
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Institute for Plasma Science & Engr.
BREAKDOWN MECHANISM
 Two competing theories of liquid breakdown
 Electronic impact-ionization process within the bulk liquid
 Breakdown process inside gas phase
 Because of high molecular
density in water, electronic
impact-ionization should be
virtually absent in bulk water in
absence of E > many MV/cm
 Electrons are known to be
solvated in water very rapidly –
must ionize very efficiently
before solvation
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Local, low-density
regions are likely
required for
breakdown
University of Michigan
Institute for Plasma Science & Engr.
BREAKDOWN MECHANISM
 Increasing static pressure
reduces likelihood for bubble
formation.
 Breakdown voltage increases
due to lack of bubbles.
 40-100 m bubbles

B. Locke et al, Trans. Ind. Appl. 45, 630 (2009).
 “The electric field increases the
instability increment for the
stratification along the field.”
 “A strong electric field (1~100
MV/cm) can induce anisotropic
decay into liquid and vapor
phases for a fluid. ”

GEC2011
A. L. Kupershtokh et al, Tech. Phys. Lett. 32, 634 (2006).
 Evidence that large
electric fields produce
regions of lower
density in liquids due
to polarization forces.
University of Michigan
Institute for Plasma Science & Engr.
MODELING PLATFORM: nonPDPSIM
 Poisson’s equation:
      ( q j N j   s )
j
 Transport of charged and neutral species:
N j
t

    j  S j
 Electron Temperature (transport coefficient obtained from
Boltzmann’s equation):
ne    
5 

 j  E  ne   i K i N i     e    Te   Te 
t
2

i
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Institute for Plasma Science & Engr.
MODELING PLATFORM: nonPDPSIM
 Radiation transport and photoionization:


Sm (ri )  N m (ri ) 

  3
 mk Ak  Nk rj 'Gk rj ' , ri d rj '
k
 Electric field emission
1
 
3
2 


q
E
0
 work  
  

 
  0  
J e  ATk2 exp 

k
T
B k
 

 


 
GEC2011

ri

  

exp     lk N l rj 'drj '
 l r '

 
j


G rj ' , ri  
2
 
4 rj 'ri
 The field emission occurs
at the gas-liquid interface
 The gas-liquid interface is
treated as a solid surface
 Field enhanced
thermionic emission
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Institute for Plasma Science & Engr.
CONFIGURATION
 A “generic” point-to-plane,
cylindrically symmetric
geometry used for study.
 Powered electrode radius:
100 m
 Bubble in contact with
electrode radius: 50 m.
 Outside boundaries
grounded.
 Inside the bubble, H2O at 1
atm; Outside the bubble,
H2OL at liquid density.
 Gas dielectric constant ε/ε0 ~
1; Liquid dielectric constant
ε/ε0 ~ 80.
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Institute for Plasma Science & Engr.
REPRESENTATIVE REACTIONS
 Reactions in Liquid Water
e + H 2 OL
Liquid Water
(H2OL)
e
↔ e L + H 2 OL
e L + H 2 OL ↔ H 2 OL  Reactions in Water Vapor
e
e
Field Emission
Electric Field
Rarefaction
e + H2O → e + e + H2O+
e + H2O+ → H + OH
e+H
→ e + H*
H* → H + hn
Water Vapor
(H2O)
hn + H2O → H2O+ + e
 Field Emission
H 2 OL → e + H 2 OL +
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Institute for Plasma Science & Engr.
INITIATION INSIDE BUBBLES
 t (ns)
0.50
1.00
0.0 ~ 1.0
 Bubble ~ 50 m
 [e]
 Vmax=+10 kV with rise time
of 1.0 ns
(cm-3 )
 Electric field emission
occurs when strong
electric field reaches the
gas-liquid interface.
 EF
 The electric field
concentrates on the axis
and leads the avalanche.
(MV/cm)
 Positive charges outline
the discharge and
produce the electric field.
ρ
(cm-3)
MIN
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MAX
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Institute for Plasma Science & Engr.
PROPAGATION: E-FIELD RAREFACTION
 A streamer can produce its own electric field
enhancement at the conductive tip.
 The enhanced electric field at the tip exceeding
a limit produces a phase-like transition, likely
on an atomic scale.
 In the model, densities, compositions and other
phase-related properties are changed to
produce a low-density volume.
 The streamer extends itself into the new lowdensity area.
 The loop continues until the streamer reaches
the grounded electrode.
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E-field
Enhancement
Phase
Transition
Low-density
Regions
Streamer
Extension
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Institute for Plasma Science & Engr.
0.0 ~ 1.7 ns
PROPAGATION
 Threshold ~ 1 MV/cm
 Vmax=+10 kV with rise time of 1.0 ns
 Streamer initiates inside the bubble
first.
 The electric field triggers the phase
transition, in which the density
decreases by about 3 orders.
 Streamer extends itself into the
changed area due to high E/N.
 The potential is expelled ahead and
compressed to produce strong
electric field.
 This mechanism makes the
streamer propagating into water by
itself.
 Flood represents the electron density
 Lines represent the electric potentials
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MIN
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Institute for Plasma Science & Engr.
PROPAGATION:
EFIELD EMISSION
 Vmax=+10 kV with rise time of 1.0 ns
 The electric field is produced by
positive charges and enhanced by
dielectric constant difference.
 The positive charge density is large
due to electronic impact ionization
at strong electric field.
0.0 ~ 1.7 ns
 A strong electric field emission
occurs at the top interface because
the electric field is strong there.
 The emitted electrons intensify the
electronic impact ionization so that
the positive charge density is
increased.
MIN
MAX
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ρ
(cm-3)
 EF (MV/cm)  Se
(cm-3s-1)
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Institute for Plasma Science & Engr.
ELECTRIC FIELD EMISSION
1
 
3
2 


q
E
0
 work  
  

 
 0  

2
J e  ATk exp 

k
T
B k
 

 


 
 The work function used for
liquid water is 1.7 ~ 1.9 eV.
 Larger emission current results
in larger propagation velocity.
Work Function
Streamer Velocity
1.7 eV
3.82×107 cm/s
1.8 eV
1.44×107 cm/s
1.9 eV
0.37×107 cm/s
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 The field emission current will
not affect the streamer
propagation until it reaches 0.1
A/cm2.
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Institute for Plasma Science & Engr.
PROPAGATION:SMALLER BUBBLE
0.0 ~ 1.1 ns
 Bubble ~ 20 um
 Vmax=+30 kV with rise
time of 1 ns
 The bubble is so small
that the electron loss is
huge and electron
impact ionization
cannot help avalanche.
 Stronger field emission
is needed to provide
more seed electrons.
 Flood represents the electron density
 Lines represent the electric potentials
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University of Michigan
Institute for Plasma Science & Engr.
PROPAGATION:
DIELECTRIC REDUCTION
 K. Schoenbach et al, Plasma Sources Sci. Technol. 17 (2008) 024010
0.0 ~ 1.6 ns
0.0 ~ 1.6 ns
 The dielectric constant is not
reduced much until the
electric field reaches 5
MV/cm (Emax ~ 1.5 MV/cm in
the case).
 The streamer becomes a little
wider due to the dielectric
constant reduction but not
affected much.
 Generally, it does not affect
much.
MIN
MAX
 [e]
(cm-3)
 ε/ε0
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Institute for Plasma Science & Engr.
CONCLUDING REMARKS
 The breakdown mechanism consists of two processes,
initiation inside the bubble and propagation due to the
electric field rarefaction.
 Electric field rarefaction may contribute to creating a
low density channel, in which the streamer can
propagate.
 Field emission contributes to the propagation process
and becomes more important for smaller bubbles.
 The dielectric constant reduction is not important at the
electric field ~ 1 MV/cm.
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University of Michigan
Institute for Plasma Science & Engr.