PLASMA DISCHARGE SIMULATIONS IN
WATER WITH PRE-EXISTING BUBBLES
AND ELECTRIC FIELD RAREFACTION
Wei Tian and Mark J. Kushner
University of Michigan, Ann Arbor, MI 48109 USA
bucktian@umich.edu, mjkush@umich.edu
2nd Michigan Institute for Plasma Science and Engineering (MIPSE)
21 September 2011, Ann Arbor, Michigan
* Work supported by Department of Energy Office of Fusion Energy Science
AGENDA
 Introduction to plasma discharges in liquids
 Breakdown mechanism: Initiation and propagation
 Description of model
 Initiation: breakdown inside the bubble
 Propagation: electric field rarefaction
 Concluding Remarks
MIPSE_SEP2011_1
University of Michigan
Institute for Plasma Science & Engr.
PLASMAS 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.
 Plasma Sources Sci. Technol. 17 (2008) 024010
MIPSE_SEP2011_2
 Plasma Process. Polym. 6 (2009), 729
University of Michigan
Institute for Plasma Science & Engr.
BREAKDOWN MECHANISM
 Due to the high atomic/molecular density in liquids, for a given
voltage, E/N (Electric Field/Number density) is small.
 Plasma breakdown, consisting of initiation and propagation of a
streamer, typically requires a critically large E/N.
 To achieve this E/N, breakdown requires a mechanism to rarefy
the liquid or to provide sources of seed electrons.
 Initiation
 Pre-existing bubbles
 Localized internal vaporization
 Molecular decomposition
 Electron-initiated Auger process
 Propagation
 Electric field rarefaction
 Gas channel cavitation
 Polarity effect
MIPSE_SEP2011_3
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
MIPSE_SEP2011_4
University of Michigan
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
ri

  

exp     lk N l rj 'drj '
 l r '

 
j


G rj ' , ri  
2
 
4 rj 'ri
 Electric field emission
1
 
3
2 


q
E
0
 work  
  

 
  0  
J e  ATk2 exp 

k
T
B k
 

 


 
MIPSE_SEP2011_5
University of Michigan
Institute for Plasma Science & Engr.
INITIATION: PASCHEN’S CURVE FOR BUBBLES
 The vapor phase in liquids
will have pressures of at
least 1 atm – usually the
vapor of the liquid or the
injected gas.
 Even breakdown in these
rarefied regions is
challenging, needing to have
large voltages.
 “Paschen’s law”, Wikipedia, Septemeber 21, 2011
(http://en.wikipedia.org/wiki/Paschen%27s_law)




Bubble (20 ~ 75 m )
Pressure (1 ATM)
Pd value (1 ~ 10 Torr cm)
Voltage (20 ~ 50 kV)
 Some E/N “amplification” may be required, as in electric
field enhancement due to geometry, permittivities or
charging.
MIPSE_SEP2011_6
University of Michigan
Institute for Plasma Science & Engr.
CONFIGURATION
 Breakdown of liquids from pre-existing bubbles was numerically
investigated.
Sharp-Tip Electrode Parallel Electrode
Bubble ~ 50 um
Bubble ~ 75 um
MIPSE_SEP2011_7
Parallel Electrode
Bubble ~ 20 um
University of Michigan
Institute for Plasma Science & Engr.
INITIATION INSIDE BUBBLES
 Initiation processes
inside the bubble within
0.1 ns
 Initiation processes are
associated with electron
impact ionization, photoionization and field
emission
MIN
MIPSE_SEP2011_8
MAX
University of Michigan
Institute for Plasma Science & Engr.
SHARP-TIP ELECTRODE
 [Sphoto]
 E-field
 Se
 [e]
(1018 cm-3, 3 dec) (5.0 ~ 7.0 MV/cm) (1027 cm-3s-1, 3 dec) (1022 cm-3s-1, 3 dec)
 The sharp tip produces electric field enhancement to 5 MV/cm, E/N to 10,000 Td.
 Electron density produces ionization of a few percent.
 Electron impact ionization dominates over photo-ionization
MIN
MIPSE_SEP2011_9
MAX
University of Michigan
Institute for Plasma Science & Engr.
PARALLEL ELECTRODE: PHOTO-IONIZATION
 [Se]
 [Sphoto]
 [EF]
 [e]
(1017 cm-3, 3 dec) (0.8 ~ 1.8 MV/cm) (1027 cm-3s-1, 3 dec) (1022 cm-3s-1, 3 dec)
 The electric field is enhanced due to the permittivity difference at the gasliquid interface
 Electron density is uniform due to uniform electric field inside the bubble
 The electron impact ionization dominates over photo-ionization
MIN
MIPSE_SEP2011_10
MAX
University of Michigan
Institute for Plasma Science & Engr.
PARALLEL ELECTRODE: FIELD EMISSION
 [Sphoto]
 E-field
 Se
 [e]
(1016 cm-3, 3 dec) (0.3 ~ 0.5 MV/cm) (1025 cm-3s-1, 3 dec) (1022 cm-3s-1, 3 dec)
 The electric field is concentrated at the top of the bubble
 Electrons are emitted from the top of the bubble, where the electric field is
strong enough
 The field emission assists the ionization
MIN
MIPSE_SEP2011_11
MAX
University of Michigan
Institute for Plasma Science & Engr.
PROPAGATION: E-FIELD RAREFACTION
 “Liquids can become phase unstable such that
gas channels form along electric field lines.”
 A streamer can propagate itself. The electric
field is expelled and advanced at the streamer
tip, because of free charges inside the streamer
and ion accumulation at the tip.
E-field
Enhancement
 The enhanced electric field is so strong that a
phase-like transition occurs there. The
densities, compositions and other phaserelated properties are changed respectively. As
a result, a low-density area is created.
Phase
Transition
 The streamer extends itself into the new lowdensity area. The loop continues until the
streamer reaches the grounded electrode.
 Plasma Process. Polym. 6 (2009), 729
MIPSE_SEP2011_12
Streamer
Extension
University of Michigan
Institute for Plasma Science & Engr.
PROPAGATION: PHOTO-IONIZATION
 Gap = 1 mm
 Vmax=30 kV, with
rising time of 0.1 ns
 Average E-Field
~ 0.3 MV/cm
 Speed ~ 400 km/s
 Flood represents the
electron density
 Lines represent the
potentials
MIPSE_SEP2011_13
MIN
MAX
University of Michigan
Institute for Plasma Science & Engr.
PROPAGATION: PHOTO-IONIZATION
 [Sphoto]
 Se
 E-field
 [e]
(1016 cm-3, 3 dec) (1.0 ~ 2.5 MV/cm) (1022 cm-3s-1, 3 dec) (1025 cm-3s-1, 3 dec)
 The streamer is a little wider than the bubble, because the photoionization is isotropic
 The photo-ionization is dominating in the bulk plasma; electron impact
ionization only occurs at the head of the streamer
MIPSE_SEP2011_14
MIN
MAX
University of Michigan
Institute for Plasma Science & Engr.
PROPAGATION: FIELD EMISSION
 Gap = 2 mm
 Vmax=20 kV, with
rising time of 0.1 ns
 Average E-Field
~ 0.1 MV/cm
 Speed ~ 100 km/s
 Flood represents the
electron density
 Lines represent the
potentials
MIPSE_SEP2011_15
MIN
MAX
University of Michigan
Institute for Plasma Science & Engr.
PROPAGATION: FIELD EMISSION
 Se
 [Sphoto]
 E-field
 [e]
(1017 cm-3, 3 dec) (0.5 ~ 1.0 MV/cm) (1025 cm-3s-1, 3 dec) (1022 cm-3s-1, 3 dec)
 The electric field is concentrated at the head of the streamer
 The streamer originates from the bubble top and propagates toward the
grounded electrode
 Its head becomes wider and wider since it gets closer to grounded electrode
MIPSE_SEP2011_16
MIN
MAX
University of Michigan
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
 A large electric field, photo-ionization or field emission is needed
to assist the initiation inside the bubble.
 Electric field rarefaction may contribute to creating a low density
channel, in which the streamer can propagate.
MIPSE_SEP2011_17
University of Michigan
Institute for Plasma Science & Engr.