PLASMA DISCHARGE SIMULATIONS IN WATER WITH PRE-EXISTING BUBBLES AND ELECTRIC FIELD RAREFACTION Wei Tian and Mark J. Kushner University of Michigan, Ann.

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 [email protected], [email protected]

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

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

AGENDA

University of MichiganInstitute for Plasma Science & Engr.MIPSE_SEP2011_1

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.

PLASMAS IN LIQUIDS


Plasma Sources Sci. Technol. 17 (2008) 024010 Plasma Process. Polym. 6 (2009), 729

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

MODELING PLATFORM: nonPDPSIM

Poisson’s equation:

Transport of charged and neutral species:

Electron Temperature (transport coefficient obtained from Boltzmann’s equation:

)( sj

jj Nq

jjj St

N

eeeiii

ie

e TTNKnEjt

n

2

5


MODELING PLATFORM: nonPDPSIM


Radiation transport and photoionization:

Electric field emission

',''

)()(3j

kijkjkkmk

imim

rdrrGrNA

rNrS

2

'

'4

''exp

,'ij

l

r

r

jjllk

ijrr

rdrN

rrG

i

j

kB

work

ke Tk

Eq

ATJ

21

0

03

2 exp

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.

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.

“Paschen’s law”, Wikipedia, Septemeber 21, 2011 (http://en.wikipedia.org/wiki/Paschen%27s_law)

CONFIGURATION


Sharp-Tip ElectrodeBubble ~ 75 um

Parallel ElectrodeBubble ~ 50 um

Parallel ElectrodeBubble ~ 20 um

Breakdown of liquids from pre-existing bubbles was numerically investigated.

MIN MAX MIPSE_SEP2011_8

INITIATION INSIDE BUBBLES

University of MichiganInstitute for Plasma Science & Engr.

Initiation processes inside the bubble within 0.1 ns

Initiation processes are associated with electron impact ionization, photo-ionization and field emission


SHARP-TIP ELECTRODE


[e] (1018 cm-3, 3 dec)

E-field (5.0 ~ 7.0 MV/cm)

Se

(1027 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

[Sphoto] (1022 cm-3s-1, 3 dec)


PARALLEL ELECTRODE: PHOTO-IONIZATION


[e] (1017 cm-3, 3 dec)

[EF] (0.8 ~ 1.8 MV/cm)

[Se] (1027 cm-3s-1, 3 dec)

The electric field is enhanced due to the permittivity difference at the gas-liquid interface

Electron density is uniform due to uniform electric field inside the bubble The electron impact ionization dominates over photo-ionization



PARALLEL ELECTRODE: FIELD EMISSION


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

[e] (1016 cm-3, 3 dec)


Se

(1025 cm-3s-1, 3 dec)


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.

The enhanced electric field is so strong that a phase-like transition occurs there. The densities, compositions and other phase-related properties are changed respectively. As a result, a low-density area is created.

The streamer extends itself into the new low-density area. The loop continues until the streamer reaches the grounded electrode.

Plasma Process. Polym. 6 (2009), 729

E-fieldEnhancement

PhaseTransition

StreamerExtension

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

PROPAGATION: PHOTO-IONIZATION



The streamer is a little wider than the bubble, because the photo-ionization is isotropic

The photo-ionization is dominating in the bulk plasma; electron impact ionization only occurs at the head of the streamer

[e] (1016 cm-3, 3 dec)


Se

(1022 cm-3s-1, 3 dec)


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

PROPAGATION: FIELD EMISSION



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

[e] (1017 cm-3, 3 dec)


Se

(1025 cm-3s-1, 3 dec)


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

PLASMA DISCHARGE SIMULATIONS IN WATER WITH PRE-EXISTING BUBBLES AND ELECTRIC FIELD RAREFACTION Wei Tian and Mark J. Kushner University of Michigan, Ann.

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