Electrical Breakdown in Liquids

High-voltage Pulsed Power Engineering, Fall 2018

Electrical Breakdown in Liquids

Fall, 2018

Kyoung-Jae Chung

Department of Nuclear Engineering

Seoul National University

Water spark gap switch

 The use of water insulated switches to transfer energy from one stage to another in large pulsed power drivers has led to a high degree of integration not possible with gas switches.

 This, coupled with the relatively high breakdown strength of fast charged water systems, allows for short gap lengths and correspondingly lower switch

inductance.

Discharges in and in contact with liquids

 Discharges in and in contact with liquids provide new scientific challenges and emerging technological opportunities for the plasma community. e.g) plasma surgery, lithotripsy, plasma oncology, decontamination and purification of water.

 Discharges in and in contact with liquids generate intense UV radiation, shock waves and active radicals (OH, atomic oxygen, hydrogen peroxide, etc) all of which are effective agents against many biological and chemical matter.

Liquid breakdown has no single comprehensive theory

 The breakdown mechanism in liquids is more complicated than in solids or gases since liquids are much denser in comparison with gases, and do not exhibit the long range order seen in solids.

 Additionally the purity of the liquid, such as dissolved gases which form micro- bubbles in the liquid, plays a significant role in the breakdown process.

 Two categories for liquid breakdown:

 Electronic mechanism (direct impact ionization): The discharge is a

consequence of avalanche multiplication of free charge carriers in the liquid and is described by the gas discharge model generalized to the liquid phase.

It implies that electrons in strong fields are accelerated in liquids and ionize molecules and atoms.

 Bubble mechanism: Discharge occurs in gas cavities either already

presented in the liquid and on the electrodes or newly formed under voltage exposure.

 A general acceptance is growing that pre-existing bubbles and field enhancement effects in the near electrode region are involved even for

nanoseconds voltage pulse widths. R. P. Joshi, Plasma Chem Plasma Process 33, 1 (2013)

Universally observed characteristic features during liquid breakdown

 The breakdown strength of fluids increases with increasing pressure.

 The time lag to breakdown increases with increasing pressure.

 The breakdown voltage is always lower when the polarity of the stressed electrode is positive than when it is negative. This means that when a

symmetrical electrode system is used pre-breakdown is preferentially initiated at the anode.

 The time lag to breakdown is polarity dependent. A formative time lag for micro- bubble formation is observed for negative streamer initiation and not for positive streamers.

 The critical electrical breakdown field decreases with increasing pulse width.

 The probability of breakdown increases with increasing surface area of the electrode. This is correlated with the increased probability of the existence of imperfections like micro-protrusion on the electrode surface which are able to locally enhance the electrical field or cause field emission to trigger breakdown.

Polarity effect: positive streamer vs. negative streamer

 Positive streamer:

 Thin and filamentary structure

 Faster initiation than negative mode

 Initiate at lower voltage

 Negative streamer:

 Thick root, bush-like or mushroom- like structure

 Slower initiation than positive mode

 Initiate at higher voltage

A. Sun, High Volt. 1, 74 (2016)

Determination of breakdown delay time (time lag)

 For a large number of experiments:

• 𝑁𝑁(𝑡𝑡): the number of pulses for which the breakdown time lag is equal or larger than 𝑡𝑡.

• 𝑁𝑁₀: the total number of breakdowns.

• 𝑡𝑡_𝑠𝑠: statistical delay time.

• 𝑡𝑡_𝑓𝑓: formative delay time.

• 𝜏𝜏_{𝑏𝑏𝑏𝑏}: total breakdown delay time (breakdown time lag).

 Laue plot

𝑁𝑁 𝑡𝑡 = 𝑁𝑁₀exp −𝑡𝑡 − 𝑡𝑡_𝑓𝑓

𝑡𝑡_𝑠𝑠 𝜏𝜏_{𝑏𝑏𝑏𝑏} = 𝑡𝑡_𝑠𝑠 + 𝑡𝑡_𝑓𝑓

− ln𝑁𝑁(𝑡𝑡) 𝑁𝑁⁄ ₀ = 𝑡𝑡 − 𝑡𝑡_𝑓𝑓 𝑡𝑡_𝑠𝑠

V. Ushakov, Impulse Breakdown of Liquids (2007)

Statistical analysis of breakdown time lag in water

Average = 55 ns SD = 18 ns

𝑡𝑡_𝑠𝑠 = 16 ns 𝑡𝑡_𝑓𝑓 = 42 ns

The time lag to breakdown ( 𝝉𝝉

) increases with increasing pressure

H. Jones, IEEE Trans. Dielectrics and Electrical Insulation 1, 1016 (1994)

Low bubble content

The time lag to breakdown ( 𝝉𝝉

) increases with increasing pressure

V. Ushakov, Impulse Breakdown of Liquids (2007)

 The strong influence of the external pressure on the statistical delay indicates that the thermal mechanism of microbubble formation is dominant.

 The statistical delay of the electric discharge from anode includes the process resulting in fast local superheating of the liquid near the electrode surface and

nucleation. _𝑡𝑡

𝑠𝑠 = 75 ns 𝑡𝑡_𝑓𝑓 = 154 ns

𝑡𝑡_𝑠𝑠 = 235 ns 𝑡𝑡_𝑓𝑓 = 180 ns

Polarity effect (with or w/o bubble)

Anode initiation Cathode initiation

S. Korobeinikov, High Temperature 40, 652 (2002)

Polarity effect with bubble

Streamer in water with bubbles

Cathode-directed streamer Anode-directed streamer

Structure of positive streamers inside bubbles

Formation of cavitation due to electrostriction force

 The initial stage of development of a nanosecond breakdown in liquids is

associated with the appearance of discontinuities in the liquid (cavitation) under the influence of electrostriction forces.

M. Pekker, J. Phys. D: Appl. Phys. 47, 025502 (2014)

Recent research direction

P. Vanraes, Appl. Phys. Rev. 5, 031103 (2018)

Recent research direction

Solvated electron in water

Field-induced desolvation Electron solvation in water

Surface deformation by electric field

Practical consideration: liquid insulation

 Insulation is the prevention of current flow. It is the major technological problem of high-voltage pulsed power applications.

 There is no simple theory of breakdown in solids and liquids. Knowledge of

insulating properties is mainly empirical. These properties vary considerably with the chemical purity and geometry of the insulating material.

 The pulsed voltage dielectric strength [MeV/cm] of transformer oil is approximately

 The dielectric strength of water is dependent on polarity:

The time during which the voltage is above 63% of the maximum value (µs)

The surface area of the high voltage electrode (cm²)

Bubble mechanism is valid for a long pulse (> 1us)

 For large pulse widths (i.e. several microseconds to dc), especially in high conductive water solutions, the process of breakdown is preceded by vapor formation due to heating by the pre-breakdown current in the liquid.

A. Olsen, J. Acoust. Soc. Am. 94, 2226 (1993)

 However, bubble formation before plasma formation in the case of sub-us pulses is likely to be incomplete and transient as bubble formation is typically at a time scale of at least 1μs.

Typical characteristics of electrical breakdown of water

• Oil well stimulation

• Rock fragmentation

• Material Processing

• Ultrasound acoustic source

• Well screen cleaning

• Green algae treatment

Pre-breakdown period

Breakdown voltage (𝑉𝑉_{𝑏𝑏𝑏𝑏})

Breakdown period

Applications

Fast framing movie

1 sec (playing time) = 0.1 ms (real time)

Water breakdown Bubble implosion

Water breakdown process (positive mode)

anode cathode

𝑽𝑽

= 𝟏𝟏𝟏𝟏 𝒌𝒌𝑽𝑽

Generation of strong shockwaves in water

φ3

Gap distance (~7mm)

Anode Cathode Before

discharge

Formation of spark channel Tungsten electrode

Ambient water (liquid)

φ8

Spark channel (plasma)

990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 0.0

5.0x10⁷ 1.0x10⁸ 1.5x10⁸ 2.0x10⁸ 2.5x10⁸ 3.0x10⁸ 3.5x10⁸ 4.0x10⁸

Pressure [Pa]

Density [kg/m³]

Tait EOS of Water Hugoniot EOS of Water

𝑝𝑝 ≈ 3 × 10⁸ 𝜌𝜌 𝜌𝜌₀

7

− 1 [Pa]

Mechanism for shock wave generation by pulsed spark discharge

Com- pressed gas

ρ p

ρ p

ρ p

ͯ ͯ ͯ

undisturbed gas

(a) (b) (c)

Shock front

Diagram of the shock wave formation First compression wave with speed of sound

Second wave propagation with a higher speed than speed of sound

The later formed wave overtakes a preceding wave

c₀

c₀ c₁+u₁ u₁

u₂

c₂+u₂

* c_0,1,2: sound velocity, u_1,2: particle velocity

(a)

(b)

(c)

c₁+u₁ c₀

[5] Y. B. Zel'dovich and Y. P. Raizer, “Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena”, Dover Publications, New York (2002)

t*

Channel radius

t Channel expansion speed u_m

t 𝒖𝒖(𝒕𝒕)

Sound velocity of 1^stwave

Faster compression waves contribute to shock wave formation

Acceleration period

Application to water well cleaning

K. J. Chung et al., The Journal of Engineering Geology 23, 29 (2013) (Korean)

Well screen Spark Shock

wave

Electric current

Shock wave

-10 0 10 20 30 40 50 60 70

-8 -6 -4 -2 0 2 4 6 8 10 12

Pressure

Current [kA], Pressure [MPa]

Time [µs]

128J (16kV) 162J (18kV) 200J (20kV) Current

Application to water well cleaning

Vertical well cleaning Horizontal well cleaning

(1) Pulsed power system (2) Coaxial cable (15m) (3) Spark generator (4) Well screen (5) Gravel pack

Hydraulic conductivity (Hvorslev theory) : 𝟐𝟐. 𝟑𝟑𝟑𝟑 × 𝟏𝟏𝟎𝟎^−𝟒𝟒 → 𝟏𝟏. 𝟕𝟕𝟑𝟑 × 𝟏𝟏𝟎𝟎^−𝟒𝟒 [ ⁄𝒎𝒎 𝒔𝒔]

Increased well efficiency ~ 21.3%

Hydrostatic pressure ~ 3 atm Cable length 110m

Application to green algae treatment

 Shock wave destroys gas vesicles to sink the water-bloom down to the bottom

w/o pulse w/ pulse

w/o pulse w/ pulse Gas vesicles

Key features of subsonic discharge

Bubble formation HV

applicatio n

Breakdown

Ohmic

heating Streamer

initiation

&

propagation

SW generation Pre-breakdown period Breakdown period

Key features

 Input energy ~ a few hundred J/pulse to generate spark discharges

 High breakdown strength of liquid

→ Discharge initiation from the low density region (i.e. bubble or vapor layer)

→ Pre-existing bubbles are particularly important

Circuit response during the pre-breakdown period ⇒ 𝑽𝑽_{𝒃𝒃𝒃𝒃}

& Thermo-electric features of underwater streamer ⇒ 𝒓𝒓_𝟎𝟎, 𝝆𝝆_𝟎𝟎, 𝑻𝑻_𝟎𝟎, 𝑹𝑹_𝟎𝟎

→ Crucial in SW generation

Use of water electrolysis for pre-breakdown acceleration

𝟐𝟐𝑯𝑯_𝟐𝟐𝑶𝑶 + 𝟐𝟐𝒆𝒆⁻

→ 𝑯𝑯_𝟐𝟐+ 𝟐𝟐𝑶𝑶𝑯𝑯⁻ (@ 𝑐𝑐𝑐𝑐𝑡𝑡ℎ𝑜𝑜𝑜𝑜𝑜𝑜)

K. Leeet al, Appl. Phys. Lett. 112 (2018) 134101

Pre-breakdown acceleration by water electrolysis

Anode

Cathode

Negative streamer discharge

394 μs

238 μs

Cathode

Anode

Cathode

Anode Bubble cluster Positive streamer

Negative streamer

200 220 240 260 280 300 320 340 360 380 -4

0 4 8 12 16

Time [µs]

Current [kA], Voltage [kV]

-2 0 2 4 6 8

τ_bd=239 µs

6.8 MPa

Pressure

Current

Pressure @ 10 cm [MPa]

Voltage

V_bd= 11.4 kV (V₀= 15 kV)

360 380 400 420 440 460 480 500 520 540 -4

0 4 8 12 16

Current [kA], Voltage [kV]

-2 0 2 4 6 8

Pressure @ 10 cm [MPa]

Voltage

Current

τ_bd=396 µs

V_bd= 13.5 kV (V₀= 22 kV)

Pressure

4.1 MPa

 Conventional positive mode

 Accelerated negative mode

More suitable to investigate the mechanism

of shock wave development Large uncertainty

Streamer propagation

Breakdown