Table Of ContentLiquid Dielectrics in an
Inhomogeneous Pulsed Electric
Field (Second Edition)
Dynamics, cavitation and related phenomena
IOP Series in Plasma Physics
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Liquid Dielectrics in an
Inhomogeneous Pulsed Electric
Field (Second Edition)
Dynamics, cavitation and related phenomena
Mikhail N Shneider
MAE Department, Princeton University, Princeton, NJ, USA
Mikhail Pekker
George Washington University, Wahington DC, USA
IOP Publishing, Bristol, UK
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ISBN 978-0-7503-2372-7(ebook)
ISBN 978-0-7503-2370-3(print)
ISBN 978-0-7503-2373-4(myPrint)
ISBN 978-0-7503-2371-0(mobi)
DOI 10.1088/978-0-7503-2372-7
Version:20191101
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To our parents
Contents
Preface to 2nd edition (2019) xi
Preface to the 1st edition (2016) xii
Author biographies xvi
Nomenclature xvii
1 Introductory description of processes related to the negative 1-1
pressure in liquids
1.1 A qualitative picture of the formation of discontinuities in a liquid 1-1
1.2 Negative pressure 1-2
1.3 Rayleigh bubble 1-3
1.4 Viscosity accounting in Rayleigh’s equation for a bubble in a liquid 1-5
1.5 Dynamics of a bubble in the liquid 1-7
1.6 Zel’dovich–Fisher nucleation 1-12
1.7 Qualitative description of the processes in a liquid dielectric in 1-15
a non-uniform pulsed electric field
1.8 Flat capacitor dipped in a dielectric fluid 1-16
1.9 The polarization (Maxwell) time 1-17
1.10 The flow induced in the vicinity of a needle-like electrode: 1-18
a hydrostatic pressure
References 1-20
2 Classic cavitation 2-1
2.1 Definition of cavitation and formulation of the basic problem 2-1
2.2 Cavitation in the subsonic flow of fluid in a pipe 2-3
2.3 Condition for cavitation bubble formation near propeller blades 2-4
2.4 Cavitation generated by acoustic and shock waves 2-5
2.5 Surface tension of a curvilinear surface with a small radius of curvature 2-7
2.5.1 The interaction of molecules in water 2-8
2.5.2 The surface tension coefficient estimate at a planar interface 2-10
2.5.3 Surface tension of a bubble interface 2-12
2.5.4 The surface tension coefficient at the boundary of a droplet 2-14
in a gas
2.6 A new look at nucleation 2-16
References 2-23
vii
LiquidDielectricsinanInhomogeneousPulsedElectricField(SecondEdition)
3 The physical properties of liquid dielectrics 3-1
3.1 Water 3-1
3.1.1 Equation of state 3-1
3.1.2 Dielectric constant of water 3-3
3.1.3 Surface tension of water 3-5
3.2 Experimental data related to oil and some other liquid dielectrics 3-5
3.2.1 Speed of sound and equation of state 3-5
3.2.2 Dielectric constant 3-6
3.2.3 Surface tension 3-7
3.3 Liquid helium 3-7
3.3.1 Equation of state 3-8
3.3.2 Dielectric constant 3-10
3.3.3 Surface tension 3-10
References 3-12
4 A liquid dielectric in an electric field 4-1
4.1 Dielectric as a system of dipoles 4-1
4.2 The potential of a system of dipoles 4-3
4.3 The dielectric constant 4-8
4.4 The energy of the electric field 4-9
4.5 Energy of a dielectric in an external electric field 4-11
4.6 Dielectric ball in a homogeneous dielectric medium in an 4-11
external constant electric field
4.7 Polarizability of atoms and molecules 4-13
4.7.1 Non-polar dielectrics (Clausius–Mossotti relation) 4-13
4.7.2 The dielectric constant of dense non-polar dielectric media 4-15
4.7.3 The dipole moment of polar molecules 4-16
4.8 Ponderomotive forces in liquid dielectrics 4-19
4.9 Forces acting on the boundary between two dielectrics 4-23
4.10 Forces acting on a boundary of a dielectric sphere 4-25
References 4-29
5 Dynamics of a dielectric liquid in a non-uniform pulsed 5-1
electric field
5.1 System of equations and boundary conditions in prolate spheroidal 5-1
coordinates
5.2 Numerical results and discussions 5-5
viii
LiquidDielectricsinanInhomogeneousPulsedElectricField(SecondEdition)
5.3 Flow arising at adiabatic switching of voltage and its rapid shutdown 5-8
5.4 Linearized equations and example results 5-8
5.5 Comparison of numerical results with measurements 5-9
5.6 Initiation of cavitation and nanosecond breakdown in oil on 5-12
water micro-droplets
5.7 Qualitative analysis of a drop deformation in the pulsed electric field 5-15
References 5-17
6 Cavitation in inhomogeneous pulsed electric fields 6-1
6.1 Ponderomotive forces in the vicinity of a nanopore 6-1
6.2 Nucleation in inhomogeneous pulsed electric fields 6-4
6.3 Expansion of nanopores in an inhomogeneous pulsed electric field 6-7
6.4 Concluding remarks for chapter 6 6-8
Reference 6-9
7 Liquid helium in a non-uniform pulsed electric field 7-1
7.1 Dynamics of liquid helium in a non-uniform pulsed electric field 7-2
7.1.1 Conditions for the discontinuity formation in helium-3 7-2
and -4 in an inhomogeneous pulsed electric field
7.2 Regimes of cavitation inception in liquid helium 7-6
7.3 Tunnel effect in liquid helium at negative pressure 7-9
7.3.1 Statement of the problem 7-9
7.3.2 Eigenvalues and eigenfunctions 7-12
7.3.3 Nucleation probability 7-14
7.4 Possible limitations associated with the dielectric strength of 7-17
liquid helium
7.5 Conclusions to chapter 7 7-18
References 7-18
8 Optical diagnostics in dielectric liquids in inhomogeneous 8-1
pulsed fields
8.1 Shadowgraph and Schlieren methods 8-2
8.2 Rayleigh scattering on the cavitation region emerging in liquids 8-6
8.3 Optical emission spectroscopy of nano- and sub-nanosecond 8-11
discharge in liquids
References 8-12
ix
