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Liquid Dielectrics in an Inhomogeneous Pulsed Electric Field (Second Edition) Dynamics, cavitation and related phenomena IOP Series in Plasma Physics Series Editors Richard Dendy Culham Centre for Fusion Energy and the University of Warwick, UK Uwe Czarnetzki Ruhr-University Bochum, Germany About the series TheIOPPlasmaPhysicsebookseriesaimsatcomprehensivecoverageofthephysics andapplicationsofnaturalandlaboratoryplasmas,acrossalltemperatureregimes. Books in the series range from graduate and upper-level undergraduate textbooks, research monographs and reviews. The conceptual areas of plasma physics addressed in the series include: (cid:129) Equilibrium, stability and control (cid:129) Waves: fundamental properties, emission, and absorption (cid:129) Nonlinear phenomena and turbulence (cid:129) Transport theory and phenomenology (cid:129) Laser-plasma interactions (cid:129) Non-thermal and suprathermal particle populations (cid:129) Beams and non-neutral plasmas (cid:129) High energy density physics (cid:129) Plasma-solid interactions, dusty, complex and non-ideal plasmas (cid:129) Diagnostic measurements and techniques for data analysis The ﬁelds of application include: (cid:129) Nuclear fusion through magnetic and inertial conﬁnement (cid:129) Solar-terrestrial and astrophysical plasma environments and phenomena (cid:129) Advanced radiation sources (cid:129) Materials processing and functionalisation (cid:129) Propulsion, combustion and bulk materials management (cid:129) Interaction of plasma with living matter and liquids (cid:129) Biological, medical and environmental systems (cid:129) Low temperature plasmas, glow discharges and vacuum arcs (cid:129) Plasma chemistry and reaction mechanisms (cid:129) Plasma production by novel means 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 ªIOPPublishingLtd2020 Allrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystem ortransmittedinanyformorbyanymeans,electronic,mechanical,photocopying,recording orotherwise,withoutthepriorpermissionofthepublisher,orasexpresslypermittedbylawor undertermsagreedwiththeappropriaterightsorganization.Multiplecopyingispermittedin accordancewiththetermsoflicencesissuedbytheCopyrightLicensingAgency,theCopyright ClearanceCentreandotherreproductionrightsorganizations. PermissiontomakeuseofIOPPublishingcontentotherthanassetoutabovemaybesought [email protected]. MikhailNShneiderandMikhailPekkerhaveassertedtheirrighttobeidentifiedastheauthorsof thisworkinaccordancewithsections77and78oftheCopyright,DesignsandPatentsAct1988. 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 IOPebooks BritishLibraryCataloguing-in-PublicationData:Acataloguerecordforthisbookisavailable fromtheBritishLibrary. PublishedbyIOPPublishing,whollyownedbyTheInstituteofPhysics,London IOPPublishing,TempleCircus,TempleWay,Bristol,BS16HG,UK USOffice:IOPPublishing,Inc.,190NorthIndependenceMallWest,Suite601,Philadelphia, PA19106,USA 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