FERROHYDRODYNAMICS R. E. ROSENSWEIG. DOVER PUBLICATIONS, INC. Mineola, New York

Transcription

1 FERROHYDRODYNAMICS R. E. ROSENSWEIG DOVER PUBLICATIONS, INC. Mineola, New York

2 CONTENTS Preface 1 Introduction 1.1 Scope of ferrohydrodynamics 1.2 Ferromagnetic solids 1.3 Magnetic fluids 1.4 Ferromagnetic concepts and units Definition of the fleld External field of a dipole source Magnetic force and torque on dipolar matter Interaction energy of two dipoles 1.5 Concepts of fluid mechanics Continuity equation Substantial derivative 1.6 Generalized Bernoulli equation 1.7 Stress tensor and its physical meaning Force resulting from a stress tensor Addendum: equivalence ofdipolar and polar representations 2 Magnetic fluids 2.1 Stability requirements Stability in a magnetic-field gradient Stability against settling in a gravitational field Stability against magnetic agglomeration Necessity to guard against the van der Waals attractive force 2.2 Preparation of magnetic colloids by size reduction 2.3 Preparation of ferrofluids by chemical precipitation Magnetite precipitation with steric stabilization Cobalt particles in an organic carrier Charge-stabilized magnetite 2.4 Other magnetic fluids Paramagnetic sah Solutions

3 vm Metallic-base ferrofluid 2.5 Surfaceadsorptionandstericstabilization Stenc repulsion mechanism Net interaction curve Dispersant structural guidelines 2.6 Ferrofluid modification Phenomenological basis Carrier liquid exchange Surfactant exchange 2.7 Physical properties Equilibrium magnetization: superparamagnetism «Magnetic relaxation 55 Viscosity 61 Concentrated suspensions 2.8 Correlation phenomena ^ 2.9 Tabulated physical properties 3 Electromagnetism and flelds 3.1 Magnetostaticfieldequations Scalar potential Magnetic-fieldboundaryconditions Maxwell stress tensor 77 Portrait ofthe Maxwell stresstensor Maxwell's equations 83 Integral equations 84 Differential equations Energy density of the electromagnetic field ^ Transformed expression for the field energy 95 QQ 98 4 Stress tensor and the equation of motion 4.1 Thermodynamic background Formulation of the magnetstress tensor 101 Stress tensor of a magnetizable fluid 103 What is the "pressure" in a magnetized fluid?,"* 4.3 Magnetic body-force density 108 Alternative general forms 110 Alternative reduced forms 111 Remarksconcerningstriction in compressible media!" 4.4 Equation of motion for magnetic fluid 7 Alternative forms ofthe equation of motion The ferrohydrodynamic BernouIIi equation Derivation nn 5.2 Boundary conditions 5.3 Categories of equilibrium inviscid flows l **

4 ix 5.4 Applications of the FHD Bernoulli equation 132 Classical Quincke problem 132 Surface elevation in a normal field 133 Magnetic nozzle 134 Modified Gouy experiment 136 Conical meniscus 137 Origin of the radial force 141 Magnetic-fluid rotary-shaft seals Eamshaw's theorem and magnetic levitation 146 Simplined treatment of the levitation of a nonmagnetic body 149 Phenomenon of self-levitation 150 Analysis of forces on an immersed body Striction effect Magnetocaloric energy conversion Thermodynamics of magnetic materials Mechanism for power generation Linear equation of State General cycle analysis Cycle efficiency for a linear material Cycle efficiency with regeneration Implementing the cycle Summary Ferrohydrodynamic instabilities Normal-field instability 178 Equation set 178 Interfacial force balance 179 Kinematics 182 Flow-field analysis 183 Perturbed magnetic field 185 Boundary conditions on the field vectors 185 Applying the magnetic boundary conditions 187 Theoretical predictions 188 Normal-field instability experiments 193 Nonlinear analysis General dispersion relation for moving media with oblique magnetic field Rayleigh-Taylor problem 200 Experimental confirmation Kelvin-Helmholtz instability 202 Criterion for Kelvin-Helmholtz instability in a ferrofluid Gradient-field stabilization Labyrinthine instability 208 Labyrinth spacing Stabilityof fluid cylinders 216 Magnetic-fluid jet in a uniform field 217

5 x Cylindrical column in a radial gradient field 7.8 Porous-medium flow: fingering instability 7.9 Thermoconvective stability 7.10 Retrospective Addendum: representation of disturbance waves Magnetic fluids and asymmetric stress Phenomena 8.2 Cauchy stress principle and conservation of momentum 8.3 Integral equation for conservation of angular momentum for nonpolar materials 8.4 Reynolds' transport theorem 8.5 Cauchy equation ofmotion 8.6 Symmetry of the stress tensor for nonpolar fluids 8.7 Analysis for polar fluids 8.8 Summary of the basic laws of continuum mechanics 8.9 Constitutive relations Magnetization relaxation process 8.10 Analogs of the Navier-Stokes equations for fluids with internal angular momentum 8.11 Ferrohydrodynamic-torque-drivenflow 8.12 Effective viscosity of a magnetized fluid 9 Magnetic two-phase flow 9.1 Background 9.2 Ordinary fluidization 9.3 Some fundamental problems in fluidization engineering 9.4 Basic relationships in two-phase flow Definition of averages Averaged continuity equations Averaged magnetostatic relationships Averaged momentum balances Constitutive relations 9.5 Summary of the averaged equations 9.6 Magnetized fluidized solids Solution in the steady State with a uniform magnetic field 9.7 Stability of the steady-state Solution Derivation of the linearized equations Form of the linearized equations for plane waves General Solution for the voidage perturbation Nature of the predicted behavior 9.8 Experimental behavior Transition velocity Influence of the field orientation Rheology of magnetically stabilized fluidized solids M

6 xi Directions for further study Appendixes Vector and tensor notation Application of the Maxwell stress tensor: analysis of a sheet jet 318 References Citation index 335 Subject index * 2