ELECTROMAGNETIC WAVES and particulate materials J. Carlos - PowerPoint PPT Presentation

Aussois 2012 ELECTROMAGNETIC WAVES and particulate materials J. Carlos Santamarina Georgia Institute of Technology

References: Santamarina, J.C., in collaboration with Klein, K. and Fam, M. (2001). Soils and Waves, J. Wiley and Sons, Chichester, UK, 488 pages. Klein, K. and Santamarina, J. C. (2003b). "Electrical Conductivity In Soils: Underlying Phenomena." Journal of Environmental & Engineering Geophysics, Vol. 8, No. 4, pp. 263-273. Klein, K. and Santamarina, J. C. (1997). "Methods for Broad-Band Dielectric Permittivity Measurements (Soil- Water Mixtures, 5 Hz to 1.3 GHz)." ASTM Geotechnical Testing Journal, Vol. 20, No. 2, pp. 168-178. Santamarina, J. C. and Fam, M. (1997b). "Dielectric Permittivity of Soils Mixed with Organic and Inorganic Fluids (0.02 GHz to 1.30 GHz)." Journal of Environmental & Engineering Geophysics, Vol. 2, No. 1, pp. 37-52. Santamarina, J. C. and Fam, M. (1995). "Changes in Dielectric Permittivity and Shear Wave Velocity During Concentration Diffusion." Canadian Geotechnical Journal, Vol. 32, No. 4, pp. 647-659. Some pdfs (these and related papers) available at http://pmrl.ce.gatech.edu under "Publications"

Soils: An Electrical View

Fluids - Water Mass Bulk stiffness Capillary forces Seepage rate Dipole Hydration and double layers Cl - 90 90 H + 120 60 120 60 H + 109 o 150 30 150 30 Cl - Cl - C 4+ 180 0 180 0 210 330 O 2- 210 330 240 270 300 240 270 300 Cl - L=1.25r L=10r

Electrical View of Soils dry soil water wet soil pore fluid Precipitated salt mineral double layer

Wet clay Laponite 1200 H 2 O 24 Na + N. Skipper (UCL)

Electromagnetic Waves

Maxwell’s Equations 1 E E d s s free dv free Gauss' Law of Electricity E v v surf vol H d s 0 H 0 Gauss' Law of Magnetism surf d d H E d l H d s E Faraday's Law of Induction dt dt loop surf d d E H d l J d s E d s H E Ampere-Maxwell's Law dt dt loop surf surf

Electromagnetic Parameters Free Materials space Conductivity 0 ε o ε * = ε ’ - j ε ” Permittivity = ’ - j ” Permeability o

Wave Equation E E E E 2 2 E in real t t 2 materials Consider solution of the form (fluctuates in y - propagates in x) E E e x e ( j t x ) y o j j 2 Then

E E e x e ( j t x ) if y o dH E Faraday dt * * H j E e j t * x j E then z o y x y z

Phase Velocity V ph Im( j ) Im j 2 1 m V c 3 10 8 In free space s ph o 0 o o o o c V o In non-ferromagnetic dielectric ph ' ' 0 o o

Attenuation Re j Re j 2 In free space 0 0 o o ' In non-ferromagnetic material 1 o 1 tan 2 1 ' j " c 2 o o

Frequency Wave Wave [Hz] length [m] 10 22 10 -14 10 21 10 -13 Gamma rays 10 20 10 -12 Electromagnetic 10 19 10 -11 10 18 10 -10 X rays Spectrum 10 17 10 -9 10 16 10 -8 Ultraviolet 10 15 10 -7 10 14 10 -6 Visible * 10 13 10 -5 Infrared 10 12 10 -4 10 11 10 -3 Microwaves 10 10 10 -2 GHz 10 9 10 -1 10 8 1 10 7 10 1 MHz 10 6 10 2 10 5 10 3 Radio waves 10 4 10 4 KHz 10 3 10 5 10 2 10 6 10 1 10 7

and God said: 1 free E v H 0 d H E dt d E H E dt and there was light…!

Light-surface interaction (Atlanta Airport) and blue butterflies?

Reflection Fresnel’s Ellipse van Gogh - La Nuit Etoilee

Scatter St. Peter - Rome

Electromagnetic Material Properties

Electromagnetic Parameters Conductivity ε * = ε ’ - j ε ” Permittivity = ’ - j ” Permeability

Note: Losses Ohmic conduction losses ε ” ω Polarization losses ” ω Magnetization losses " tan Non-Ferromagnetic '

Conductivity  charges & mobility

Electrical Conductivity of the Pore Fluid 40 conductivity [S/m] 30 NaOH NaCl 20 CaCl 2 10 0 0 2 4 6 8 10 12 concentration [mol/L] [ mS / m ] 0 . 15 TDS [ mg / L ] At low concentration (P. Annan): fl

Archie’s Law? n soil el

Electrical Conductivity Pore fluid Surface conduction n 1 n S Wet Soil soil el g s

Electrical Conductivity of Soils 1 n Archie soil fl mix [S/m] c = 0.1 mol/L 0.1 mixture conductivity, c = 10 -5 mol/L n 1 n S 0.01 soil fl s 0.001 0.4 0.5 0.6 0.7 0.8 0.9 1 porosity, n

Summary el = soil g S s Controlled by (1-n) 10 0 soil [S/m] Controlled by clays el n 10 -3 S s sands 10 -3 10 -6 10 0 el [S/m] de-ionized fresh sea water water water

Summary: Electrical Conductivity g λ S s el = soil Controlled by (1-n) 2 10 0 soil [S/m] Controlled by n el clays 10 -3 S s sands 10 -3 10 -6 10 0 el [S/m] de-ionized fresh sea water water water

Permittivity  Polarizability

Single phase Direction of Applied Field Orientational Ionic Electronic (relaxation) (resonance) (resonance) - 16 s t - 12 s =10 - 13 s t × t = 9 10 =10 (Ultraviolet) – (Microwave water) (Infrared)

Polarization spectrum 0 200 150 spatial orientational 100 ionic electronic ' 50 " 0 conduction polarization losses losses 50 100 1 103 1 104 1 105 1 106 1 107 1 108 1 109 1 10101 1011 1 10121 10131 1014 1 10151 1016 1 10171 1018 1 10 2 10 4 10 6 10 8 10 10 10 12 10 14 10 16 10 18 1 10 frequency [Hz]

Water-Ion Interaction 90 f = 1.3 GHz 80 70 KCl 60 ' FeCl 3 LiCl 50 40 NaCl 30 CaCl 2 20 0 1 2 3 4 5 6 ionic concentration [mol/L]

Double layer effects Direction of Applied Field Bound water (relaxation) Stern layer (Infrared) (Radio frequency) Double layer (deionized) Double layer (electrolyte) Double layer - Normal particle interactions (surface conduction)

Two-phase media - Spatial polarization Direction of Applied Field Maxwell relaxation (no relaxation) Wagner relaxation Semi-permeable membrane

Polarizations single phase material log(size/m) mixture (interfacial polarization - relaxation) 0 macrospace polarization -3 scatter micro-space visible polarization grain range bound. -6 double layer molecular -9 orient. relax ionic -12 electronic reson. resonance -15 -3 0 3 6 9 12 15 log(frequency/Hz)

Summary: Relative Permittivity water 78 ice ~3 air, gasses ~1 most organic fluids 2-6 minerals 5-10 ' ' ' 1 n n 1 S nS Linear mixture soil m w 2 ' ' ' 1 n n 1 S nS CRIM soil m w ' 2 3 3.03 9.3 146.0 76.7 Topp et al. 1980 soil v v v

Summary: Single materials water 78.5 quartz 4.2 - 5 methanol 32.6 calcite 7.7 - 8.5 most minerals 6 – 10 most organic fluids 2 - 6

Free Water - Consolidation Orientational Pol. 40 1.3 GHz 0.20 GHz (Table 11.9) Permittivity DeLoor 35 ' 30 ' 25 0.48 0.5 0.52 0.54 0.56 0.58 0.6 0.62 local volumetric water content Volumetric Water Content s

Summary: Soils VOLUMETRIC WATER CONTENT 2 ' 2 . 6 1 . 6 n 7 . 9 v 2 ' 40 3 . 9 44 . 8 392 1600 v v v 2 ' 1 . 40 87 . 6 18 . 7 v v 2 3 ' 3 . 03 9 . 3 146 . 0 76 . 7 v v v 2 ' 3 . 14 23 . 8 16 . 0 v v 2 ' 3 . 3 41 . 4 16 . 0 v v

Summary 90 Kaolinite Topp et al. (1980) Bentonite 80 Based on CRI - S=100% Mixed clays Selig and Mansukhani (1975) Sands and silts 70 real relative permittivity [ ] Wang (1980) 60 50 Wensink (1993) 40 30 20 10 0 0 20 40 60 80 100 volumetric water content [%]

Permeability  Magnetizability

Kingston Fossil Plant (12/22/2008) [Photo: U.S. Environmental Protection Agency]

XRD: Mill Creek Hopper Magnetically separated fraction: hematite Fe 2 O 3 (weakly magnetic), magnetite Fe 3 O 4 and maghemite Fe 2 O 3 (both strongly magnetic).

Magnetization Electron orbits orbit alignment Diamagnetism Electron spin unpaired Paramagnetism Alignment within domains move domain walls Ferromagnetism domain 1 wall domain 2

Permeability iron fillings in kaolinite – f = 10 kHz 3 2.5 μ’ rel = 1 + 4 v Fe + 7 v Fe μ’ rel = 1 + 3 v Fe 2 Maxwell ' rel Wagner 1.5 1 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 volume fraction of iron filings

Permeability iron in kaolinite – f = 10 kHz 2.2 2 1.8 1.6 ' rel (a) (b) (c) (d) (e) (f) (g) 1.4 1.2 1 10 3 10 4 10 5 10 6 10 7 10 2 frequency [Hz] 0.5 Series1 (a) 0.4 Series2 (b) Series3 (c) Series4 0.3 (d) " Series5 (e) rel (f) Series6 0.2 (g) Series7 0.1 0 10 2 10 3 10 4 10 5 10 6 10 7 frequency [Hz]

Summary '/ Single materials o water, quartz, kaolinite ~0.9999 (diamagnetic) montmorillonite, illite, granite, hematite 1.00002-1.0005 (paramagnetic) nickel, iron > 300 (ferromagnetic) Predictive relations 1 3v spherical ferromagnetic inclusions Fe for v Fe <0.2 1 4v 7v 2 Kaolinite with iron filings (at 10 kHz) Fe Fe for v Fe <0.3

Measurement

Testing Standing Quasi-DC Wave propagation wave f res f Complex V R, C, L α Reflectivity

Quasi-static