ESTABLISH THE DIELECTRIC PROPERTIES OF A NUMBER OF

WOOD SPECIES FOR A RANGE OF FREQUENCIES,

TEMPERATURES AND PRESSURES

Georgiana Daian

Doctor of Philosophy

2005

SWINBURNE UNIVERSITY OF TECHNOLOGY

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Abstract

The present research offers an assessment of a new way of approaching the

dielectric properties of wood. The concept takes into consideration a probable

influential factor which has never been considered and refers to the elevated pressure

which develops within wood during microwave processing. In addition, in order to

understand and analyse the wood dielectric properties’ dependency on the internal

temperature and pressure, a custom-made device and the appropriate measuring

procedure, as well as a numerical model which calculates complex dielectric

permittivity of an anisotropic wood structure is presented.

Initially, the fundamentals of microwave–wood interaction including

polarisation mechanism, factors affecting the dielectric response of wood, microwave

related characteristics of wood and its microwave heating process are examined. The

importance of measuring the wood dielectric properties is also posed.

Subsequently, an insight into the main aspects of the techniques used in other

industries to measure the materials dielectric properties is provided. The report ends

with a comparative discussion of the measurement techniques applicability.

A method for measuring the dielectric permittivity of wood is then presented

together with a description of the software required to extract the dielectric parameters

from the measured quantities. The experimental results of the dielectric parameters of

the main Australian wood species are also presented.

Besides, a numerical model built to describe the 3-D wood structure is put

forward. This model was introduced into an efficient solver that calculates the effective

dielectric constant of any three dimensional structure of dielectric materials. The

analysis of the calculated results for the permittivity and the comparison to the

measured values shows a very practical qualitative and quantitative agreement between

all the measured and calculated values.

Finally, the importance of the research, the key results and the

recommendations for further work are emphasized.

Keywords: dielectric properties of wood, microwave processing, 3-D wood model,

wood internal temperatures and pressures, measurements techniques.

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Acknowledgement

I would like to express my gratitude to my academic supervisor, Dr. Alex Taube of the

Swinburne University of Technology, for his kind assistance and invaluable guidance

throughout this study. I am grateful to Professor Gregory Torgovnikov of Melbourne

University for serving on my Ph.D. committee and for his support and valuable

feedback.

I would like to extend my gratitude to the Cooperative Research Center for Wood

Innovations, especially to Professor Peter Vinden for providing motivation behind this

research program and the funding to make it possible. Additionally, I thank to the

Industrial Research Institute Swinburne for all the facilities that were made available to

me in order to undertake this research.

I am deeply grateful to Dr Amikam Birnboim of University of Haifa for his effective

collaboration and valuable guidance in performing the computer-aided simulation.

Sincere appreciation is also extended to Dr. Yury Shramkov (Industrial Research

Institute Swinburne) for providing considerable technical support.

Special thanks go to Professor Elias Siores for having confidence in my research

abilities and offering encouragement on numerous occasions.

I would like to thank my parents for their continuous moral support and for their simply

being there despite the distance which separated us, and I would like to thank my

husband for his unfailing support.

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DECLARATION

This thesis contains no material which has been accepted for the award of any other

degree or diploma, except where due reference is made in the text of the thesis. To the

best of my knowledge contains no material previously published or written by another

person except where due reference is made in the text of the thesis.

Signed: Georgiana Daian

Dated: August 2005

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Table of Contents

Abstract.............................................................................................................................i Acknowledgement ...........................................................................................................ii Table of Contents ...........................................................................................................iv List of Figures................................................................................................................vii List of Tables ..................................................................................................................xi Nomenclature ...............................................................................................................xiii Abbreviations ................................................................................................................xv Introduction.....................................................................................................................1

PART I LITERATURE REVIEW

CHAPTER 1: MICROWAVE–WOOD INTERACTION FUNDAMENTALS........5

1.1 Microwave History, Applicability and Definition ...................................................5 1.2 Maxwell’s Equations and Electromagnetic Waves..................................................7 1.3 Polarisation of Wood..............................................................................................10

1.3.1 Time and frequency dependent polarisation.....................................................11 1.3.2 Wood dielectric response as the result of dipole polarisation ..........................12

1.4 Factors Affecting the Dielectric Properties of Wood.............................................14 1.4.1 Structural Components of Wood......................................................................15 1.4.2 Wood Moisture Content ...................................................................................16 1.4.3 Wood Anisotropy .............................................................................................18 1.4.4 Wood Density...................................................................................................19 1.4.5 Wood Internal Temperature .............................................................................20 1.4.6 Microwave Frequency......................................................................................21

1.5 Wood Characteristics Related to Microwave Heating ...........................................22 1.5.1 Heterogenous and anisotropic ..........................................................................22 1.5.2 Poor thermal, moderate electrical conductor and non permeable under microwave energy .....................................................................................................23

1.6 Microwave Heating Process of Wood....................................................................24 1.7 The Importance of Measuring the Dielectric Properties of Wood .........................27

CHAPTER 2: TECHNIQUES FOR MEASURING THE DIELECTRIC PROPERTIES OF MATERIALS AT MICROWAVE FREQUENCIES ...............32

2.1 Classifications of the Dielectric Properties Measurement Techniques..................32 2.2 Transmission Line Techniques...............................................................................35

2.2.1 Transmission lines fundamentals and electromagnetic field distribution ........35 2.2.2 Operating frequency domain; measurements errors and results accuracy; advantages and disadvantages in using the different transmission line techniques ..40 2.2.3 Understanding the Fundamental Principles of the Transmission Line Measurements............................................................................................................42

2.2.3.1 Measurement system set-up.......................................................................43

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2.2.3.2 Reflection and transmission parameters ....................................................43 2.2.3.3 Transmission lines terminations. Fundamentals of electromagnetic waves for each particular case ..........................................................................................47

2.2.4 Algorithms for calculating the dielectric parameters .......................................49 2.2.4.1 Transmission-Reflection method algorithms.............................................50 2.2.4.2 Reflection methods algorithms..................................................................56

2.2.5 Transmission line calibrations..........................................................................58 2.3 Free Space Technique ............................................................................................61

2.3.1 Operating frequency domain; measurements errors and results accuracy; advantages and disadvantages in using the technique...............................................61 2.3.2 Measurement system set-up .............................................................................62 2.3.3 Free-space calibration.......................................................................................64 2.3.4 Algorithms for calculating the dielectric parameters .......................................64

2.4 Open-End Coaxial Probe Technique......................................................................65 2.4.1 Operating frequency domain; measurements errors and results accuracy; advantages and disadvantages in using the technique...............................................65 2.4.2 Coaxial probe calibration .................................................................................67 2.4.3 Measurement system set-up .............................................................................67 2.4.4 Models for calculating the dielectric parameters..............................................68

2.5 Resonant Cavity Techniques..................................................................................69 2.5.1 Resonant structures fundamentals and electromagnetic field distribution .......70 2.5.2 Operating frequency domain; measurements errors and results accuracy; advantages and disadvantages in using resonant cavities techniques .......................72 2.5.3 Measurement system set-up .............................................................................74 2.5.4 Cavity perturbation method: the principle for calculating the dielectric parameters..................................................................................................................75

2.6 Comparison of the Permittivity Measurement Techniques and the Review’ Outcome .......................................................................................................................77

PART II RESEARCH METHODOLOGY, DEVELOPED

TECHNIQUES, RESULTS AND ANALYSIS

CHAPTER 3: RESEARCH METHODOLOGY .......................................................81 3.1 Defining the Research Question and Objectives....................................................81 3.2 Approach to the Research Problem........................................................................83

CHAPTER 4: MEASURING DIELECTRIC PROPERTIES OF WOOD AT MICROWAVE FREQUENCIES, ELEVATED TEMPERATURES AND PRESSURES..................................................................................................................85

4.1 Measurement Technique and Experimental System Set-Up..................................85 4.2 Measurement Device Calibration...........................................................................88 4.3 Experimental Method.............................................................................................88 4.4 Numerical Procedure..............................................................................................92 4.5 Verification of Experimental Method and Numerical Procedure ..........................95

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CHAPTER 5: MODELING DIELECTRIC PROPERTIES OF WOOD AT MICROWAVE FREQUENCIES ................................................................................98

5.1 Structural Design of the Wood Modelling Software..............................................99 5.2 Method for Calculating the Permittivity and the 3-D Wood Model ....................100 5.3 Software’s Input Instructions ...............................................................................104

5.3.1 To create wood model geometry ....................................................................104 5.3.2 To attribute different densities and moistures ................................................105 5.3.3 To calculate the structure’s permittivity.........................................................107

5.3.3.1 Dielectric parameters of air .....................................................................107 5.3.3.2 Dielectric parameters of free water..........................................................107 5.3.3.3 Dielectric parameters of wood substance/moist wood substance............110 5.3.3.4 Dielectric parameters of rays ...................................................................113

CHAPTER 6: RESULTS AND DISCUSSION ........................................................115 6.1 Complex Permittivity of Australian Wood Species .............................................115

6.1.1 Experimental results and analysis ..................................................................115 6.1.2 Modeling results and analysis ........................................................................121

6.2 Discussion ............................................................................................................126

CHAPTER 7: CONCLUSIONS AND RECOMMENDATIONS FOR FURTHER WORK..........................................................................................................................136

References ....................................................................................................................140

APPENDIX A: Additional Data Related to the Fundamental Principles of the Transmission Lines and Resonant Cavities ..............................................................150 APPENDIX B: The Input File Interface of the Software which Extracts the Dielectric Parameters from the Measured Quantities Via the Solution of a Transcedental Equationin in the Complex Plane.....................................................162 APPENDIX C: The Input File Interface of the Software which Predicts the Dielectric Properties of Wood....................................................................................169 APPENDIX D: Additional Data Related to Dielectric Parameters of Free Water, Bound Water and Cell Wall Substance in Wood .....................................................174

List of Publications......................................................................................................181

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List of Figures

Figure 1: The potential of microwave applications in wood industry ..............................6 Figure 2: Propagation of a plane wave..............................................................................8 Figure 3: Electromagnetic spectrum and frequencies used in microwave processing .....9 Figure 4: Frequency dependence of the various polarisation mechanisms.....................12 Figure 5: Permittivity of the CWS at 109 GHz and high temperatures...........................15 Figure 6: Dielectric parameters of water as a function of temperature, at f = 2.45 GHz

..........................................................................................................................17 Figure 7: Typical structure of hardwood.........................................................................18 Figure 8: Dielectric parameters of wood as a function of density and moisture content,

at f = 2.45 GHz and T = 20°C..........................................................................20 Figure 9: Dielectric parameters of wood (ρ0 = 0.7 g/cm3) as a function of moisture

content and temperature, at f = 2.45 GHz ........................................................21 Figure 10: Microwave frequency response of the wood dielectric parameters at 20°C .22 Figure 11: Principal directions on wood stem ................................................................23 Figure 12: Physical model of microwave heating of wood.............................................25 Figure 13: Microwave drying periods for wood .............................................................26 Figure 14: The scheme for scaling-up a microwave process ..........................................28 Figure 15: Exploratory research description...................................................................28 Figure 16: Exponential decay of the electric field in a lossy dielectric ..........................30 Figure 17: Measurement techniques versus frequency and dielectric loss of MUT.......34 Figure 18: Equivalent circuit of a transmission line .......................................................35 Figure 19: Waveguide types ...........................................................................................36 Figure 20: Coaxial transmission line...............................................................................37 Figure 21: Field distributions in coaxial line ..................................................................38 Figure 22: Parallel plate transmission line ......................................................................38 Figure 23: Microstrip line - configuration and field distribution....................................39 Figure 24: Strip line configuration..................................................................................40 Figure 25: Transmission line measurement system ........................................................43

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Figure 26: Definition of the two-port network................................................................44 Figure 27: S-parameters ..................................................................................................44 Figure 28: Measuring S-parameters ................................................................................45 Figure 29: Familiar forms of the reflection/transmission parameters.............................45 Figure 30: Reflection parameters ....................................................................................46 Figure 31: Transmission parameters ...............................................................................46 Figure 32: Transmission line terminated with Z0 ............................................................47 Figure 33: Transmission line terminated with Short.......................................................48 Figure 34: Transmission line terminated with Open.......................................................48 Figure 35: Standing waves ..............................................................................................49 Figure 36: A dielectric sample in a transmission line (waveguide/coaxial line) and the

incident and reflected electric field distributions .............................................54 Figure 37: Short-circuited waveguide with two-layer medium ......................................56 Figure 38: Error model for one-port measurements........................................................59 Figure 39: Forward two-port error model .......................................................................60 Figure 40: Schematic figure of the free-space measurement system..............................63 Figure 41: Coaxial probe technique; reflection from the MUT ......................................68 Figure 42: Coaxial probe model......................................................................................69 Figure 43: A parallel resonant circuit formed from conventional circuit elements ........70 Figure 44: A rectangular cavity resonator and dielectric field distributions for the TE101

and TE102 resonance modes..............................................................................71 Figure 45: Cylindrical cavity resonator ..........................................................................72 Figure 46: Microwave resonant cavities .........................................................................74 Figure 47: Transmitted power response of unloaded resonator at resonant frequency...76 Figure 48: Microwave pressure windows availability and their applications.................86 Figure 49: Designed high-pressure cavity.......................................................................86 Figure 50: Measurement system set-up ..........................................................................87 Figure 51: Schematic representation of the experiment..................................................89 Figure 52: Three dimensional plot of minus the imaginary part of tanh(z)/z .................94 Figure 53: Structural design of the wood modeling software .........................................99

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Figure 54: Algorithm principle: a three dimensional box divided into a mesh of small cells ................................................................................................................100

Figure 55: Typical structure of hardwood.....................................................................101 Figure 56: A cross section through the 3-D wood model .............................................102 Figure 57: A radial section through the 3-D wood model ............................................103 Figure 58: A tangential section through the 3-D wood model......................................103 Figure 59: Specific gravity of bound water...................................................................106 Figure 60: 3-D ray’s cell model ....................................................................................114 Figure 61: Measured dielectric parameters of Blue Gum as a function of moisture

content and structural direction, at 20-25°C ..................................................117 Figure 62: Dielectric constant of different Australian wood species at 2.45GHz, elevated

temperatures and pressures ............................................................................119 Figure 63: Loss factor of different Australian wood species at 2.45GHz, elevated

temperatures and pressures ............................................................................120 Figure 64: Modeling vs. measurement. Dielectric constant of Mountain Ash,

ρ0=0.75g/cm3..................................................................................................127 Figure 65: Modeling vs. measurement. Loss factor of Mountain Ash, ρ0=0.75g/cm3..128 Figure 66: Modeling vs. measurement. Dielectric constant of Mountain Ash,

ρ0=0.60g/cm3..................................................................................................128 Figure 67: Modeling vs. measurement. Loss factor of Mountain Ash, ρ0=0.60g/cm3..129 Figure 68: Modeling vs. measurement. Dielectric parameters of Messmate................129 Figure 69: Modeling vs. measurement. Dielectric constant of Blue Gum....................130 Figure 70: Modeling vs. measurement. Loss factor of: Blue Gum...............................130 Figure 71: Estimated dielectric parameters of bound water in wood at 2.45 GHz and

room temperature ...........................................................................................132 Figure 72: Calculated dielectric parameters of pure water (or free water in wood) at

2.45GHz, as function of temperature .............................................................133 Figure 73: Dielectric parameters of cell wall substance for fiber at 2.45GHz, as function

of temperature ................................................................................................133 Figure 74: Estimated dielectric parameters of bound water in wood at 2.45 GHz, as a

function of temperature ..................................................................................134

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Figure A-1: Field distributions and key expressions of calculation for modes in rectangular waveguide (NMAB, CETS, and NRC, 1994) .............................156

Figure A-2: Field distributions and key expressions of calculation for modes in cylindrical waveguide (NMAB, CETS, and NRC, 1994)..............................157

Figure A-3: Instantaneous values of incident and reflected waves on an open-ended line (Integrated Publishing 1998)..........................................................................158

Figure A-4: Electromagnetic-field configuration of TEmnk mode in rectangular cavity resonator (Pozar 1998) ...................................................................................159

Figure A-5: Electromagnetic field configuration of TEmnk mode in rectangular cavity resonator (Pozar 1998) ...................................................................................160

Figure A-6: Field configuration of TE011 and TE111 mode in cylindrical cavity resonator (Pozar 1998) ...................................................................................................161

Figure A-7: Field configuration of TM011 and TM111 mode in cylindrical cavity resonator (Pozar 1998) ...................................................................................161

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List of Tables

Table 1: Measurement techniques according to the operation in the broad/narrow band frequency..........................................................................................................33

Table 2: Measurement techniques classified upon their destructive features .................34 Table 3: Comparison of the permittivity measurement techniques ................................78 Table 4: Complex solutions of the transcendental equation together with the values of

the dielectric constant derived from each solution...........................................95 Table 5: Dielectric permittivity of Soda Lime Glass measured at various positions of the

short..................................................................................................................97 Table 6: Fractional volumes formulas...........................................................................105 Table 7: Calculation of the specific gravities of wood .................................................106 Table 8: Relaxation parameters of bound water ...........................................................111 Table 9: Oven-dry densities of wood pieces from a set of six ......................................115 Table 10: Measured dielectric permittivity of Blue Gum at 2.45GHz and 20-25°C ....116

Table 11: Measured dielectric properties of different Australian wood species at 2.45GHz, elevated temperatures and pressures..............................................118

Table 12: Anatomical dimensions of the macroelements in Eucalyptus globulus........122

Table 13: Proportional volume of wood components for the six Blue Gum samples ..123

Table 14: Dielectric parameters of moist wood substance and ray material for the six Blue Gum samples .........................................................................................123

Table 15: Calculated and measured dielectric permittivity for Blue Gum wood samples (data obtained and calculated at temperature 20o-25oC) ................................124

Table 16: Calculated and measured dielectric permittivity for wood samples at elevated temperatures and pressures ............................................................................125

Table D-1: Free water relaxation parameters function of temperature .........................175 Table D-2: Free water dielectric parameters function of frequency and temperature ..176

Table D-3: Dielectric parameters of the cell wall substance for fibers as function of frequency and temperature.............................................................................177

Table D-4: Dielectric parameters of the cell wall substance for rays as function of frequency and temperature.............................................................................178

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Table D-5: Estimated dielectric parameters of bound water in wood at 2.45GHz .......179

Table D-6: Estimated dielectric parameters of bound water in wood at 0.915GHz .....180

Nomenclature

a Radius of a dipole molecule

1a , 2a Incident waves

B Magnetic field [T]

1b , 2b Reflected waves

C Capacitance

c Speed of light in free space ( m/s) 81099792458.2 ×=

c′ speed of electromagnetic waves propagating through a dielectric [m/s]

D Electric flux density [C/m2]

pD Penetration depth [m]

d Sample length [m]

E Electric field strength [V/m]

E Voltage [V]

f Oscillation frequency of the fields at a given point in space [Hz]

Resonant frequency [Hz]. Chapter 2, Eq 54 to 59

0G Conductance accounting for radiation losses

H Magnetic field intensity [A/m]

I Current [A]

J Current density [A/m2]

k Boltzmznn’s constant ( J/K) 231038066.1 −×=

FSPk Volumetric shrinkage coefficient at fiber saturation point

Q Quality factor

11S , 22S Reflection scattering parameters (S-parameters)

12S , 21S Transmission scattering parameters (S-parameters)

0SG , , xSG FSPSG Specific gravity of wood at 0% moisture content, x% moisture

content and fiber saturation point, respectively.

xbwSG , , FSPbwSG , Specific gravity of bound water at x% moisture content and fiber

saturation point, respectively

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T Temperature [°C]

Transmission coefficient. Chapter 2

t Time [s]

δtan Loss tangent

Lδtan , Rδtan ,

Tδtan

Loss tangent values in longitudinal, radial and tangential

direction

V Resonant cavity volume [m3]

wsV , , fw irbwV V , aV Fractional volume of wood substance, bound water, free water

and air

v Sample volume [m3]

Y Admittance

0Z Characteristic impedance[Ω]

inZ Line impedance [Ω]

LZ Load impedance [Ω]

α Relaxation time distribution constant. Chapter 1, Eq 13

Attenuation constant [Np/m]. Chapter 1, Eq 16, 17 and 18

δ Phase angle [rad]

0ε Permittivity of free space ( 0854.8 × 121 −= C2/N·m2) ∗ε Complex permittivity ∗effε Effective permittivity

ε ′ Dielectric constant of the dielectric medium

TRL εεε ′′′ ,, Dielectric constant in longitudinal, radial and tangential direction

∞′ε Dielectric constant at very high frequency (optic)

sε ′ Dielectric constant at very low frequency (static)

ε ′′ Dielectric loss factor

Φ Phase of the transmission coefficient [rad]

Γ Reflection coefficient

0γ Propagation constant of the empty waveguide

γ Propagation constant of the filled waveguide η Viscosity [N⋅s/m2]

ϕ Phase of the reflection coef rad]ficient [

xiv

0λ Wavelength in free space ( 122.0= m)

cλ Cutoff wavelength [m]

gλ Wavelength in waveguide [m]

∗effµ

Effective permeability

0µ Permeability of free space ( Wb/A·m) 7104 −×= πρ Volume charge density [C/m ] 3

tion coefficient. Chapter 2 Magnitude of the reflec

0ρ Oven-dry density of wood [g/cm3]

eσ Electronic conduction

iσ Ionic conduction

τ Relaxation time [s]

Magnitude of the transmission coefficient. Chapter 2

ω Angular frequency [rad/s]

Abbreviations

t (%)

er test

dure

tic waves

NA Vector Network Analyser

VSWR Voltage Standing Wave Ratio

CWS Cell wall substance

DUT Device under test

FSP Fiber saturation poin

mc Moisture content (%)

MUT Material und

NRW Nicolson-Ross-Weir proce

RL Power loss

TE Transverse electric waves

TEM Transverse electromagne

TM Transverse magnetic waves

TR Transmission-reflection

V

xv