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Fluid and microfluidic dielectric measurement using a cavity perturbation method at microwave C-band

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FLUID AND MICROFLUIDIC DIELECTRIC MEASUREMENT USING A CAVITY
PERTURBATION METHOD AT MICROWAVE C-BAND
APPROVED BY SUPERVISING COMMITTEE:
________________________________________
Ruyan Guo, Ph.D., Chair
________________________________________
Amar Bhalla, Ph.D.
________________________________________
Kevin Grant, Ph.D.
Accepted: _________________________________________
Dean, Graduate School
DEDICATION
To my Parents,
Maryam and Mohammad Rasoul,
And my two beloved sisters,
Hanieh and Hedieh,
Without whom none of my success would be possible.
FLUID AND MICROFLUIDIC DIELECTRIC MEASUREMENT USING A CAVITY
PERTURBATION METHOD AT MICROWAVE C-BAND
by
AREF ASGHARI, B.S.
THESIS
Presented to the Graduate Faculty of
The University of Texas at San Antonio
in Partial Fulfillment
of the Requirements
for the Degree of
MASTER OF SCIENCE IN ADVANCED MATERIAL ENGINEERING
THE UNIVERSITY OF TEXAS AT SAN ANTONIO
College of Engineering
Department of Electrical and Computer Engineering
December 2015
ProQuest Number: 1605168
All rights reserved
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ACKNOWLEDGEMENTS
Firstly, I would like to express my gratitude to my advisor Prof. Ruyan Guo for the
continuous support of my master studies and related research, for her patience, motivation, and
immense knowledge. Her meticulous consideration provided me an opportunity to join her team
as a master’s student in Advanced Material program, and have access to the laboratory and
research facilities in all the time of research and writing of this thesis. Without her precious
support it would not be possible to conduct this research.
My sincere thanks also goes to the rest of my thesis committee members: Dr. Amar
Bhalla for co-advising and Dr. Kevin Grant for his support and help. I also thank my fellow lab
mates for all the help and also the fun moments we have had in the past two years.
I also acknowledge the partial financial support received in form of the Materials
Research Graduate Fellowship made available by the National Science Foundation under the
grant #1002380.
Last but not the least, I would like to thank my family: my parents and my sisters for
supporting me spiritually throughout my life.
December 2015
iii
FLUID AND MICROFLUIDIC DIELECTRIC MEASUREMENT USING A
CONVENTIONAL CAVITY PERTURBATION METHOD AT MICROWAVE C-BAND
Aref Asghari, M.S.
The University of Texas at San Antonio, 2015
Supervising Professors: Ruyan Guo, Ph.D. and Amar Bhalla, Ph.D.
The utilization of cavity perturbation technique in dielectric property measurement of fluid
and micro-fluid is investigated in this thesis to better assist the ever-growing needs of science
and technology for analysis and characterization of such materials in various applications from
genetics, MEMS devices, to consumer product industry. Development of different techniques
for measuring complex dielectric properties of fluid and micro-fluids at Giga (109)-Hz
frequencies is of significant importance as their usage is increasingly coupled with infrared and
microwave electromagnetic wavelengths.
Conventional cavity perturbation method could
provide a sensitive and convenient system for measuring fluids of low (e.g., εr <10) permittivity
that meets the assumptions of negligible perturbation to the electromagnetic field distribution in
the cavity. Developing a methodology that uses conventional cavity perturbation method that is
however suitable for a sensitive, accurate, and reliable measurement of high permittivity polar
liquids at microwave C-band is the goal in the current work. Systematic studies are carried out,
using de-ionic (DI) water as test specimens, to evaluate the influence of sample’s container,
volume, dimension, and temperature on the sensitivity and reliability of microwave dielectric
measurement. The cavity perturbation measurement of DI water in a 1 mm diameter capillary
tube showed well-defined temperature dependence of dielectric permittivity and loss coefficients
of water. Observation of a permittivity peak in temperature range tested at 4GHz around -10 °C
implies an important relaxation in low temperatures at microwave C-band, which corresponds to
a critical slowing down of polarization reorientation in crystallized (icy) H2O.
Numerical
simulations using Finite Element Analysis (FEA) COMSOL suites were conducted to established
the optimum amount of liquid water for cavity perturbation testing at microwave C-band (in
perfectly conducting condition). The results showed at TE103 mode the tube D4= 4mm diameter
(272 µL liquid volume capacity) provides the best measurement sensitivity in terms of resonant
iv
shift and low loss while for TE105 the 2mm 68 (µL liquid volume capacity) tube is the most
promising. The experimental results yielded a shape factor of around 2 and 1 for ε’ and ε”
, respectively. The examination of ε’ and ε” interdependence using Kramers-Kronig concept
showed the permittivity loss values is 4 times more dependent to the quality factor than
permittivity. On the other hand, the dielectric permittivity dependence to resonant frequency
was calculated around 2 times bigger than dielectric loss which signifies the importance of ε” in
high loss liquid measurement with cavity resonant perturbation method.
v
TABLE OF CONTENTS
Acknowledgements ........................................................................................................................ iii
Abstract ............................................................................................................................................v
List of Tables ............................................................................................................................... vii
List of Figures .............................................................................................................................. viii
Chapter One: Introduction ...............................................................................................................1
Chapter Two: Theory .......................................................................................................................5
2.1. Resonant Cavity Method..............................................................................................6
Chapter Three: Method and Procedure ..........................................................................................10
3.1. System and analysis ..................................................................................................10
3.2. Experimental measurement .........................................................................................11
3.3. Finite Element Simulation ..........................................................................................13
Chapter Four: Result and Discussion.............................................................................................14
4.1. Calibration and analysis ..............................................................................................14
4.2. The effect of liquid containing tube size ....................................................................18
4.3. Liquid volume effect ...................................................................................................27
4.4. Temperature dependence of dielectric permittivity ....................................................33
4.5. Liquid Concentration dependence of dielectric permittivity .....................................37
4.6. ε' and ε” coefficient shape factor determination .........................................................39
4.7. ε” and ε’ interdependence in resonant frequency and quality factor variation ...........40
Conclusion .....................................................................................................................................37
References ......................................................................................................................................38
Vita
vi
LIST OF TABLES
Table 1
Teflon and Alumina permittivity measured experimentally near 4 (TE103 15
mode) and 5 (TE105 mode) GHz.
Table 2
The experimental results compared to numerical simulation of resonant 16
frequency and quality factor at two TE103 and TE105 mode.
Table 3
The resonant frequency at different modes TE10n for n=1-6.
17
Table 4
Tubes of 1 to 9 mm diameter with their correspondent volume and volume 19
ratio inside the waveguide
Table 5
The dielectric permittivity and loss comparison with literature over 37
temperature range [-20 – 20°C]
Table 6
The permittivity (ε') shape factor determination for liquid water and ethanol at 39
TE103 and TE105
Table 7
The permittivity loss (ε′′) shape factor determination for liquid water and 40
ethanol at TE103 and TE105
vii
LIST OF FIGURES
Figure 1
The Electromagnetic spectrum across the range of wavelengths.
1
Figure 2
Dielectric permittivity spectrum over a wide range of frequencies. ε′ 5
and ε″ (Yeh & Shimabukuro, 2008)
Figure 3
Schematic representation of a resonant cavity method (R = reflected 6
power, T = transmitted power [adapted from (Venkatesh & Raghavan,
2004)]
Figure 4
Dielectric spectrum of water in a wide range of frequency and temperatures 9
[Chaplin, Martin. "Water and Microwaves". Water Structure and Science]
Figure 5
The Scattering parameter simulation of 12 and 11 in the cavity resonant 17
structure in the [0.3-6] GHz microwave region.
Figure 6
The transverse electric (TE) mode propagation simulation inside the 17
waveguide at a) 103 and b) 105 mode.
Figure 7
The ε’ and ε” coefficient in different tubes from D1 to D9
Figure 8
The electric field intensity inside the sample of various diameter, a) 1 mm, 23
20
b) 4 mm, c) 5mm, d) 7 mm, e) 8 mm and f) 9 mm.
Figure 9
S21 parameter variation in frequency range [3-6GHz] following tube size 24
increase filled completely with water: A. D1-D2, B. D2-D4 and C. D4-D6.
Figure 10
The S21 parameter variation in different tube in frequency spectrum of [3-6] 25
GHz.
Figure 11
(a) The water filling of D1 capillary with different volumes. (b) water filled 27
volume as low as 550nL. (c) the laminar viscose flow of water filled D1
tube
Figure 12
(a) The frequency shift of different water volume insertion in tubes D1 to D3 29
(b) The maximum liquid water measured at different tubes
Figure 13
The electric field intensity inside D1 tube with (a) different filled fraction 31
(b) The 0.091 filled ratio and (c) The 0.91 filled ratio.
Figure 14
The water filling ratio effect on: (a) ε’ coefficient (b) ε” coefficient and (c) 32
both in comparison.
viii
Figure 15
The variation of a) dielectric permittivity coefficient (ε’) and b) loss 33
coefficient (ε”) at two different resonance frequency mode of TE103 and
TE105 over the temperature range [-20 − 25°C].
Figure 16
The dielectric permittivity and loss variation over the temperature region of 35
[-20,20°C] (Bertolini et al., 1987; Buchner et al., 1999)
Figure 17
The effect of Ethanol concentration in liquid water on :(a, b) ε’ coefficient 38
and (c, d) ε” coefficient.
Figure 18
The (a) Resonant frequency and (b) quality factor shift at different ε’-ε” 42
combination in liquid water.
ix
CHAPTER ONE: INTRODUCTION
In recent years, the fluid and microfluidic research which deals with the science and
technology of systems that process and manipulate small amount of liquids (Whitesides, 2006) has
been largely investigated. The first and main application of small-scale fluids has been in analysis
field of study. Micro-fluids are capable of carrying very small quantities of samples and reagents
thus provide a detection capability with high resolution and sensitivity. The micro-analytical
branch of chemical analysis has been revolutionized thanks to the combination of micro fluids with
other available technologies such as laser for optical detection. Developing detectors for chemical
and biological threats, advanced analytical sensitivity for studying human genes, microfluidic
devices for microelectromechanical systems (MEMS) and micro channels as essential element of
micro chemical factories on chip are other reasons so much has been invested on studying fluids
and micro fluids.
Electromagnetic fields are used to probe inaccessible domains and to reveal the properties
of many media including fluids. Among them, microwave is an interesting choice for the
unique properties it offers based on it wavelength range (mm-m) (Fig.1) and highcompatibility to living cells characterization and modification system requirements.
Figure.1. The Electromagnetic spectrum across the range of wavelengths.
Microwave techniques for accurate measurements and characterization of the materials have
been used for a long time (Gennarelli, Romeo, Scarfi, & Soldovieri, 2013; Kent, 1987; “Microwave
Non-destructive Evaluation and Test,” 2001; Ryyniinen, 1995). Their practical implications in
electronic, medicine and pharmaceutical industries make the real time monitoring of process
1
quality possible at a relatively low cost, higher adaptability and flexibility.
The following can summarize the main reason for the growing and rapid development of
microwave-based methodologies:
1. Electromagnetic field in the microwave range can penetrate almost all materials and the
related scattered fields are representative of the overall volume of the object under test not
only its surface;
2. Microwave imaging modalities are very sensitive to the water content of the specimen; and
3. Dielectric spectroscopy has the great advantage of being non-invasive, nondestructive and
non-contact.
Among all the fluids and micro fluids sensing methods, the microwave dielectric spectroscopy
represents a promising solution since it benefits from the extensive research that has been
previously realized at tissues and cells suspensions levels for several decades (Fear, Li, Hagness, &
Stuchly, 2002).
The discrimination of tumorous and non-tumorous tissues and the wide
development of breast and liver cancer imaging utilizes using microwave is rapidly emerging.
The sensing principle can be simply stated as follows. Depending on the type of liquid and
amount of a chemical ingredient in the fluids under test, a variation of the complex dielectric
permittivity is produced after impinging electromagnetic field into the material. The changes in
the electromagnetic wave propagation by the material insertion can be used as an indication of
materials dielectric permittivity and loss.
In the microwave region, the complex dielectric properties of liquids can be determined by
several methods using different microwave measuring methodologies. Methods for measuring
these properties vary even in a given frequency range. Nyfors and Vainikainen (Nyfors, 2000)
give four groups of measurement methods: lumped circuit, resonator, transmission line and
free-space methods. In lumped circuits, the sample is a part of the insulator of the lumped circuit.
This method can be used only at low (under 100 MHz) frequencies. Although being suitable for
all material types, except gases, the method is not suitable for very low-loss materials.
A
microwave resonator, partly or completely filled with a material, is also used for the
determination of permittivity. The measurement frequency range is from 50 MHz to above 100
GHz.
The permittivity of a material can also be measured by using the material sample as a part
of a transmission line section. The permittivity of gases is too low with these methods and the
permittivity measurement accuracy is not as good as with resonators.
2
One of the most commonly used measuring methods employs resonant cavities, known as
the cavity perturbation technique. For samples of the known geometry and volume, the shift in
resonant frequency can be directly related to the permittivity. The loss factor can be determined
from the change in the Q-factor of the cavity. These methods can be very accurate and they are
also very sensitive to low-loss tangents (Petersan & Anlage, 1998).
The resonant cavity
systems restrict the measurements to a single frequency. Each cavity needs calibration but, once
the calibration curves have been obtained, calculations are rapid.
Sample preparation is
relatively easy, and a large number of samples can be measured in a short time. This method is
also easily adaptable to high (up to + 140°C) or low (-20°C) temperatures.
Besides the cavity methods, there are two other popular techniques, namely open-ended
coaxial probe and transmission line methods. The probe method has a coaxial line, w h i c h
has a special tip. The tip is brought into contact with the substance by touching the probe to
a flat face of a solid or by immersing it in a liquid. The reflected signal is related to the dielectric
properties of the substance. While the method is very easy to use and it is possible to measure
the dielectric properties over a wide range of frequencies (500 MHz-110 GHz), unfortunately
the accuracy is limited, especially when measuring low values of permittivity and loss. In
transmission line methods a sample of the substance is put inside an enclosed transmission line.
Both reflection and transmission are measured. Although this method is more accurate and
sensitive than the probe method, it has a narrower range of frequencies. As the substance must
fill the cross-section of the transmission line (coaxial or rectangular), the sample preparation is
also more difficult and time consuming. Time domain spectroscopy (or reflectometry) methods
have been much developed in the 1980s. They cover a frequency range from 10 MHz to 10
GHz. Measurement is very rapid and accuracy is high, within a few percent errors. The sample
size is very small and the substance measured must be homogeneous. These methods are still
quite expensive.
Several techniques are available in the frequency domain for analyzing the dielectric
properties of liquids and their composition. (Tsyrenzhapov, 2002) Although broadband techniques
(Artemov & Volkov, 2014) can be adopted, resonant perturbation methods (Petersan & Anlage,
1998) are preferable because of their higher accuracy. Such techniques are based on the fact that a
variation of the complex permittivity of the dielectric material under test produces a change of the
resonant frequency and the 3-dB bandwidth (or the Q-factor). Various resonant-type sensors have
been reported for measuring the liquid compounds. A dielectric resonator coupled to a probe tip
3
has been developed in (Tanaka & Sato, 2007) to detect changes of sodium chloride concentration
in deionized water. A similar structure has been later used by the same authors as a biosensor for
monitoring the glucose concentration in water (Haase & Jacob, 2013). A device based on an openended coaxial resonator embedded in a microfluidic chip has been recently proposed in for
compositional analysis of solvents at microwave frequencies. A cylindrical resonator using the
TM010 mode and based on reflection measurements has been optimized for measuring the
concentration of binary liquid mixtures (Eremenko & Ganapolskii, 2003)
Therefore, microwave spectroscopies have found numerous applications in areas including
nondestructive evaluation and testing. The employment of interrogating microwave is
recognized as a suitable diagnostic tool due to its close interaction with material structure and
has demonstrated its advantages with respect to standard techniques.
At the same time, the manipulation of fluids in channels with dimensions of tens of
micrometers —has emerged as a distinct new field. Microfluidics has the potential to influence
subject areas from chemical synthesis and biological analysis to optics and information
technology but the field is still at an early stage of development.
This work focuses on the development of a conventional cavity perturbation platform for
performing fluidic and microfluidic experimental measurement at microwave C-band along with
a corrective numerical analysis approach. The limitation and potential of the system and the
approaches to improve the measurement accuracy capabilities of the system are addressed as
well.
4
CHAPTER TWO: THEORY
Dielectric permittivity is a quantity used to describe dielectric polarization responses of a
material to an electromagnetic field, which influences electromagnetic waves’ reflection at
interfaces, transmission velocity through the material, and the storage or attenuation of wave
energy within materials. In frequency domain, the complex relative permittivity ε* of a material to
that of free space can be expressed in the form of ε* = ε’ – jε”. The real part ε’ is referred to as the
dielectric constant and represents stored energy when the material is exposed to an electric field,
while the imaginary dielectric constant ε” influences energy absorption and attenuation. One more
!”
important parameter used in EM theory is the tangent of loss angle (loss factor): tan δ = .
!’
Mechanisms that contribute to the dielectric loss in heterogeneous mixtures include dipolar,
electronic, ionic (or atomic), and Maxwell–Wagner responses. At RF and microwave frequencies
in water, ionic conduction and dipole rotation are dominant loss mechanisms. (Fig 2)
Fig 2: Dielectric permittivity spectrum over a wide range of frequencies. ε′ and ε″ (Yeh & Shimabukuro, 2008)
5
2.1. Resonant Cavity Method
Resonant cavity methods are also widely utilized in measuring complex dielectric
permittivity of lossy materials. The most popular resonant cavity method is the cavity perturbation
method (CPM), which is based on a comparative analysis of certain EM characteristics between
empty and a partially loaded rectangular or cylindrical resonance cavity. A schematic diagram of
an experimental setup of CPM is shown in Fig. 3.
Figure 3. Schematic representation of a resonant cavity method (R = reflected power, T =
transmitted power [adapted from (Venkatesh & Raghavan, 2004)]
Cavity perturbation method has been widely used to study the dielectric parameters in the
microwave frequency region. The dispersive and dissipative terms of the materials are directly
related to the change in the resonant frequency and the quality factor of the cavity from the
respective empty cavity values. Conventional microwave cavity perturbation techniques have been
known as fast and convenient methods for evaluating gigahertz dielectric permittivities of materials
that are typically isotropic, of low εr, and small (compared to the wavelength) in size.
The resonant frequency fr and the quality factor Q of a rectangular cavity waveguide, for a
given standing wave TE10N mode in the microwave region, are expressed by the following
equations:
6
fr =
Q=
1
2 ε 0 µ0
2
⎛ 1 ⎞ ⎛ N ⎞
⎜ ⎟ + ⎜ ⎟
⎝ a ⎠ ⎝ d ⎠
2
(1)
ηπbd 3
(2)
2 RS (2 N 2 a 3b + 2bd 3 + N 2 a 3d + ad 3 )
Where a, d, ε0, µ0, N, Rs, and η are respectively the width of the waveguide, length of the
waveguide, permittivity of free space, permeability of free space, mode number, surface resistance
of the cavity, and intrinsic impedance. Inserting a sample into the cavity causes a shift in the
resonant frequency fr and a change in the quality factor Q of the waveguide. This perturbation is
dependent on the relative volumes of the cavity VC and of the sample within the cavity VS, the
permittivity er of the sample and thus the electric field concentration in the cavity EC and in the
sample ES as shown in the general perturbation equation below:
⎛ f − f s ⎞
⎟⎟ −
2 ⎜⎜ c
⎝ f s ⎠
*
∫ Ec E s dv
⎛ 1
1 ⎞
⎟⎟ = (ε r − 1) Vs
j ⎜⎜
−
2
⎝ Qs Qc ⎠
∫ Ec dv
(3)
Vc
A determination of the complex permittivity by the perturbation technique thus is dependent
of both these changes and the integration of the electric field over the volumes of the sample within
the cavity. For a sample with length parallel to the electric field direction, assuming a small
perturbation of the field, the above relation can be easily simplified and used to find the complex
permittivity. Under these conditions the electric fields in the sample (ES) and in the cavity (EC) are
approximately equal; one can then derive the following expressions for the real and the imaginary
parts of the complex permittivity:
! ∆!
 ! = 1 + !! !! !
!
!
!
(4)
!
!
" = !! !! ( ! − ! )
!
!
!
(5)
Where ! and ! are the resonance frequency and Q factor of the empty cavity, ! and !
are the resonance frequency and Q factor of the cavity with a sample,  is the cavity volume, 
is the sample volume; and Δ = ! - ! , A and B are the coefficients that depend on several
parameters: shape, sizes, and location of the sample in the cavity, and configuration and excited
operating mode of the cavity. In some cases, A and B may be found analytically for a lossy sheet
material placed in a rectangular cavity with operating mode TE103 (Komarov, Wang, & Tang,
7
2005), or they may be determined empirically with calibration of the experimental setup. Equation
(2) is valid when three main assumptions are satisfied: (1) the dielectric sample does not disturb the
general distribution of the EM field in the cavity, (2) metallic wall losses do not influence the
resulting losses in the cavity, and (3) ! and ! are measured at the same frequency. Appropriate
location of the sample is also a very important factor that affects the accuracy of the measurement.
Preliminary numerical modeling of the microwave setup with lossy dielectric material inside the
cavity may be a useful approach for determining an optimum sample position in this case
(Komarov et al., 2005). Sometimes, measurement errors are possible when there are air gaps
between the specimen and the conducting parts of the metallic resonator. There are also some
restrictions in using conventional resonance CPM for measuring the dielectric loss tangent of lowloss media. If conduction losses in cavity walls are higher than (or comparable to) the dielectric
losses of the specimen, the resonator Q factor may change and one will not obtain the correct
values of ". In this case, application of hybrid high-order modes called whispering-gallery modes
or a special calibration procedure of Q factor characterization as a function of frequency can help
to eliminate the drawbacks of this method. CPM is fast, non-invasive and with high accuracy
compared to the other methods and precisely shaped small-sized samples are usually used with this
technique. Speaking of limitations, CPM provides dielectric properties measurements only at a
fixed frequency. Also, Commercial systems like network analyzer are more expensive than the
open-end coaxial probe system.
As it is already been established, the permittivity generally depends on the frequency at which
the sample is radiated. For polar species, it fits the Debye model quite well, which is expressed
as:
ε”(ω)-ε∞=
!"
!!!!"
(6)
where ε∞ is the permittivity at the high frequency limit, Δε = εs − ε∞ where εs is the static, low
frequency permittivity, ω = 2πf where f is the frequency and τ is the characteristic relaxation time
of the medium. The real part of permittivity (also known as dielectric permittivity) is associated
with the stored energy within the substance. The imaginary part (also known as dielectric loss)
represents the ability of the substance to absorb electromagnetic energy.
The dielectric properties of fluids are primarily determined by their chemical composition
and, to a much lesser extent, by their physical structure. The influence of water and salt content
depends to a large extent on the manner in which they are bound or restricted in their movement
8
by the other components.
This complicates the prediction, based on data for single
ingredients, of the dielectric properties of a mixture. For example, laminated or fibrous
structures have higher ε′ than granular ones do. The relaxation frequency (the frequency of the
maximum dielectric loss) of bounded water molecules is lower than free molecules.
For all substances with a high water content, a sharp increase in dielectric permittivity is
observed in the melting zone and, after melting, it decreases with further temperature increase.
For pure water, dielectric loss decreases with increasing temperature (Fig 4).
Figure 4. Dielectric spectrum of water in a wide range of frequency and temperatures [Chaplin,
Martin. "Water and Microwaves". Water Structure and Science]
The dielectric measurements are a unique research tool in understanding aqueous
solutions, water activity, food preservation, shelf life, hydration phenomena, and phase
transitions. Properly designed and calibrated electrical instruments are used to quickly
determine the moisture content. It is worth to mention here that bound water versus free water
dielectric properties varies differently. There have been reports that the temperature coefficient
of bounded water is positive but the free water dielectric constant decreases with temperature
(Bordonsky, Gurulev, & Krylov, 2009).
9
CHAPTER THREE: METHOD AND PROCEDURE
3.1. System and analysis
Waveguide is a hollow conductive pipe that can carry the high frequency microwaves with
much less power loss (Terms, 1979). In an open space, the microwave propagates in different
directions and power loss is proportional to the square of the distance. In the waveguide, the
waves are confined to propagate in one direction with no power loss in ideal conditions. Thus,
waveguide is a perfect medium that can perform the function to carry the microwaves into the
chamber.
The Vector network analyzer (HP 8753E) as a source of high frequency electric field is being
used in this work. As highlighted, the liquid sample must be located at or around the of the electric
field maximum field intensity to achieve the highest sensitivity. Moreover, the design of the
coupling element strongly affects the sensitivity. The design of a cavity resonator implies to solve
the Maxwell equations inside that cavity, respecting the boundary conditions. As a consequence,
the resonance frequencies appear as conditions in the solutions of the differential equation
involved. The measurement of the complex permittivity can be made using the small perturbation
theory. In this method, the resonance frequency and the quality factor of the cavity, with and
without a sample, can be used to calculate the complex dielectric permittivity of the material. In
this study, the ε′ and ε′′ is plotted and the resonance frequency (f) and the full width at halfmaximum (∆f) are measured for an empty as well as the sample loaded cavity. The quality factor
(Q) of the cavity, defined as f/∆f, is also measured for an empty as well as the sample loaded
cavity. The change in the resonance frequency and quality factor with and without the sample
gives the complex dielectric permittivity.
The calculation of the quality factor from the
measurement of is a conventional process and takes a considerable amount of time. In order to
avoid this lengthy process, continued signal monitoring and automatic calculation of resonant
frequency and quality factor are made via a LabVIEW interface which aids the data collection
process to be fast and accurate. The Lab-view interface designed to systematically obtain the
waveguide resonant or near resonant frequency, calculating the quality factor and transforming
them into the permittivity and loss data using conventional cavity perturbation formula. The
formula fits well for small size low permittivity. For materials with high losses, the perturbation
10
can be very high, making the assumption of small electromagnetic field distributions is invalid and
numerical correlation needs to be considered ( Mclntosh et al, 2012).
Considering the operational procedure as sensor acting over a circuit, the sensitivity of the
system to different factors in measuring the permittivity of aqueous samples is required. In order
to do that, the measurement always starts with the testing of the Teflon sample as a material with
low and high reliable data and also a sample of alumina. After getting reliable data out of system
for bulked samples with known  ! − " values, the high loss liquid can be measured.
The
temperature sensitivity of the liquid water dielectric permittivity and loss is being measured by
measuring DI water in two different modes of TE103 and TE105. The measurement frequency is
part of the IEEE microwave C-band and two different odd modes in basic propagation mode of
TE10n is used to achieve the highest electric field at the sample insertion position in the middle of
the waveguide.
3.2. Experimental measurement
Sensors can take different forms for liquid characterization and developing conventional
waveguide acting as a reliable fast sensor for an in-depth material characterization is a challenging
one. The shift in the resonant frequency of the system over different temperature and various tube
filling with different tube sizes is a good reference point to find the effect of each on the
measurement parameters alteration. The different capillary diameter filled with water inserted in
E-field maximum direction enables measurement of different volumes of high loss liquid. Also,
the more coherent the high loss liquid sample placed throughout the waveguide height, more
reliable and accurate measurement is attainable. This increase in the sensitivity comes at the price
of lowering high loss liquid volume measured to avoid the high attenuation of the electromagnetic
wave by the dielectric material.
In order to study the microwave properties of fluid solution, the liquid water solution has
been prepared using deionized water. The deionized water poured into the clean laboratory glass
container and then sealed in order to avoid air contamination and changing the purity of samples.
Three different glass tubes of D1, D2 and D3 have been used for liquid water to be measured inside
the waveguide. The measurement of resonance and near resonance frequency is being done and
data gathered at 30 points of resonance and near resonance in the system. The 3dB bandwidth
11
lower than the resonant peak is being considered for quality factor determination.
Two
approximations are made: 1. It is assumed that the fields loss in the empty part of the cavity is
negligible. 2. The wave alteration in intensity and propagation by the insertion of the high loss
liquid inside the waveguide is uniform over its surface.
For temperature dependent measurement of dielectric permittivity and loss, The set-up is
being placed inside a temperature and humidity chamber made by Espec (model ECT-2) and the
humidity and temperature also being measured constantly by a thermometer using an external
sensor.
In order to perform concentration measurement sensitivity, different solutions of
water/ethanol mixture using standard polar samples of DI water and Ethanol 96% with varied
concentrations are being prepared from pure water to half-half
mixture of both.
The
concentrations are given in % percentage. The samples are then filled into the capillaries and the
resulting resonant frequency parameters are recorded.
The RF module of COMSOL Multiphysics helps in determining material properties at
frequency time-domain very accurately. Modeling the test set up consisted of a waveguide with
different liquid tubes is the first part that can be done. After that, finding the values of the resonant
frequency measurement system at situation most close to the experimental situation like size of the
tubes and the modes of electromagnetic propagation wave can gives more refined data to analyze
the system accuracy and sensitivity.
Measuring the high loss liquid water permittivity at different temperature and finding the
temperature dependence of complex dielectric properties is addressed in this study.
The
temperature dependence of these dispersion parameters is a consequence of the temperature
dependence of the viscosity of water. Upon increasing temperatures the relaxation time decreases,
which means a quicker response to the field.
As the conductivity of the sample increases due to the irradiation, the quality factor
decreases. All in all, the quality factors are drastically lower when measuring high loss aqueous
solutions inside the waveguide (compare Table 2). This is caused by high losses of water at
microwave frequencies and by strong coupling between the sensor and the sample, which is
necessary for high sensitivity. The loss tangent of water according to the well established Debye
model increases by up to almost 2 in the higher GHz range (Grenier et al., 2010). Therefore,
resonant sensors could be challenging for measurements on aqueous based substances at
microwave C-band frequencies since the quality factor of the sensors will be extremely low leading
12
to difficulties in evaluation of the resonance. It is therefore makes it more interesting to discuss the
sensitivity limits which will be dealt with later in result and discussion section.
3.3. Finite Element Simulation
An accurate control over the wave propagation and measuring electric field concentration is
of great importance in cavity resonant parameters analysis.
Considering difficulties in
experimental measurement of the EM parameters, the importance and necessity of using finite
element method for resonant cavity is inevitable. The numerical method modeling using COMSOL
Multiphysics provides valuable results in terms of interpretation of the field distribution inside
cavity when material of different dielectric permittivity and loss are being placed inside the
waveguide. In the current work case, polar liquid with both high permittivity and loss provides a
complicated case inside the waveguide cavity and the experimental data alone does not provide the
comprehensive study of the permittivity and loss measurement of the material. Also, collecting
experimental data that are usually subjected to error requires solid verification by physical
modeling of the structure enabling accurate interpretation and analysis of the data. As a result, two
Comsol RF interfaces are being utilized in the current investigation; Eigenfrequency and
Frequency Domain. Acquiring network scattering parameters and the resonant frequency along
with its correlated quality factor are parameters obtained through finite element simulation
conducted.
13
CHAPTER FOUR: RESULT & DISCUSSION
4.1. Calibration and analysis
Microwave resonant system needs calibration verifying sensitivity and accuracy of the
measurement system for dielectric spectroscopy means. It has been shown by (Ray & Behari,
1986) that for a jump of 0.05 dB during the calibration there is as much as 23% uncertainty in ε”
(especially below 5 GHz). Tedious modified automated network analyzer calibration is needed in
order to improve the system accuracy for dielectric loss evaluation. Calibration of the sensitivity in
our device is performed using two well-known low dielectric permittivity (ε’) samples along with
low loss (ε”). Only after acquiring meaningful result out of resonant cavity perturbation method,
one can further proceed with the measurement system for materials with higher induced field
perturbation. In the current work, dielectric properties of standard Alumina and Quartz sample of
known dimension and permittivity have been measured and the results obtained (Table .1) shows a
good compliance with the values derived through numerical analysis values by
!
! 5%
error.(McIntosh et al, 2012)
Table 1. Teflon and Alumina permittivity measured experimentally near 4 (TE103 mode) and 5 (TE105
mode) GHz.
Frequency ≈ 4 GHz
Dielectric
Error +/-
Constant ε’
Teflon
Alumina
Frequency ≈ 5 GHz
Dielectric
Error
Dielectric
Error
Dielectric
tangent
+/-
Constant ε’
%
tangent
Error %
1.9894
0.022
0.0007
0.0001
1.8784
0.0004
0.0026
0.0005
8.421
0.031
0.008
0.001
8.312
0.0006
0.0007
0.0005
Assuming that the resonant structure operates in a closed-loop configuration, the minimal
detectable frequency change is related to the short-term frequency stability of the resonance
frequency.
Improving the quality factor of the resonance generally yields better frequency
stability. Since, in a gaseous or liquid measurement, the quality factor Q of a typical resonant
microstructure is dominated by gas/liquid damping, the corresponding energy loss to the
surrounding medium must be minimized to develop high-Q-factor structure operating in a non14
vacuum environment. In our setup, Measures including the cleaning and deoxidizing the interior
surface of the waveguide have been taken to reduce error sources to the minimum level so the
sensitivity and accuracy of the system get improved.
The sensitivity of the experimental measurement and its results were verified with the
numerical simulation conducted at perfect boundary condition (PBC) system. PBC is used as an
appropriate indication of the minimum loss in the system and leads to a better approximation of the
values compared to the perfect situation. A good deal of computational procedure time has been
saved in choosing to calculate the perfect boundary condition compared to the impedance
boundary situation. The experimental measurement for obtaining cavity resonant frequency and its
correlated quality factor were conducted and the results versus numerical simulation have been
analyzed. The resonant frequency of about 3.96 GHz in the experimental measurement does match
by 1% to the characteristic resonance of the cavity structure at TE103 mode.
Table 2. The experimental results compared to numerical simulation of resonant frequency and quality
factor at two TE103 and TE105 mode.
The results at TE105 mode yield even more compliance to the experimental resonance
measurements by showing only 0.5% errors compared to the numerical simulation. A Q factor of
4120 and 4231 has been extracted from the 3-dB bandwidth of the resonance of the cavity at
TE103 and TE105 mode in room temperature, respectively. The former does vary with the
perfectly simulated waveguide quality factor by about 2176 while the latter varies by around 443
(Table. 2). The sources of error could be different from the embedded sharp edges in waveguide
structure to the fact that the wave propagation medium is not perfectly sealed. The slots designed
in the waveguide center for sample insertion at two different perpendicular and parallel direction to
the electric field direction results in resonant peak attenuation and noise accumulation.
15
Irregularities on the waveguide surface would results in more loss and increasing noise to signal
ratio throughout the system.
To find out the characteristic resonant frequency of the waveguide in the microwave region,
two main scattering parameter (S11 and S21) of waveguide using the frequency domain interface of
Comsol Multiphysics have been characterized and plotted in Fig. 5. The results illustrate the TE10n
[n=1-6] mode up to 6GHz frequency range. As shown in correspondent Table 3, the transmission
S21 amplitude value at different TE mode does alter. In TE10 mode, the basic mode of the
rectangular waveguide used here, the first frequency, which allows the electromagnetic wave
propagation between two ports is the cutoff frequency of the waveguide. Here, at the TE101 mode,
3.26 GHz is the minimum frequency at which the structure allows wave transmission throughout
the waveguide and therefore is the cutoff frequency of the structure. The more transmission means
more sensitivity and accuracy for measurements at the waveguide. Thus, according to table 3, The
TE103 and TE104 are best choices for conducting an accurate measurement because of the highest
absolute transmission they provide. The measurements are done at the middle of the waveguide
and therefore, only odd modes of electric field can provide the highest electric field concentration
inside the material. Consequently, the TE103 mode is the best choice in terms of providing
accuracy and sensitivity for resonant shift and quality factor measurement at the microwave Cband.
Fig. 6 is a demonstration of numerically simulated wave propagation inside the waveguide
at two different modes of TE103 and TE105. As shown, the maximum electric field requirement at
the middle of the waveguide is achieved and therefore, the sample exposure to electric field
concentration is at the highest.
16
TE101
TE102
TE106
TE105
TE103
TE104
Fig 5. The Scattering parameter simulation of 12 and 11 in the cavity resonant structure in the [0.3-6] GHz
microwave region.
Table 3. The resonant frequency at different modes TE10n for n=1-6.
Mode
TE101
TE102
TE103
TE104
TE105
TE106
fr (GHz)
3.26
3.62
4.01
4.62
5.224
5.88
 dB
60.4
70.5
84.7
86.3
80
73.2
(a)
(b)
17
Fig 6. The transverse electric (TE) mode propagation simulation inside the waveguide at a) 103 and b) 105 mode.
4.2. The effect of liquid containing tube size
The permittivity and loss calculation in a waveguide perturbing electric field structure requires
meticulous consideration for the size, geometry and position of the sample. The fact that only
small perturbation to the electric field yields acceptable results for permittivity calculation of the
dielectric material makes sample size selection a crucial aspect of the measurement. For lossy
liquids, a potential disadvantage of the cavity resonator TE odd modes is that the sample is placed
in a maximum field region. Therefore, unless the sample volume is very small, the resonance can
be heavily damped and legible Q-factors may not be obtained. Preliminary numerical modeling of
the microwave setup with lossy liquid material inside the cavity can be a good approach for finding
an optimum sample size in high loss liquid measurement. There have been very rare published
cases (Gennarelli et al., 2013; Gregory & Clarke, 2006) of liquid measurement that deals with the
liquid size inside the waveguide. For samples of low loss-low permittivity, the filling factor or the
sample volume to the cavity volume is suggested to be around
!!
!!
= 10!! in order to sustain the
sensitivity of the measurement system and obtain valid resonant shift based on first order
perturbation method. However, for lossy medium, the energy stored ratio in the material to the one
inside the waveguide should be small enough to achieve a reasonable Q factor of order 100 or
higher (Gregory & Clarke, 2006). In order to do that, a range of glass tubes filled with liquid water
inside the waveguide is being numerically modeled. The permittivity of water at room temperature
based on literature value (Bertolini et al., 1987) at 4 GHz frequency is being determined by
complex value of 74.56-14.56i in which the real number indicates permittivity and imaginary part
stands for the loss. The samples were designed to be filled end to end inside the waveguide to
avoid any E-field distribution inhomogeneity throughout the samples length. The tubes maximum
volume capacity for liquids measured inside the waveguide and also the ratio of liquid volume to
!
the cavity ( !! ) is being illustrated in table 4, accordingly. The results in the form of complex Eigen
!
frequency value were collected and used to calculate the
the liquid water and the also the ∆
!
!
!!
!!
as the ε’ (permittivity) coefficient of
as the ε” (loss) coefficient at each tube. The results being
shown in Fig 7 shows that the ε’ (permittivity) coefficient increases with the diameter of the
sample up to 4 mm diameter sample (D4) and after that, the resonant frequency shift becomes
18
Table 4. Tubes of 1 to 9 mm diameter with their correspondent volume and volume ratio inside the waveguide
negative and the resonance frequency of the cavity increases as the result of the lossy polar liquid
induced field perturbation.
The result of numerical simulation for obtaining the Eigenfrequency of each at the TE103 mode is
being analyzed using two ε’, ε” correlated coefficients. First, the variation in resonant frequency
divided by the cavity resonant (Δf/fc) is being associated to ε’ coefficient since the first order
perturbation assumes Δf/fc ≈ ε’. The other assumption is made by relating the change in inverse
quality factor of the peak resonant to the dielectric loss of the sample (Δ(1/Q) ≈ ε”) and name it the
ε” coefficient of the sample. As a result, the effect of tube contained high loss water diameter to
the change of cavity resonant structure and its quality factor is being illustrated in Fig 7.
result shows valuable information regarding the maximum amount of sample (
!!!"#
!!
The
) allowed
inside the waveguide. As it’s shown in Fig 7.a, the tube diameter increase does have a positive
correlation to the ε’ coefficient up to the tube D4 with the 4mm diameter. The D4 tube shows the
biggest ε’ coefficient of about 0.11.
This clearly is resulted from the maximum EM wave
absorption by the sample and shows that the sample permittivity is the highest at this tube and its
!
associated filling volume ratio ( !! = 1.43 − 03). After that, the change in resonant frequency
!
follows an arbitrary trend with increasing resonant frequency (negative Δf) at all of the tubes
except D7 with 7 mm diameter. The results obviously depict some characteristic changes in the
way the electromagnetic(EM) field is being propagated inside the material.
19
(a)
(b)
Fig 7. The ε’ and ε” coefficient in different tubes from D1 to D9
20
For ε” coefficient change, the trend plotted in log Δ(1/Q) versus the sample volume ratio
!!
!!
to better illustrate the coefficient change distribution. Although the ε” coefficient variation in the
first 4 tubes does not follow a very specific trend, the minimum loss achieved at the D4 tube is
noteworthy. As it was mentioned earlier, D4 tube also shows the maximum resonant frequency
shift or the Δf/fc (ε’ coefficient) at the same time. As a result, the sample volume that shows the
highest permittivity and lowest loss equals to
!!
!!
= 1.43 − 03 which is the optimum in TE103
mode simulated here.
Basically, the material inside the waveguide permittivity is measured by its electric field
capacitance and the material is the capacitor of the circuit being formed with the aid of network
analyzer as the voltage source and the waveguide as part of the circuit. It is well-known that the
insertion of the dielectric sample inside the waveguide would change the propagation of the field.
In case of lossy mediums like aqueous samples, even small changes in the sample volume results
in considerable E-field distribution alteration.
Therefore, in sample volumes bigger than
1.43 − 03 there could be a variety of reasons as why the resonant cavity showed increase in
resonant frequency. The first one is the propagation mode alteration induced by the sample inside
the waveguide. Changing the mode would change the resonant frequency of the structure and the
system can exhibit bigger resonant frequency.
The increase in resonant frequency of the
waveguide can also be supported through the reduction of electromagnetic field volume of the
resonator oscillations. As a result, bigger frequency values are required to resonate inside the
structure with a smaller cavity medium. On the other hand, as it shown in Fig 7.b, the loss
coefficient values in tubes bigger than D4 becomes increasingly higher than the smaller tubes and
the resulted very low quality factors undermines the accuracy and reliability of the measurement
system. This high attenuation of the system at tubes D5-D9 along with the inverse resonant shift
clearly shows that for measuring lossy mediums like water, there is a always a maximum amount
of sample (
!!!"#
!!
). Above that, the system accuracy and sensitivity becomes extremely low and ε’
and ε” values cannot derived using the linear perturbation theory.
Fig 8 shows the electric field intensity in different tubes inside the waveguide. The E-field
norm referred to E-field intensity derived out of averaging Ey and Ez electric field. As can be seen,
the electric field intensity around samples of low diameter e.g. D1 and samples of high diameter
e.g. D5 and larger is higher than the middle sized tubes. According to Fig 7 and 8, the underlying
21
reason behind this higher electric field concentration could be different. In tubes D1 to D4, the
numerical modeling electric field intensity shows that by increasing the diameter there is more
homogenous distribution of electric field around sample and the E-field intensity in sample
decreases as well.
Since Electric field concentration inside the material is an indication of
insulating properties, it can be deduced that as tube diameter increases from D1 to D4, the sample
electric field absorption increases. This happens due to the fact that glass wall insulating thickness
is constantly 0.5 mm in all tubes and by increasing tube size, the ratio of high loss liquid to the wall
increases and more homogenous electric field absorption is expected.
On the other hand, at tubes D5 above, the electric field concentration around sample is
almost constantly increasing and shows more dispersive behavior inside the sample. The behavior
of the electromagnetic field on the surface of a high loss liquid is similar to that on the surface of a
metal. As a result, the electromagnetic field penetrates into the liquid just to a moderate depth,
which is known as the liquid skin-layer by analogy with the metal. (Eremenko & Ganapolskii,
2003). It’s been reported by Eremenko et al that the region of strongest E-field becomes displaced
when the surrounding liquid has high loss. The increase in the resonant frequency of the cavity can
be correlated to electromagnetic field extrusion out of high loss liquid like water. It’s also been
reported by the same authors that in case of low loss liquids e.g. ethyl alcohol EM field extrusion is
not observed. This phenomenon can be seen only in case of high loss liquids. The numerical
calculation in our work supports the resonant frequency increase in tubes D5 and above with one
exception for tube D7. As a result, it is suggested that the effect of the EM field extrusion and the
induced propagation mode change both contribute to the resonant frequency elevation of the
structure in simulation results.
22
(a)
(b)
(c)
(d)
(e)
(f)
Fig 8. The electric field intensity inside the sample of various diameter, a) 1 mm, b) 4 mm, c) 5mm, d) 7 mm,
e) 8 mm and f) 9 mm.
23
To investigate the effect of different tube size of D1 to D6 over the waveguide propagating modes,
the frequency domain of Comsol Multiphysics aids in determining the transmission peak at
different frequencies. Fig 9 below illustrates the transmission parameter (S21) inside the waveguide
after insertion of different diameters tube filled with water in the frequency range of 3 to 6 GHz.
The results clearly show how the transmission is changing from D1 to D6 gradually.
D1
D2
D2
D3
D4
D4
D5
D6
Fig 9. S21 parameter variation in frequency range [3-6GHz] following tube size increase filled completely with water:
A. D1-D2, B. D2-D4 and C. D4-D6.
24
The peak transmission of the waveguide with different tubes differs as the high loss water volume
insertion is different. As can be seen in Fig 9, the sample D2 at the waveguide results in a peak
transmission at or around 5 GHZ which is close to the characteristic resonance of the TE105 mode
in the structure. As it was discussed earlier, to achieve the best result out of CPM, the system
resonance after insertion of the dielectric material should not deviate significantly from the
characteristic resonant of the cavity structure. The low resonance shift of the structure at a specific
frequency along with high quality factor guarantees the best accuracy and sensitivity. In frequency
domain of 3-6 GHz simulated above, finding the best mode of transverse electric field for testing
the sample is desirable.
Fig 10. The S21 parameter variation in different tube in frequency spectrum of [3-6] GHz.
For better illustration of the transmission spectrum of the waveguide after different tubes insertion,
the 3D plot of 4 different tubes transmission parameters is plotted over frequency range of [36GHz]. As can be seen in Fig.10, the transmission peak at D2 and D4 tubes significantly stands out
compared to the other two tubes in D1-D4 tube range sizes. The sample of D2 shows the best
25
transmission at or around 5GHz(TE105) and the D4 makes in the best transmission around
4GHz(TE103). These are very important findings in figuring the best tube size for measurement of
lossy aqueous medium inside the waveguide in frequency range of [3-6GHz]. Obviously, the
transmission parameter of the waveguide is altered as a result of high loss water inside of the
resonant cavity. The structure with dielectric material does show one or two specific transmission
peaks in frequencies, which are close to the characteristic resonant frequency of the empty cavity.
26
4.3. Liquid volume effect
To investigate the effect of liquid volume, three different glass tube similar to D1, D2 and D3 in
numerical simulation have been chosen. They have been partially filled in different ratios to
measure the shift in resonant frequency and quality factor of the structure in TE103 mode. The
ability to make small sections of steady state water inside tubes of different size (Fig 11) enables
high precision measurement inside the waveguide. The result from fully filled tubes shows that
only D1 with the least diameter (1mm) can spare us detectable resonant peak with a known valid
quality factor. The other two liquid water filled tubes of 2 and 3 mm diameter range (D2 and D3)
(a)
(b)
(c)
Fig 11: (a) The water filling of D1 capillary with different volumes. (b) water filled volume as
low as 550nL. (c) the laminar viscose flow of water filled D1 tube
data for resonant frequency parameters cause high damping in the system. The experimental
situation compared to numerical situation posses more error sources to the measurement, which
27
makes the measurement resolution lower. It was shown that the quality factor of the experimental
measurement deviate by 30% to the one measured with numerical simulation. This discrepancy
manifests its eminence in measuring the high volume of high loss aqueous samples. The maximum
liquid volume measured in TE103 mode was shown to be in tube D4 (≈272µL) with finite element
simulation analysis. However, in experimental situation shown in Fig 12.a, the ε’ coefficient
change with liquid water volume inside tube D1, D2 and D3 illustrates three different increasing
fashion that makes them distinguishable. The D1 tube result depicts an increasing trend that can be
best described by a power regression mode, which rises exponentially as the liquid volume
increases. For tubes of D2 and D3 however the trend increases more linearly as the volume
diameter becomes more. This clearly shows that bigger tube results in more linear resonant
frequency shift. In general, the total volume of the liquid is a more important limiting factor than
tube size. The Fig 12.b illustrates the maximum amount of liquid water measured in experimental
setup. At high damping, the system would yield many similar resonant peaks instead of one main
resonant at or around the characteristic resonance of the system. The big shift in resonant
frequency with material results in poor resolution of the system signal to noise ratio and leads to
measurement inaccuracy. The tube of the lowest diameter (D1) indicates a capability to yield
resonant shift results up to the point of complete filling inside the waveguide which equals to
17µL. The tubes with the higher diameters (D2 and D3) though do not yield accurate resonant
frequency when filled to the end. In that manner, the sample with 2 mm diameter (D2) shows
detectable field up to 47µL and the tube with 3 mm diameter (D3) yield results up to 43µL.
28
Fig 12: (a) The frequency shift of different water volume insertion in tubes D1 to D3 (b) The
maximum liquid water measured at different tubes
29
Partially filled tube does change the electric field distribution inside of the cavity and does have a
direct effect on the electric field perturbations inside of the cavity. Since the highest electric field
resides just outside the surface of the high dielectric constant material, as the surface to volume of
the material increases the electric field concentration inside waveguide increases (Fig 13.a). The
two effects of sample total volume and the
!"#$%&'
!"#$%&
ratio determines the electric field distribution
and intensity around the high loss liquids.
As it is illustrated in Fig 13.b, the electric field increases dramatically around the water
cross-section inside the tube filled by 90% compared to the one filled in by 10%. The Electric
field is about 12 (KV/m) compared to the 4.4 (KV/m) at samples filled by 10% with water inside
the waveguide. The increase in electric field follows an almost linear trend from about 20% to
80%(Fig 13.a). As a conclusion, as the sample filling level inside tube increases and water-air
interface stays closer to the walls, electric field intensity becomes dramatically high and very
sensitive to tiny changes in the amount of water added or deducted. This sensitivity is manifested
through parameters including the resonant frequency and quality factor (Fig 11 & 12).
(a)
30
(b)
(c)
Fig 13: The electric field intensity inside D1 tube with (a) different filled fraction (b) The 0.091
filled ratio and (c) The 0.91 filled ratio.
The presence of liquid water inside the waveguide enables more electric field concentration at the
two end of sample and more perturbation as a result. Thus, for an equal high loss liquid volume, as
the diameter increases and the water filled length decreases, the electric field concentration
increases. The material induced perturbation is also affected by the dielectric sample
!"#$%&'
!"#$%&
ratio.
The more the field gets perturbed, the less the accuracy and harder the measurement. Therefore,
increasing the sample tube diameter cannot solely provides the best measurement accuracy through
raising liquid volume (Fig 12.b). The optimum tube size was found to be D2 in Fig. 12 as opposed
to numerical simulation analysis that found the D4 to be the best for TE103 mode (Fig 7).
The experimental result gives a guideline in terms of the length and maximum liquid water
at the ambient temperature that can be used inside the waveguide. The cavity waveguide measured
showed a structure with a 40% reduction in quality factor which may be caused due to different
factors being classified in previous section like material insertion slots, interior surface
irregularities and the edges inside the structure. The experimental result also indicates the presence
of a lower detection level for measuring high loss liquid resonant frequency shift.The more field
gets perturbed and non-uniform electric field expanded, the more difficult obtaining the accurate
values out of the system with already embedded non-uniformity in electric field dispersion with the
slots at the middle of the waveguide. As the finite element method shows (Fig 14), the more
variation occurs in dielectric loss compared to the permittivity and as the water volume ratio inside
31
the tube increases, the shift in quality factor surpasses the frequency shift. As a result, the quality
factor depression or loss escalation is of a more important value in measuring high loss liquids.
(a)
(b)
(c)
Fig 14. The water filling ratio effect on: (a) ε’ coefficient (b) ε” coefficient and (c) both in comparison.
32
4.4. Temperature dependence of dielectric permittivity
The resonant frequency change in TE103 induced by completely filled tube D1 over the
range of temperature from -20 to 25 °C is plotted in Fig 15.
(a)
(b)
Fig 15. The variation of a) dielectric permittivity coefficient (ε’) and b) loss coefficient (ε”) at two
different resonance frequency mode of TE103 and TE105 over the temperature range [-20 − 25°C].
33
The data at each temperature is being calibrated by the initial presence of glass tube inside the
waveguide over the range of temperatures. The DI water temperature dependent permittivity
measurement at TE103 (≈4GHz) and TE105 (≈5GHz) microwave frequency yields valuable
information about the sensitivity of the measurement at microwave C-band for fluids and its
accurate correlation with literature values. For pure water, as it was shown in Fig. 4, the static
permittivity value does not change up to the frequency range of microwave and the dielectric
permittivity starts to decrease smoothly by increasing frequency around 1GHz. As a result, the
higher the frequency, the lower the permittivity at microwave region. Though this fact does not
apply for dielectric loss throughout the whole microwave region but in microwave C-band, higher
the frequency the more the permittivity loss. The effect of temperature at microwave permittivity
of water has been dealt with in numerous articles before (Artemov & Volkov, 2014; Bertolini,
Cassettari, Salvetti, Tombari, & Veronesi, 1990; Buchner et al., 1999; Eremenko & Ganapolskii,
2003; Rosenkranz & Fellow, 2015). However, the microwave C-band dielectric properties of
water has been poorly dealt with and to the knowledge of the author, no publication has
investigated the effect of temperature region of [-20–25°C] at two-microwave frequency of 4 and 5
GHz. It’s been well established by past researchers that the temperature at microwave frequency
does play a significant role in the permittivity values and this is being reinforced in the current
work at microwave C-band. The room temperature permittivity measurement of water at capillary
tube by (Bertolini et al., 1987) at 9.61 GHz shows a continuous increase in permittivity with
temperature. However, for dielectric loss the increasing trend would reach to a peak around -3°C
and starts declining at or around 5°C up to the ambient temperature. The other study conducted by
(Buchner et al., 1999) around 1GHz shows the permittivity and loss declining fashion with
temperature from -20 °C to 20 °C. Having these two well-known works into attention, the
decreasing trend of dielectric permittivity with temperature at lower microwave frequency and the
almost ever-increasing trend of it around 10GHz throughout the temperature variation from -20 °C
to 20 °C implies a temperature dependent behavioral change. It gives the hint that the temperature
dependence of DI water at the frequency interval of [1-10GHz] might undergo some phenomenon
change that makes it exhibit different dielectric behavior over the course of temperature range [20–20°C] at different frequency. The two modes studied in this work (TE103 (≈4GHz) and TE105
(≈5GHz)) provide valuable information about the temperature dependence of dielectric properties
of water in microwave C-band. This is one of the important frequency regiment for investigating
liquid water dielectric permittivity. The temperature sensitivity variation of dielectric constant and
34
(a)
(b)
Fig 16. The dielectric permittivity and loss variation over the temperature region of [-20,20°C] (Bertolini et
al., 1987; Buchner et al., 1999)
imaginary to the frequency in this frequency region is noticeable. The two well-known studies
along with numerous articles on dielectric permittivity of water at different temperature range
(Artemov & Volkov, 2014; W J Ellison et al., 1996; W. J. Ellison, 2007; Medcraft et al., 2013) has
shown that the liquid water permittivity temperature dependent behavior is very sensitive to
frequency at microwave region esp. 1-20GHz.
This relationship between the temperature
dependence of liquid water permittivity to the microwave frequency before the γ dispersion
(around 20 GHz) could bring in a lot of useful information in developing aqueous sensors. This
sensitivity can be employed in a lot of aqueous matter characterization in the relatively wide
temperature regime of [-20, 20°C]. The inverse relationship of liquid water dielectric permittivity
with temperature at lower microwave frequency (Fig 16.a) gradually turns to a direct correlation at
higher frequencies (Fig 16.b) and the current work conducted at microwave C-band targets a very
important region of this behavioral change. As is seen in Fig 15.a, the ε’ coefficient can be divided
into two separate temperature regimen in TE103 mode. Below -3°C, the permittivity coefficient
almost linearly increases with temperature but after an almost constant value regime in [-7−0°C],
the temperature escalation results in permittivity lessening up to the ambient temperature.
35
Comparing the temperature-permittivity dependence at two different modes tested (TE103 and
TE105) makes it more prominent to understand the role of frequency on temperature dependent
behavior of water. It becomes interesting to know that the trend in TE103 does not comply with the
one in TE105. At the temperature regime tested in TE105, the gradual increase in ε’ coefficient
occurs from temperature as low as -20 to room temperature. This increase follows a sharper trend
below -10 compared to above this temperature. In general, the rule of thumb in microwave range
for permittivity values of polar liquids is by increasing frequency the permittivity decreases and
loss increases (Bertolini et al., 1987). This has been proved right in this case. Current results are a
good example of the temperature sensitivity of the liquid water at the waveguide in microwave Cband. The electric field gets affected (perturbed) by the sample and the sensitivity is high enough
for reaching the verifiable pattern for dielectric variation over the tested temperature range.
Investigation of the dielectric loss coefficient temperature dependence trend does indicate even
more facts about the dielectric properties of liquid water. The work done by (Buchner et al., 1999)
shows at low microwave frequency of 1GHz, the loss increases constantly as temperature increases
from -20 to the room temperature. The γ dispersion in water at microwave around 20 GHz indicate
loss peak at the room temperature, which is in contrast with the ever-decreasing trend at the 1 GHz
frequency. As a result, having a temperature at which the frequency shows the maximum loss at
lower frequency in microwave region would be below the temperature region tested in both
(Buchner et al., 1999) and current work. The relaxation frequency is temperature dependent in
nature (Sihvola, 1998) in which as the frequency increases, the relaxation occurs at higher
temperatures in microwave region. The shift of dielectric relaxation to higher temperature with
increasing frequency does follow a gradual shift in which transition points is of high importance.
As a result, it’s expected that frequency escalation result in lessening the decreasing slope of
dielectric loss with temperature. Thus, the temperature of the dielectric relaxation at 9.61 GHz can
be observed in the temperature region of [-20, 20°C] (Bertolini et al., 1987). This behavioral
change is being proven in results obtained as shown in Table. 5 below. The result shows at TE105
the decreasing slope of ε” coefficient reduces compares to the one at TE103. Knowing that, the
liquid water permittivity loss values are positively correlated to the frequency before relaxation
frequency, having a lower ε” coefficient at TE103 compared to TE105 is predictable. However,
temperature variation does affect the loss values as well and at temperatures below -10°C, the ε”
coefficient from TE103 surpasses the TE105. This fact does indicate the more dielectric loss values
of super cooled water at lower frequency in lower temperatures regions.
36
Table 5. The dielectric permittivity and loss comparison with literature over temperature range [-20 – 20°C]
Literature
Current work
F
T [-20 − 20°C]
ε’
ε”
0.92 GHz
é
ê
ê
9.61 GHz
é
é
é [-3°C] ê
≈4 GHz
é
é [-3°C] ê
ê
≈5 Ghz
é
é
ê
4.5. Liquid Concentration dependence of dielectric permittivity
The DI water and Ethanol structures both consisted of polar molecules with a large
difference in the electric permittivity values. As it’s been well established by past researchers
(Bertolini et al., 1987; Gregory & Clarke, 2006; Ray & Behari, 1986) the DI water at ambient
temperature shows static permittivity of around ≈80 and the Ethanol (C2H6O) have a value of
static electric permittivity around ≈10. In the microwave region C-band, these differences even
become more intensified by having the water permittivity with little decrease to be around 75 and
Ethanol dielectric value by a bigger change to be about 5. This big discrepancy in terms of
electrical permittivity between these two popular solvents makes them an interesting choice for
measuring the sensitivity of microwave dielectric spectroscopy sensors in aqueous solutions.
(Abduljabar, Rowe, Porch, & Barrow, 2014; W J Ellison et al., 1996; Gregory & Clarke, 2006)
Knowing that, for finding out the permittivity effect of ethanol in ethanol/water mixture, different
solution with ethanol concentrations of 5% to 50% have been measured and tested. To maximize
the testing volume sample, the tube r2 with the maximum allowed measureable volume of ≈50 µL
was selected. Having bigger volume could help increasing the detection capability of the system
through the bigger contrast and distinguishable resonant frequency and quality factor of the
measured samples. The results in terms of ε’ and ε” versus ethanol concentration is being plotted
37
As it is expected, adding ethanol with a lower permittivity should decrease the liquid water volume
but the frequency dependent of this effect is unknown. In the microwave C-band, as the result
shows (Fig 17), the increase in frequency results in even higher permittivity values at high
(a)
(b)
(c)
(d)
Fig 17. The effect of Ethanol concentration in liquid water on :(a, b) ε’ coefficient and (c, d) ε” coefficient.
concentration of ethanol. This is meaningful while the permittivity at low concentration is higher
for TE103 mode. Higher frequency, though provides less accuracy, could be effective in some cases
as high concentration mixture of ethanol/water. It is assumed that the higher sensitivity of TE105
mode is the reason of the linear decreasing trend observed in Fig 17.b.
38
The results indicate ethanol concentration up to 20% directly increases the quality factor of the
solution at both TE103 and TE105 mode. After that, the ethanol increase does not significantly
influences the resonant peak quality factor.
4.6. ε' and ε” shape factor coefficient determination
According to (1), in cavity perturbation method (CPM), the shift of resonant frequency is
!
attributed to the dielectric permittivity and loss of the material knowing the !! and shape factor of
!
the sample tested.
! ∆!
 ! = 1 + !! !! !
!
!
(7)
!
!
!
 !! = !! !! ( ! − ! )
!
!
(8)
!
shape factor is dependent to the geometry of the structure and also the material shape and position.
Knowing the permittivity of the material in a variety of standard condition and also the correlated
∆!
ε' coefficient ( ! ), shape factor can be extracted out of the linear perturbation formula. To verify
!
the accuracy of results, the perturbation should be small enough and as a result, the smallest tube
D1 may provide a good choice for this case. In table 6 below, the results of two different high loss
liquids measurement at microwave C-band TE103 (f ≈ 4 GHz) and TE105 (f ≈ 5 GHz) are being
Table 6. The permittivity (ε') shape factor determination for liquid water and ethanol at TE103 and
TE105
DI Water
Ethanol
f ≈ 4 GHz
f ≈ 5 GHz
f ≈ 4 GHz
f ≈ 5 GHz
ε'
74.921
73.231
5.602
5.222
Δf / fc
0.003276308
0.003276308
0.00024061
0.000226925
Vc / Vs
10989.538
10989.538
10989.538
10989.538
A-1
2.0808
2.1167
2.1180
2.1087
A-1 = 2.106
39
∆!
!
shown. The correlated ε' coefficient ( ! ) and the !! are determined as well. Based on (1), the shape
!
!
factor or A-1 is calculated for each and the result shows a good consistency at different resonant
mode in two different liquids. On average, the number obtained for A-1 is 2.106 which is
Table 7. The permittivity loss (ε′′) shape factor determination for liquid water and ethanol at TE103
and TE105
DI Water
Ethanol
f ≈ 4 GHz
f ≈ 5 GHz
f ≈ 4 GHz
f ≈ 5 GHz
ε′′
14.451
15.341
4.76
3.98
1/ΔQ
0.001109222
0.001251543
0.0004011
0.000325718
Vc / Vs
10989.538
10989.538
10989.538
10989.538
B-1
1.18
1.11
1.08
1.112
B-1 = 1.12
considered as the shape factor of the testing at D1 tube. The results can be verified further by
correlating liquid water permittivity values over a vast temperature region (Fig 15).
The same is true for dielectric loss measurement by having the " coefficient (Δ (1/Q)) and
the permittivity loss (Table 6). The B-1 or permittivity loss shape factor does play the linear
correlation between the system loss due to materials presence and it should be physically
meaningful inside the quantitative calculation as well.
It’s being established that for CPM
!
calculation in rectangular waveguide, the sample dielectric loss shape factor is ! which is half of
!
the permittivity shape factor of about !. The almost same ratio of these two shape factor constants
in the extracted data here can be deemed as another proof for its accuracy and usefulness.
4.7. ε” and ε’ interdependence in resonant frequency and quality factor variation
Based on Kramers-Kronig relations, the ε” and ε’ in complex dielectric permittivity are not
independent of each other (Feldman, Puzenko, & Ryabov, 2006) and their dependency is
formulated through Hilbert transformation:
∞
ε '(ω ) = ε∞ + (2 / π ) ∫
0
xε "(x)
dx
x2 − ω 2
40
(9)
∞
ε ''(ω ) = (2ω / π ) ∫
0
ε '(x)
dx
x2 − ω 2
(10)
when the  is angular frequency in a harmonic field and the ! is the dielectric permittivity at
infinite frequency. This interdependence superposition effect of dielectric loss and permittivity can
be investigated through numerical simulation by simple mathematical calculations in high loss
liquids like water as well. (Chretiennot, Dubuc, & Grenier, 2013)
To investigate the interdependence relationship of dielectric loss and permittivity, the resonant
shift and quality factor change through changing the permittivity and loss is being investigated.
The dielectric permittivity values are set at ε’ = 5, 25, 45, 65, 75, 85 and the dielectric loss values
are ε” = 5, 15, 25, 45, accordingly. For each constant dielectric permittivity, the loss is being
changed and the results are being illustrated in Fig 18.
41
Fig 18. The (a) Resonant frequency and (b) quality factor shift at different ε’-ε” combination in liquid
water.
By simple mathematical description, it can be shown that the ε’-ε” interdependence to the resonant
frequency and quality factor shift can be formulated as:
∆!
∆!
∆!
∆!
∆ = ∆!! ∆ ! + ∆!" ∆"
∆ = ∆!! ∆ ! + ∆!" ∆"
(11)
(12)
For which, if we assume ε’ or ε” as constant values and the other as variable, the equation would
always be correct. Having that into mind, 4 different coefficients can be defined as:
∆!
∆!!
∆!
= !
∆!!
∆!
∆!
= !
∆!"
∆!"
= !
= !
(13)
(14)
Where the A1, A2, A3 and A4 are sensitivity coefficients and all can be driven out of formula by
substituting the values from Fig 17 into the formulas. By averaging the values obtained, the 4
coefficient values are as follows:
42
A1 = 13.14,
A3 = 11.16
A2 = 2.64,
A4 = 29.78
And as a result the resonant frequency and quality factor dependence on ε’-ε” is expressed as :
∆ = 13.14 ∆ ! + 2.64 ∆"
∆ = −11.16 ∆ ! − 29.78 ∆"
The calculated values from the sensitivity coefficients determination clearly shows that resonant
frequency shift is more dependent on dielectric permittivity change than dielectric loss. The ratio
!".!"
!.!"
= 4.97 for resonant frequency shift and
!!".!"
!!!.!"
= 2.67 .
This in turn shows that the
permittivity loss value is more dependent on quality factor change in comparison to the resonant
frequency dependence of dielectric permittivity.
43
CONCLUSION AND FUTURE WORK
In the work presented, the microwave dielectric permittivity dependence of aqueous
samples at microwave C-band to volume, temperature and concentration was investigated
thoroughly.
Numerical simulation and experimental results showed the tube diameter for
measuirng the high loss liquid is frequency dependent and at TE103 mode the best tube is D4= 4mm
diameter while for TE105 the results are better achieved in D2= 2mm. Temperature dependence of
liquid water at 4GHz showed two different increasing and decreasing fashion with a permittivity
peak around -10°C while at 5 GHz the permittivity values is positively associated with temperature
and increases with it. Investigating the interdependence effect of ε’ and ε” shows the dielectric
loss is a more determinant factor in resonant frequency and quality factor shift in resonant cavity.
The ε’ and ε” dependency to resonant cavity factors determines the shape, geometry and volume of
the high loss aqueous sample to be measured with the best sensitivity-accuracy combination.
For future studies, different approaches can be taken to improve the measurement accuracy
based on the application requirement. PDMS tubes are commonly used to carry fluid of micro and
nano sizes and a continuous flow of commonly used aqueous samples can be tested via them. The
lower reflection coefficient of plastic at microwave is of high value in high loss liquid
measurement. The optimized length of the rectangular waveguide in microwave C-band for TE101
and TE103 modes can be simulated and manufactured to achieve the best coupling in high loss
liquids inside the cavity. In the new design, insertion of the tubes through fully filled slots to avoid
any waveguide-air-sample induced losses sounds imperative. The measurement up to range of
10GHz is still recommended to have good accuracy and sensitivity. However, exploring further in
a wide range of frequency up to 50GHz is a challenging task that needs to be addressed in high loss
liquids related future works. Last but not least, the multiphasic aqueous based samples in different
testing conditions (temperature, pressure, humidity etc.) is the most promising application to
investigate through the systematic measurement studies presented here and can be fully addressed
in near future.
44
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48
VITA
Aref Asghari, The first and only son of Rasoul, was born in Tehran, Iran in 1990.
He decided to study throughout his life and never give up since he opened his eye to the
world as a little child!! . Thus, after completing school years, he got accepted into
college and received his Bachelor of Science degree in Material and Metallurgical
Engineering from University of Tehran on July 2013.
He did study mechanical
properties of advanced high strength steels as his B.Sc. thesis. For graduate studies, he
joined University of Texas at San Antonio in 2013 to study Advanced Material
Engineering as a Master student.
Electronic materials and devices has been the
concentration of his degree. Thus, he investigated the dielectric complex behavior of
fluids and micro fluids at microwave C-band using cavity perturbation method as his
Master of Science thesis.
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