Download Electrical Parameter And Permittivity Measurement Of Water

International Journal of Water Resources and Environmental Sciences 2(3): 66-75, 2013
ISSN XXXX-XXXX
© IDOSI Publications, 2013
DOI: 10.5829/idosi.ijwres.2013.2.3.2938
Electrical Parameter and Permittivity Measurement
of Water Samples Using the Capacitive Sensor
G. Behzadi and L. Fekri
Department of physics, East Tehran Branch,
Islamic Azad University, P.O. Box 33955-163, Tehran, Iran
Abstract: In this study, we reported the effect of frequency on the electrical parameter and permittivity of
water samples using an invasive capacitive sensor. The measured capacitance, resistance and dissipation
factor for distilled water, mineral water, tap water and salt water for different frequency is reported and results
compared. Comparison of the measured capacitances for water samples shows a decrease by increasing the
frequency. For salt water measured capacitance decrease from 7.98 µF to 4.11 µF when the frequency rise from
100 Hz to 2 Khz. The measured relative complex permittivity for distilled water in the frequency 100 Hz
equal 29.41×106 and for salt water is 309.8×106. This big difference is because of electrical conductivity (EC)
effects on the imaginary part of the relative complex permittivity. The imaginary part is increased by rising in
the electrical conductivity. Our results show for water samples the relative complex permittivity is decreased
by rising the frequency. Results show that the reported cylindrical capacitive sensor is a good tool to
measure the electrical properties in the low frequency.
Key words: Frequency
Capacitive sensor
Dissipation factor
INTRODUCTION
Permittivity
media by the capacitive method is described by [2]. In the
year, 2010, Wu et al. [3] reported the relationship between
dielectric constant and soil water content using the
capacitive method. Through the coaxial capacitive probe,
the permittivity sensor for water-in-oil emulsions reported
in [4].
The EC is the most important physical quantities
that effect on the complex permittivity of water.
The electrical conductivity is associated to the
imaginary part of complex permittivity. Conductivity
effects on the capacitance measurement of water liquids
using cylindrical capacitive sensor investigated in [5].
They stated that the measured capacitance is increased
by rising in the EC. In another study comparison of
invasive and non-invasive cylindrical capacitive sensors
for electrical measurements of different water solutions
and mixtures is reported by [6]. They described that the
reactance capacitance is the dominating term in the
capacitance measurement for the invasive cylindrical
capacitive sensor.
Frequency is another parameter that effect on the
complex permittivity measurement of water. In recent
years, development of different measuring systems and
Recently capacitive sensors have been used in
various sensing applications, such as pressure
measurement, liquid level testing, dielectric thickness
measurement, capacitive tomography and displacement
measurements. Such capacitance sensors can be designed
in the form of macro-and micro-structures, which can
play important roles in the advanced micro-sensor
technology.
There are various approaches to measure the
permittivity of water. The most important type of these
approaches is a capacitive method through capacitance
measurement. Design of the system consists of a
capacitance probe and the measuring module for the
capacitance change monitoring. The measuring module,
such as LCR module, resonance, charge/discharge and
capacitance to phase conversion methods are used in
the different way.
The dielectric permittivity and conductivity
measurement of water with non-blocking electrodes in the
5 Hz- 13 MHz frequencies are given [1]. The determination
of liquid water content and dielectric constant in porous
Corresponding Author: G. Behzadi, Department of Physics, East Tehran Branch, Islamic Azad University,
P.O. Box 33955-163, Tehran, Iran.
66
Intl. J. Water Resources & Environ Sci.., 2(3): 66-75, 2013
study of complex permittivity in different frequencies
are reported. In terms of researches, complex permittivity
of water as a function of frequency and temperature [7].
He described a set of complex permittivity values for
pure water is presented for nine temperatures among 0
and 50°C and for microwave frequencies from 1.1 to 57
Ghz. The frequency 9.355 Ghz complex permittivity
of water from 1°C to 90°C is reported in [8] and
complex permittivity of water from 65 to 75 GHz is
reported in [9]. A model for the complex permittivity
of water at the frequency below 1 THz is introduced by
[10]. Evaluation of water permittivity models from
ground-based observations of cold clouds at frequencies
among 23 and 170 GHz is described by [11]. Wentz [12]
reported the complex dielectric constant of pure and sea
water from microwave satellite observations are
discussed. Another study considers characterizing a
temperature dependence of the permittivity of water [13].
Capacitive method used in various sensing
applications. A capacitive sensor system for study
of oil-water flow in pipes is proposed by [14].
The liquid-level measurement system based on a
remote grounded capacitive sensor is described by [15].
A radio-frequency resonance capacitive sensor with
variable capacitance for gas/liquid volume ratio
measurement is presented by [16].
The main goals of this study divided into three parts.
The first aim is to compare the complex permittivity of
water samples with different ECs. The second aim is to
study of the frequency effects on the capacitance
measurement. At the last but not least, describe the
relationship between permittivity and measured
capacitance by auto balancing bridge method.
The frequency range of LCR-816 is 100 Hz-2 KHz. In
the frequency range the resistance of four wire of
LCR-06A is-688.46 µ and the capacitance is 1.845 pF.
Display range of the unit for the capacitance is from
0.00001 pF to 99999 µF, for the resistance is from 0.00001
to 99999 k and for the dissipation factor (DF) is from
0.0001 to 9999. The accuracy for C and R measurements is
about 0.10% (basic) + another error term, that is defined
from a given formula has given in the device technical
manual and accuracy about 0.001% for dissipation factor
measurements [17].
The cylindrical probe is made up aluminum.
The diameter of the inner electrode is 14 mm and the
inner diameter of the outer main electrode is 22 mm and
has a thickness wall diameter of 4 mm. The radial gap
between the two tube electrodes are about 4 mm and the
diameter of the probe is about 30 mm. The height of the
probe is 16 mm. The measured full liquid volume for the
cylindrical probe is about 3.5 cc.
The capacitance measurement for the cylindrical
probe depends on the permittivity and electrical
conductivity than the sample liquid. Fig.1b shows the
equvalent circuit of the cylindrical probe. As can be seen
of Fig.1b, the affect of permittivity and conductivity of
water sample as a parallel capacitor and resistor are
considered.
There are different impedance measurement
methods from low frequencies up to the microwave
region. The measuring module, such as Bridge method,
Resonant method, I-V method, RF I-V method, Network
analysis method and Auto-balancing bridge method is
used in different way. Considering only measurement
accuracy and ease of operation, the Auto-balancing
bridge method is the best possible choice for
measurements up to 110 MHz. For measurements from
100 MHz to 3 GHz the RF I-V method has the best
measurement capability and from 3 GHz and up, the
network analysis is the recommended technique [18].
Fig. 2 (a) shows the bridge method for impedance
measurement. The value of the unknown impedance (Z x)
can be obtained by the relationship of the other bridge
parts when no charge transferred from the detector (d),
MATERIALS AND METHODS
Fig. 1a shows the experimental setup that includes the
cylindrical cell probe and a LCR meter modules (Yuke-816,
Good Will Instrument, Gw Instek). The LCR-816 includes
a LCR-06A measuring probe. It uses the structure of four
wires measurement, which allows accurate and stable
measurements and avoids mutual inductance and
interference from measurement signals, noise and
other factors inherent with other types of connections.
The only way to measure resistance and permittivity
reliably in this case is to use four contact method, which
eliminates charge accumulation at the inner electrodes.
Fig.1c shows the principle set-up of a four electrode
impedance measurement for electrode-sample interface.
Zx= Rr (R3/R2)
(1)
Where Rr is the rang resistor and (R3, R2) are known
resistors. The circuit of Auto balancing bridge method is
shown in Fig.2 (b). By operation of the I-V converter,
current that flows through the device under test (dut)
67
Intl. J. Water Resources & Environ Sci.., 2(3): 66-75, 2013
Fig. 1: (a) Experimental setup of capacitance measurement (b) Equivalent circuit of probe (c) principle set-up of a four
electrode impedance measurement for electrode – sample interface
D
Rr
Zx
A
C
d
R3
R2
B
(a)
(b)
Fig. 2: Equivalent circuit of (a) Bridge method (b) Auto balancing bridge method
also transferred from the resistor Rr. Therefore, because
of current balances, the potential at the point D is
maintained at zero volts. Using voltage measurement at
high terminal and over resistance Rr the impedance is
measured. In our case, the liquid sample is placed inside
the probe as the device under test [18].
Zx= Rr (Vdut/Vi)
A LCR meter, in a low frequency range typically
below 100 kHz, employs a simple operational amplifier for
its I-V converter. This type of instrument has a
disadvantage in accuracy at high frequencies because of
performance limits of the amplifier. Wideband LCR meters
and impedance analyzers employ the I-V converter
consisting of sophisticated null detector, phase detector,
integrator (loop filter) and vector modulator to ensure a
(2)
68
Intl. J. Water Resources & Environ Sci.., 2(3): 66-75, 2013
where Cx is the liquid capacitance. The DF is the ratio
of an insulating materials resistance to capacitive
reactance at a specified frequency. It measures the
inefficiency or loss of the material, is always greater than
0, but usually much smaller than the dielectric constant.
DF measurements are an excellent means of quality
control, which can yields an indication of contamination
or deterioration. We calculated the DF from division of
equivalent series resistance (ESR, that adequate to Rm)
to the reactance capacitance of the unknown capacitance
(Xs) [18]. For the case that the XCx is greater than Rx we
can obtain the DF from:
DF = − Rm / Rx ,
Fig. 3: Equivalent circuit of the (a) series method (b)
parallel method
high accuracy for a broad frequency range over 1 MHz.
This type of instrument can attains to a maximum
frequency of 110 MHz [18].
In Fig. 3a, the series equivalent circuit is shown
where Rs and C show
the series resistance and
s
capacitance parameters. Fig. 3b shows the parallel
equivalent circuit where as Rp and Cp respectively show
the parallel resistance and capacitance parameters.
The component of the primary display of the LCR module
depends on which equivalent circuit is chosen.
Capacitance measures the electronic charge stored
between two terminals. Generally, for small capacitors
(<10 pF, 100 KHz) parallel method and for large capacitor
(>1µF, 100Hz-2 KHz) series method is recommended [17].
The capacitance formula for series method is obtained
from:
Cs= - (1/ Xs)
with the substitution of Eq. (6) into Eq. (5) we obtain
the measured capacitance from:
C m =C w + C x2 + ( DF ) 2 /
=
Cx
2
R x2
(7)
C m2 − ( DF ) 2 /
2
(8)
R m2
cylindrical cell probe. There are theoretical approaches
such as Gauss law, Laplace equation and Coulomb’s law
for the capacitance determination. The formulations of
liquid capacitance for cylindrical capacitive probe by
coulomb law is given in [5, 19].
C x = f (  , GF )
(9)

l
l 2


z − + a 2 +  z −  − 2a 2 cos ′ + a 2

2
2

)d ′
 ln(
2

l
l

2

z + + a +  z +  − 2a 2 cos ′ + a 2
2
2


f ( , GF ) = 8 2  L 

l
l 2


z − + b2 +  z −  − 2b2 cos ′ + b 2
2
2


)d
 − ln(
2

l
2 +  z + l  − 2b2 cos ′ + b 2
z
b
+
+



2
2


(4)
∫
Where Rx is the liquid resistance and Xcx is
the reactance capacitance of the liquidcapacitance.
With substitution of Eq. (4) Into (3) the capacitance Cs
can be obtained from:
C x2 + 1/
Rm2 ,
The liquid capacitance depends on the complex
permittivity (  ) and geometric factor (GF) of the
Where Xs is the reactance capacitance of the
unknown capacitance and is the angular frequency.
For water liquids the reactance capacitance Xs is
obtained from:
=
Cs
2
The parasite capacitance (Cw) is the capacitance of
wires of the LCR-06A that is parallel with Cs. The parasite
capacitance for Cw is 1.854 pF [17]. For small capacitor
such as air capacitance we cannot eliminate the Cw, while
for large capacitor the liquid capacitance Cw is negligible.
Using Eq. (7) the liquid capacitance Cx obtained from:
(3)
-jXS= [Rx (-jXCx)]/[Rx - jXCx]
(6)
(
)
∫
(5)











′



−1
(10)
69
Intl. J. Water Resources & Environ Sci.., 2(3): 66-75, 2013
Where L is the length of the probe, a is the inner
electrode radius and b is the outer electrode radius.
Using Eq. (8, 9) the complex permittivity of water can be
obtained from:
2
2
=
1/ f ( GF )  Cm − ( DF ) /
Fig. 5 shows the capacitance measurement of water
samples in the frequency range 100Hz-2 KHz. Fig. 5 shows
two important points. The first point, for salt water, tap
water and mineral water the measured capacitance is
decreased by increasing as the frequency. The second
point, liquids with high electrical conductivity have
greater capacitance. The salt water has the highest
capacitance with electrical conductivity 3140 µS/cm and
mineral water has the lowest capacitance with electrical
conductivity 223 µS/cm.
The measured capacitance for salt water is 7.98 µF,
for tap water is 5.92 µF and for mineral water is 5.09 µF at
the frequency 100Hz. Repeatability of capacitance
measurement for water samples in frequency 1 KHz is
shown in Fig. 6. The capacitance difference among
frequent measurements for salt water equal ± 0.31
µF, for tap water equal ± 0.28 µF, for mineral water is ± 0.25
µF and for distilled water is ± 0.05 µF in the frequency 1
KHz.
The main reason for this difference is related to the
temperature changes and humidity in the environment.
The obtained results show this difference increased by
rising in the electrical conductivity.
For better comparison, the DF and measured
resistance of distilled water in the different frequencies
are plotted in Fig. 7. As can be seen in Fig. 7, the
measured resistance is increased by raising the frequency
and measured DF is decreased. Fig.7 shows the slope of
resistance and the DF variation is reduced by rising in
the frequency. Comparison of Fig. 4 and Fig. 7 shows that
for distilled water, incline measured capacitance is
reduced by reducing the slope of the resistance and the
DF changes.
(11)
2 2
Rm
using Eq. (10) the relative complex permittivity of
water can be obtained from:
r 1/ f
=
(
0 , GF
)
Cm2 − ( DF ) 2 /
2 2
Rm
(12)
where 0 is the relative complex permittivity and f
( 0, GF) is the air capacitance (C0). Using coulomb law the
measured air capacitance is 0.16 pF. Eq. (12) shows, we
can measure precisely the relative complex permittivity
by measuring the capacitance, resistance and dissipation
factor at a known frequency.
RESULTS AND DISCUSSION
In the initial experiment, the capacitance measurement
results of water samples at different frequencies are
presented. The measured capacitance for distilled water at
frequency range 100Hz-2 KHz is shown in Fig. 4.
As can be seen in Fig.4, measured capacitance is
decreased by rising in frequency. The measured
capacitance is 3.84 µF in frequency 100 Hz and is 39.69 nF
in frequency 2 KHz for temperature 17.5°C. Fig. 4 also
shows, the capacitance variation as a function of
frequency is not linear.
Fig. 4: Measured capacitance of distilled water at frequency range 100Hz – 2 KHz
70
Intl. J. Water Resources & Environ Sci.., 2(3): 66-75, 2013
Fig. 5: Measured capacitance of different water at the frequency range 100Hz – 2 KHz
Fig. 6: Repeatability of Measured capacitance for different water in frequency 1 KHz
Fig. 7: Measured resistance and measured DF for distilled water at different frequency
71
Intl. J. Water Resources & Environ Sci.., 2(3): 66-75, 2013
Fig. 8: Measured relative complex permittivity for distilled water as a function of frequency
Fig. 9: Measured resistance of salt water, tap water and mineral water in the frequency range 100Hz – 2 KHz.
where r is the real part, / 0 is the imaginary part of the
relative complex permittivity, is the angular frequency
and is the electrical conductivity of liquid. Eq. (13)
shows the imaginary part of permittivity is decreased by
increasing in frequency. Therefore, it is plausible that the
increase in frequency the relative complex permittivity is
reduced.
In the next study, the measured resistance and the
DF for other water samples are investigated. Fig. 9 shows
the measured resistance of salt water, tap water and
mineral water in the frequency range 100Hz-2 KHz.
The measured resistance for mineral water is 284 , for tap
water is 271 and for salt water is 101 at the frequency
From Eq. (12), the measured relative complex
permittivity as a function of frequency for distilled water
is shown in Fig.8. As can be seen in Fig.8, in the
frequency 500 Hz the measured relative complex
permittivity is 29.41×106 that shows in low frequencies
the distilled water is a good dielectric medium. Fig. 8
furthermore, shows the measured relative complex
permittivity is decreased by increasing in frequency.
The relative complex permittivity r of liquids can be
obtained from:
=
r
r
−j /
0
(13)
72
Intl. J. Water Resources & Environ Sci.., 2(3): 66-75, 2013
Fig. 10: Measured DF of different water liquids in the frequency range 100Hz – 2 KHz
Fig. 11: Measured relative complex permittivity for different water liquids as a function of frequency.
100 Hz. Comparison of the measured resistances in
different frequency shows that the measured resistance
is decreased by rising in the electrical conductivity.
At the frequency 2 KHz the measured resistance for
mineral water is 158 , for tap water is 155 and for salt
water is 37 . The measured DF of different water liquids
in frequency range 100Hz-2 Khz is shown in Fig. 10.
The results of Fig.10 show two important points.
The first point, the measured DF is decreased by
increasing in the electrical conductivity. In the frequency
100 Hz, the measured DF of mineral water with electrical
conductivity 223 µS/cm is 1.092 and for tap water with
electrical conductivity 318 µS/cm is 1.006. The second
point, the measured DF is increased by rising in
frequency.
The measured value of relative complex permittivity
for water samples are shown in Fig.11. As can be seen in
Fig. 11, the measured relative complex permittivity is
decreased by increasing in frequency. The measured
value of permittivity for salt water in the frequency
100 Hz equal 309.8 ×106 and is 160.7×106 in the
frequency 2 Khz. Comparison of the measured results
for water samples show that the relative complex
permittivity
is proportional with the electrical
conductivity in the low frequency. The relative
complex permittivity is increased by rising in the
electrical
conductivity. The measured value of
permittivity for salt water is 190.3 ×106, for tap water equal
120.6 ×106 and for mineral water is 114.1 ×10 6 in the
frequency 1 KHz.
73
Intl. J. Water Resources & Environ Sci.., 2(3): 66-75, 2013
Now it is useful that compare the results of this
study with the researches of other authors. Comparison
of Fig.11 and Fig. 8 shows that the relative complex
permittivity for distilled water, mineral water, tap water
and salt water is decreased by increasing in frequency.
For distilled water in the frequency 1 KHz the measured
value of permittivity equal 6.62 ×106 and for water
reported in the Ref. [1] is 0.5×106. That paper using nonblocking electrodes measured the dielectric permittivity
for different thicknesses of the sample and for various
oscillator levels. The measured dielectric permittivity for
water in the given reference shows reasonable agreement
with our experimental data. As indicated in the Ref. [1]
the dielectric permittivity of water is decreased by
increasing as the frequency, so far as the dielectric
permittivity decreased to 80 at the frequency 915 MHz.
The main reason for this behavior of
dielectric
permittivity related to the imaginary part. In the low
frequency, compare to the imaginary part the real part of
dielectric permittivity is negligible and conversely in the
high frequency the real part is greater than the imaginary
part. The real part of dielectric permittivity for water is 80
and the imaginary part is 4.09 at the frequency 915 MHz.
The results of measured relative complex permittivity
for different water samples show that in the low
frequencies, the dielectric permittivity increased by
rising in the EC of water sample. This behavior of
dielectric permittivity shows that in the low
frequencies in compare to imaginary part the real part
is negligible.
The obtained results show the relative complex
permittivity is decreased by increasing in frequency.
The main reason for this behavior is that the
imaginary part of relative complex permittivity is
decreased by increasing in the frequency. In the high
frequencies, the real part of relative complex
permittivity is important.
ACKNOWLEDGEMENTS
The authors like to acknowledge the support has
given by the Department of physics, East Tehran Branch,
Islamic Azad University.
REFERENCES
1.
Rusiniak, L., 2004. Electric properties of water. New
experimental data in the 5Hz- 13 MHz frequency
range, Acta Geophysica Polonica, 52: 63-76.
2. Fen-chong, T., A. Fabbri, J. Guilbaud and O. Coussy,
2004. Determination of liquid water content and
dielectric constant in porous media by the capacitive
method, Mecanique, 332: 639-645.
3. Wu, S., Q. Zhou, G. Wang, L. Yang and C. Ling, 2010.
The relationship between electrical capacitance-based
dielectric constant and soil water content, Environ
Earth Sci.
4. Jakoby, B. and M. Vellekoop, 2004. Physical sensors
for water-in-oil emulsions, Sens. Actuators A,
110: 28-32.
5. Behzadi, G. and H. Golnabi, 2010. Investigation of
electrical conductivity effects on the capacitance
measurement of water liquids by cylindrical
capacitive sensor, J. Applied Sci., 10: 261-268.
6. Behzadi, G. and H. Golnabi, 2011. Comparison of
invasive and non-invasive cylindrical capacitive
sensors for electrical measurements of different
water solutions and mixtures, Sens. Actuators A.,
167: 359-366.
7. Kaatze, U., 1989. Complex Permittivity of Water as a
Function of Frequency and Temperature, J. Chem.
Eng., 34: 371-374.
8. Barajas, O. and H. Buckmastert, 1992. 9.355 GHz
complex permittivity of water from 1°C to 90°C, J. phy:
Condens. Matter, 4: 8671-8682.
CONCLUSIONS
Capacitive sensors are means that can measure the
physical/chemical parameter through changing in the
capacitance. There are different methods for measuring
the relative complex permittivity, that capacitive method
is one of the most important ones. In this study by a
cylindrical capacitive sensor and LCR meter, the relative
complex permittivity of water samples is investigated.
Main conclusions of this study are:
The auto balancing bridge method and cylindrical
capacitive probe are a precise technique for the
relative permittivity measurement. As the results of
this approach is in good agreement with other
methods.
Eq.12 shows that the exact formula for calculating
the relative complex permittivity.
Results show that the measured capacitance for
distilled water, mineral water, tap water and salt water
is decreased by increasing in the frequency. Also,
the measured capacitance is increased by rising in
the electrical conductivity.
The measured resistance for distilled water with
lowest electrical conductivity is increased by rising
in frequency. Vice versa, for water samples with high
electrical conductivity the measured resistance is
decreased by increasing in frequency.
74
Intl. J. Water Resources & Environ Sci.., 2(3): 66-75, 2013
9.
10.
11.
12.
13.
Mattar, K. and H. Bstckmastert, 1990. 25°C complex
permittivity of water from 65 to 75 GHz, J. Phys. D:
Appl. Phys., 23: 1464-1467.
Liebe, H., G. Hufford and T. Manabe, 1991. A model
for the complex permittivity of water at frequencies
below 1 THz, Int. J. Infrared and Millimeter Waves,
12: 659-675.
Cadeddu, M. and D. Turner, 2011. Evaluation of
water permittivity models from ground-based
observations of cold clouds at frequencies between
23 and 170 GHz, IEEE Transactions on Geosciences
and Remote Sensing, 49: 2999-3008.
Meissner, T. and F. Wentz, 2004. The complex
dielectric constant of pure and sea water from
microwave satellite observations, IEEE Trans.
Geosci. Remote Sens, 42: 1836-1849.
Catenaccio, A., Y. Daruich and C. Magallanes, 2003.
Temperature dependence of the permittivity of
water, Chemical Physics Letters, 367: 669-671.
14. Demori, M., V. Ferrari, D. Strazza and P. Poesio, 2010.
A capacitive sensor system for the analysis of
two-phase flows of oil and conductive water, Sens.
Actuators A., 163: 172-179.
15. Reverter, F., X. Li and G. Meijer, 2007. Liquid-level
measurement system based on a remote Grounded
capacitive sensor, Sens. Actuators A., 138: 1-8.
16. Jaworek, A. and A. Krupa, 2004. Gas/liquid ratio
measurements by rf resonance capacitance sensor,
Sens. Actuators A., 113: 133-139.
17. Technical information at web site: http://
www.gwinstek.com.tw.
18. Agilent Impedance Measurement Handbook. A guide
to measurement technology and techniques, fourth
ed., USA, 2009. http://www.agilent.com.
19. Azimi, P. and H. Golnabi, 2009. Precise formulation of
electrical capacitance for cylindrical capacitive
sensor, J. Applied Sci., 9: 1556-1561.
75