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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. 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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