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Measurements of the electrical parameters for different water samples
Measurement 44 (2011) 2175–2184
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Measurements of the electrical parameters for different water samples H. Golnabi Institute of Water and Energy, Sharif University of Technology, Tehran, Iran
a r t i c l e
i n f o
Article history: Received 21 July 2010 Received in revised form 18 July 2011 Accepted 21 July 2011 Available online 29 July 2011 Keywords: Water Cell probe Electrical conductivity Resistivity
a b s t r a c t The resistance and capacitance values of the water samples are measured by using two different cell probes (length 10 cm and 5 cm) and a measuring module. Measured conductivities for the different water samples are compared where the lowest conductivity is obtained for the distilled water (3.28 lS/cm) and the highest value is for the boiled water 325.91 lS/cm. Using the measured series resistance values, and by knowing the frequency (1 kHz), the imaginary part of permittivity value is also determined. The imaginary part of the permittivity for the distilled water with the long cell probe is about 0.524 107 F/m (for the short probe is 0.523 107 F/m) while for the boiled water sample is the highest value of 53.58 107 F/m (for the short probe is 51.87 107 F/m). Imaginary part of the permittivity factor for the given samples from measurements with the long and short probes are compared. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction Physical and chemical properties of water result from strong attraction that hydrogen atoms have for each other in water molecules. For many applications water solution is grouped into ultra pure, pure, and regular water depending on the percentage of impurities. Although pure water is a poor conductor of electricity, but natural impurities found in water can transform it into a relatively good conductor. Conductivity effects on capacitance measurements of the two-component fluids using the charge transfer method are given [1]. In another study [2] design and performance of a planar capacitive sensor for water content monitoring in a production line are reported. The fundamental conductivity and resistivity of water is described [3]. More details about physical and chemical properties of the water solution can be found [4]. Salts and other contaminates in water can dissociate into components called ions. Ions in water are considered as impurities especially when referring to pure water, while in other aqueous solutions such as sodium hydroxide, the ions define the actual chemical deposition. In general, the electrical conductivity
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of the solution has been one of the important physical quantities in this respect and many probes and devices such as conductive sensors have been devised. Design and performance of a cylindrical capacitive sensor to monitor the electrical properties of different liquids are described by author [5]. In the following work a new method for the simultaneous measurements of the resistance and capacitance of waters using a cylindrical sensor system is introduced [6]. In another study the details of the capacitance sensor systems for measurement of phase volume fraction in two-phase pipelines are given [7]. Another study considers the characterization of a liquid-level measurement system based on a grounded capacitive sensor [8]. A feasibility study of the capacitance method for wetness measurement is reported [9]. In another design consideration, the comparison of the use of internal and external electrodes for the measurement of the capacitance and conductance of fluids in pipes is given [10]. In practice, many probes are used to measure conductivity of the solutions at the given concentration and temperature. Capacitance sensors for measurement of phase volume fraction in two-phase pipelines are discussed [7]. Persson and Haridy [11] have been able to estimate water content from electrical conductivity measurements with the short time-domain reflectometry probes. Capacitor
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sensors can have many applications. Development and applications of different capacitance sensors and measuring systems are reported in recent years. In terms of applications, an automatic liquid level detection method for capillary-gravity viscometer based on capacitance sensors is reported [12]. Development of a capacitive mass measuring system is reported [13] and a study on the soft capacitive sensing weight mechanism is reported [14]. Many attempts have been also made to develop or improve the capacitance measuring circuits. For example, in a report by Chiang et al. [15] a low-cost CMOS integrated sensor transducer implemented as a capacitance-to-frequency converter for capacitive measuring is described. In another report a differential charge-transfer readout circuit for multiple output capacitive sensors is described [16].
On the other hand, if the identical electric field were produced by electrostatic charge, Q, on the two metallic conductors, then by Gauss’ law (assuming very long conductors) we can write
2. Electrical conduction
which, is a relation between the equivalent resistance of the medium and the effective capacitance of the electrostatic problem. It is also evident that the quantity e/g has the time dimension and it is called the time constant or relaxation time, tc, of the medium, so one can write
Consider a homogeneous, isotropic medium characterized by conductivity g and permittivity e. Steady-state conduction problem may be solved in the same way as electrostatic Laplace’s equation. Consider two separate metallic conductors in a homogeneous, isotropic, and ohmic medium of moderate conductivity, g, like a salt solution. If the metallic conductors are maintained at the potentials U1 and U2, then the current flow, I, between two electrodes is given by
I¼
U1 U2 ; R
ð1Þ
where R is the resistance of the medium. Such a current may be considered as the steady-state current in a medium without a source of electromotive force. Now consider the produced electric current in the inhomogeneous medium. Let us consider a conduction object composed of ohmic material, but which is not necessarily as before homogenous, so that the conductivity g is independent of the local electric field but vary from point to point in the medium. For this case instead of a constant conductivity factor, g, we must consider g(x, y, z). Suppose two points on the boundary of the conducting object are maintained at the potentials U1 and U2, respectively. The current lines for such a medium from Ohm’s law follow those of the local electric field (J = gE), and the equipotential surfaces intersects the current lines at right angles are not necessarily parallel to each other for this medium. In this case actually we can consider a large resistance network constructed from many elemental resistors Ri in the shape of short wire segments. According to the resistance formula for a resistor we have
‘i Ri ¼ ; g i Ai
ð2Þ
where gi(x, y, z) is the local conductivity, Ai is the cross-sectional area of the segment, and ‘i is the distance between the equipotential surfaces. In the limiting case where the number of the equipotential surfaces between U1 and U2 becomes very large and the number of elemental resistors becomes correspondingly large, the resistors Ri fill the entire space occupied by the conducting object. Thus such a network has an equivalent resistance R that can be considered in Eq. (1).
I
E n da ¼
S
Q
e
ð3Þ
;
where e is the permittivity of the medium, and in this condition two conductors form a capacitor with the charge value of
Q ¼ CðU 1 U 2 Þ;
ð4Þ
and by insertion of Eqs. (6) and (5) into (4) we can write
e
RC ¼ ; g
tc ¼
e g
ð5Þ
¼ eq;
ð6Þ
where q is defined as resistivity of the medium (X m). Time constant is measure of how fast the conducting medium approaches the electrostatic equilibrium; precisely, it is the time required for the charge in a specific region to decrease to 1/e of its original value. A material will reach its equilibrium charge distribution in a specific application when its time constant is much shorter than the characteristic time required to make the pertinent measurement. For some applications a time constant of less than 0.1 s is sufficient to ensure conductorlike behavior; since most permittivities fall into the range e0– 10e0, this require a material with resistivity q less than 109 or 1010 ohm-m. For high-frequency applications a shorter time constant, and a correspondingly smaller resistivity, is required for the true conductorlike behavior. In fact
tc
1 ; f
ð7Þ
must be satisfied in which f is the highest frequency involved in the experiment. In general the complex permittivity of a medium can be written as
g
e ¼ e0 je00 ¼ e0 j ; x
ð8Þ
where e0 is the real, e00 is the imaginary part of the permittivity and x = 2pf. The condition for a good conductor medium is that the imaginary part to be much larger than the real part, i.e.
g 2
e0 x
1;
ð9Þ
where g is the conductivity. For a good dielectric medium the given ratio must be much less than unity. For the metallic conductive materials the conductivity is high
H. Golnabi / Measurement 44 (2011) 2175–2184
(for copper 5.88 107 mho/m or S/m) while for the good dielectric medium the permittivity is high (for a pure distilled water is about 80e0). Generally water molecules are in continuous motion, even at low temperatures and when two water molecules collide, a hydrogen ion is transferred from one molecule to the other. The other molecule that losses the hydrogen ion becomes negatively charged hydroxide ion. The molecule that gains the hydrogen ion becomes a positively charged hydrogen ion and this process is commonly called the self-ionization of water. In fact at room temperature (25 °C), each concentration of hydrogen ions and hydroxide ions is only of the order of 1 107 M, and as a result this dissociation allows a minute electrical current to flow. The current flow is in the range of conductivity of 0.05 lS/ cm at room temperature. It is important to note that the amount of (H)+ and (OH) ions are approximately equal and this solution is described as a neutral solution. In other aqueous solutions, the relative concentrations of these ions are unequal and one ion is increased by one order of magnitude while the other one shows some decrease, but the relationship is constant and the ion product is always constant given by Kw, which is called the ionproduct constant for water. Water is a polar solvent with an uneven distribution of electron, and the application of electric field causes one portion of the molecule to be somewhat positive and another part negative (polarization effect). In an external DC electric field, the dissolved electrolyte substances are free to move and positive charged particles move towards negative electrode while negative charged particles migrate toward the positive electrode. The migration of the charged particles causes the electric current flow in liquid. Such DC polarization can be eliminated by using AC voltage at 60 Hz or higher frequencies and in practice by increasing the cross sectional area of the electrodes. The mechanism of electrical conduction through a liquid is different in comparison with a solid. In solid, when a potential is applied to a solid conductor, the flow of current is instantaneous, and is virtually proportional to the applied potential. In addition, different types of materials conduct electrical charges with different efficiencies. In metals, there are free electrons, which are available for conduction even at a very low temperature. One major difference of a metal with semiconductor and isolator materials is that metal resistance increases as the metal heated because of the decrease in electron mobility. Conversely, the resistance of semiconductors and insulators decreases with increasing temperature because the number of charge carries increases. Therefore, in semiconductor and in particular in insulators, more activation energy is needed to excite electrons to be available to conduct a charge. The conductivity of a solution relates to the total dissolved solid (TDS) and amount of the suspended solids (SS) or insolvable solids in a water sample. Total dissolved solid includes solid particulates such as ions, inorganic substances, salts, and metals. Total solid (TS) is defined as the sum of TDS and SS. In laboratory analysis measurement of these parameters are made by filtering and weighing to determine SS, then drying and weighing to determine TDS. In analysis of water the conductivity
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measurements are classified for the ultra-pure, high-purity and pure water samples, which show accordingly an increase in the conductivity value from 0.053 lS/cm to 10 lS/cm.
3. Experimental arrangement Our experimental system as shown in Fig. 1 includes a sensing cylindrical probe and a measuring module. Fig. 2 shows the block diagram for the two tested cell probes with different effective lengths of 100 mm and 50 mm, respectively. A temperature senor is also used for the temperature monitoring of the liquid sample in the cell. The measuring modules are a LCR (Yuke-816, Good Will Instrument, Gw Instek) meter and a 4-wire test clip as shown in Fig. 1. Two measurement leads as indicated in Fig. 1; are connected to the inner electrode and outer electrode, respectively. Measuring instrument specified as LCR-816 2 kHz high precision LCR meter and a LCR-06A measuring probe [17]. 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 (Kelvin clip). The LCR module operates based on the automatic balanced bridge circuit in which the impedance can be determined for the resistance and reactance values. For the case of capacitance measurement; capacitive reactance (XC) and for the inductance measurement the inductive reactance (XL) are measured and displayed. Reactance (X) measures the imaginary part of impedance (Z), and is caused by capacitors or inductors and admittance is the reciprocal of the reactance, Y = 1/Z. In general, capacitance measures the amount of electronic charge stored between two electrodes of a capacitor. The resistance of the medium to the flow of current as a result of applied voltage; is considered as the resistance factor, R. Conductance, G, is the potential of the flow of the electricity in a medium and is given as the inverse of the medium resistance. Impedance that is neither a pure resistance nor a pure reactance can be represented at any specific frequency by either a series or a parallel combination of resistance and reactance as shown in Fig. 3. Such representation is called the Equivalent Circuit (EC) for the probe. In Fig. 3a the Series Equivalent Circuit (SEC) is shown where Rs, and Cs show
Fig. 1. Block diagram for the measurement system.
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4 mm
(a) 5 mm
Gap (Plexiglass)
Filling Gap
100 mm
Outer Electrode (Aluminum)
Main Electrode Lead 10mm
8mm 18mm 24mm 44 mm
Plexiglas s Base Inner Electrode (Aluminum)
4mm
(b) 5mm
Cap (Plexiglass)
Filling Gap
50 mm Outer Electrode (Aluminum)
Main Electrode Lead
10mm
8mm 18mm 24mm 44 mm
Plexiglas s Base Inner Electrode (Aluminum)
Fig. 2. Block diagram for the two tested cylindrical probes. (a) Long probe with an effective length of 100 mm, and (b) short probe with the length of 50 mm.
the series resistance and capacitance parameters. Fig. 2b shows the Parallel Equivalent Circuit (PEC) whereas Rp, and Cp respectively show the parallel resistance and capacitance parameters. Depending on the function selection; series capacitance (Cs) and parallel capacitance (Cp) can be measured by the LCR module. Resistance can be also obtained from the series resistance (Rs) or parallel (Rp) in
diagrams shown in Fig. 3. The component of the primary display of the LCR module depends on which equivalent circuit (EC) is chosen. In normal condition, the component manufacturers specify how a component is to be measured (usually series) and at what frequency. Normally for low value of inductance (<10 lH, SEC method) and capacitance (<10 pF, PEC method) and high measurement frequency of
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4. Measurement results
Fig. 3. Circuit diagram for the probe under study. (a) Equivalent series circuit, and (b) equivalent parallel circuit.
the order of (100 kHz) are recommended. For measuring resistors lower than 1 kX, SEC method and high frequency (1 kHz) are suggested. Four combinations of two parameters can be measured and displayed that could be parameters L (Inductance) and Q (quality factor), C (capacitance) and D (dissipation factor is inverse of quality factor), C and R (resistance) or R and Q. Usually determination of C and R pairs is the goal in our experimental measurements. In this configuration meter displays the C, R and measurements can be performed in either series or parallel equivalent circuit. The accuracy for C and R measurements is about 0.05% (basic) plus another error term that is defined from a given formula [17]. For the cell probe a cylindrical geometry as shown in Fig. 2 is chosen and aluminum materials are used as the capacitor tube electrodes. The diameter of the inner electrode is about 18 mm and the inner diameter of the outer electrode is about 24 mm and has an overall diameter of about 44 mm. Two cell probes are constructed with the similar structures with the effective length of 100 mm and 50 mm, which are referred to as the long and short probes, respectively. The radial gap between the two tube electrodes for filling medium is about 3 mm. The cylindrical gap volume measured when filled with water for the long sensor (10 cm-length) is 20 cc and for the short one (5 cm-length) is 10 cc. The distilled water used in this experiment is produced by an apparatus operating based on the heating and boiling/condensation technique. The mineral water is purchased as bottled water and normally same brand from the single producing company is used. Tested tap water is the regular refined drinkable municipal city (Tehran) water, and the boiled water is the tap sample type boiled, similar to the water sample types used for the tea or coffee making. Salt water solutions are prepared by dissolving small amount of the regular grade salt in distilled water. To analyze the electrical condition of the tested water liquids, another device is used to measure the electrical conductivity (EC) and the total dissolved solid (TDS) density of the water samples in this experiment. The EC of different water liquids measured using conductive meter (Sension5). The conductive meter is a contacting style conductivity sensor in which its plane electrodes are in direct contact with the solution being measured. It provides functions for EC and TDS measurements at a test temperature. Electrical conductivity values in the range of near zero to199.9 mS/cm can be measured with a resolution of about 0.1 lS/cm and TDS in the range of near zero to 50,000 mg/L can be measured with a resolution of about 0.1 mg/L. The specified accuracy of the Sension5 device for EC is about ±0.5% of the full range and for TDS is about ±5% of the full scale range.
In experimental measurements, the resistance and capacitance of different water samples are measured simultaneously at a fixed temperature and a test frequency of 1 kHz using either the long or short cell probe. Table 1 shows the electrical parameters obtained with the long sensor and Table 2 indicates the same parameters measured with the short cell probe. In these tables subscript, s, shows the series, p the parallel values, and factor D shows the dissipation factor measured for the effect of the resistance energy loss in the capacitance measurements. The test samples are (DW), mineral water (MW), tap water (TW), boiled water (BW), dilute salt water solution (SW1), and finally salt water solution (SW2). As can be seen in Table 1, among all samples the DW shows the highest value of D (55.1) and on the other hand SW2 shows the lowest dissipation factor D (0.44). As can be seen in Table 2, a similar behavior for factor D is observed for the short cell probe (compare 57.1 for DW with 0.43 for SW2). The high value of dissipation factor D for DW indicates the high degree of the resistivity of this sample in the equivalent circuit measurements. As can be seen in Tables 1 and 2 the factor D is decreased for the given samples and salt water solution (SW2) shows the lowest D factor of 0.43 and as a results the highest conductance. A careful look at Tables 1 and 2 shows that the capacitance value is about twice for the long probe in comparison with the short probe. For the series resistance values the situation is reversed and the resistance values for the long probe are almost half of the short probe values. The measured capacitance values for the two probes are compared in Fig. 4. Different samples including distilled water (DW) mineral water (MW), tap water (TW), and boiled water (BW), dilute salt water (SW1), and salt water (SW2) samples are considered for this investigation. As can be noticed in Fig. 4, DW sample shows a low series capacitance value of 6.3 lF (3.3 lF for the short probe) and the salt water shows the highest value of 32 lF (14.6 lF for the short probe). In general for all the tested samples the series capacitance is higher for the long probe in comparison with that of the short probe. The actual active length of the long probe (10 cm) is twice of the short probe (5 cm) and considering results a factor of about 2 is observed in the capacitance ratio results for the two probes. In Fig. 5 the measured series resistance values for the two probes are compared. Different tested samples are as before distilled (DW) mineral water (MW), tap water (TW), and boiled water (BW), dilute salt water (SW1),
Table 1 Electrical parameters obtained with the long cell probe. Sample
Rs (X)
Rp (X)
Cs (lF)
Cp (lF)
D
DW MW TW BW SW1 SW2
1389 21 15 13.6 3.5 2.2
1390 23.1 17.7 16.3 11.1 13.4
6.3 23.53 25 26.15 30.83 32.02
0.002083 2.21 3.8 4.36 21.11 26.7
55.1 3.1 2.3 2.2 0.67 0.44
s: Series equivalent circuit, p: Parallel equivalent circuit.
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Table 2 Electrical parameters obtained with the short cell probe. Sample
Rs (X)
Rp (X)
Cs (lF)
Cp (lF)
D
DW MW TW BW SW1 SW2
2788 42.1 30.1 28.1 7.1 4.6
2788.9 46.7 35.9 33.8 24.2 95.6
3.32 11.35 11.96 12.47 14.43 14.8
0.000981 1.13 1.95 2.13 10.20 12.5
57.1 3.0 2.3 2.2 0.64 0.43
s: Series equivalent circuit, p: Parallel equivalent circuit.
Fig. 6. Comparison of the series and parallel resistances of samples for the long probe.
Fig. 4. Comparison of the electrical capacitances of samples for two probes.
Fig. 5. Comparison of the electrical resistances of samples for two probes.
and salt water (SW2). As indicated in the inset of Fig. 5, for presentation of all the results for the series resistance in one figure, the measured value of DW is divided by ten to be comparable with the other results. As can be seen in Fig. 5, result for the DW sample shows the highest series
resistance value of 2788 X (1389 X for the short probe) and the salt water (SW2) shows the lowest value of 2.2 X (4.6 X for the short probe). In general for the long probe measurement the series resistance is higher for the DW in comparison with those of the other samples. Same behavior is observed for the short cell probe measurements. In comparing the results of the short and long probe it is noted that the series resistance values for the long probe for the related samples is almost half of those of the short probe. The actual active length of the long probe (10 cm) is twice of the short probe (5 cm) and considering results a factor of about 1/2 is observed in the series resistance ratio results for the two probes. Fig. 6 shows a comparison of the series and parallel resistances of the tested samples for the long probe. As indicated in Fig. 6, for presentation of all the results for the resistance values in one figure, the measured value of DW is divided by ten to be comparable with the other results. As usual tested samples are the distilled water (DW) mineral water (MW), tap water (TW), boiled water (BW), dilute salt water (SW1), and salt water (SW2). As can be seen in Fig. 6, for the distilled water sample the value of the measured series resistance is 1389 X while for the parallel resistance is 1407 X. For the case of the distilled water sample the relative deviation is about 1.27%. For the next sample such a deviation is increased, and finally for the SW2 such a deviation is the maximum value of 83.58% (compare series resistance 2.2 X with parallel 13.4 X). The result of this study is the important point that for the DW both the series and parallel EC methods can be used, however for other samples, in particular, salt water electrolyte solution one must be careful in choosing the measuring method for a correct resistance measurement. In Fig. 7 a comparison of the series and parallel resistances of the tested samples for the short probe is shown. Tested samples as before are distilled water (DW) mineral water (MW), tap water (TW), boiled water (BW), dilute salt water (SW1), and salt water (SW2). As shown in the inset of Fig. 7, for presentation of all the results for the resistance
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in one figure, the measured value of DW is divided by a factor of ten to be comparable with the other results. As can be seen in Fig. 7, for the distilled water sample the series resistance is 2788 X while for the parallel resistance is 2788.9 X. For this case the relative deviation is about 0.032%. For the next sample such a deviation is increased, and finally for the SW2 such a deviation is the maximum value of 95.18% (compare series resistance 4.6 X with parallel 95.6 X). Similar to the case of the long probe, the result of this study leads to the fact that for the DW both the series and parallel EC schemes can be used, however for other samples, in particular, salt water electrolyte solution one must be careful in the selection of the correct method of the resistance measurement. Considering the previous finding that the series method gives precise results for the water samples in the next
Fig. 7. Comparison of the series and parallel resistances of samples for the short probe.
studies only electrical parameters are derived for such samples. In the next investigation the electrical conductivities of different water liquids are determined from the measured series resistance value Rs for the long cell probe. The results for different water samples are listed in Table 3. As described before for all the water samples both the SEC and PEC provide reliable results. Therefore in this section a more precise measurements are reported for such samples. From the series resistance value the resistivity for the cylindrical probe is determined from the relation
q ¼ 2pRL=Lnðb=aÞ;
ð10Þ
where L is the cell length, b the radius of the outer cylinder and, a, is the radius of the inner electrode. From given series resistivity the electrical conductance is obtained from
g 0 ¼ 1=q;
ð11Þ
and listed in Table 3. Using the EC meter the electrical conductivity for the sample samples are also measured and given in Table 3. As can be seen in Table 3, the resistance value is the highest for distilled water (1389 X) and the lowest for the boiled water sample, which is about 13.6 X. Correspondingly, the resistivity parameter is decreasing in the same order while for the DW is about 3033.41 X m and for BW is decreased to about 29.7 X m. The conductivity determined form Rs measurements of different samples is obtained and compared with the ones measured in Table 3. For a better comparison the relative errors as result of the direct measurements with EC meter and the one obtained with the cell probe are indicated in the last column of the Table 3. As can be seen in Table 3, the relative error for two measurement methods is at maximum about 4.0% that is acceptable for such measurements. In a similar method, the electrical conductivities of the same liquid samples are determined from the related measured series resistance value Rs for the short cell probe. The results of electrical parameters for different water samples are listed in Table 4 for the short probe. As can
Table 3 Electrical conductivities obtained with the long cell probe. Water sample
Rs (O) T = 15 °C
q (X m) T = 15 °C
g´ (lS/cm) probe T = 15 °C
g (lS/cm) EC T = 20.6 °C
Relative error (g g´)/g (%)
Distilled Mineral Tap Boiled
1389 21 15 13.6
3033.41 45.86 32.76 29.70
3.30 218.05 305.27 336.69
3.41 223 318 341
3.3 2.2 4.0 1.3
g: Conductivity with EC meter, g´: Conductivity with cell probe.
Table 4 Electrical conductivities obtained with the short cell probe.
Water sample
Rs (O) T = 15 °C
q (X m) T = 15 °C
g´ (lS/cm) probe T = 15 °C
g (lS/cm) EC T = 20.6 °C
Relative error (g g´)/g (%)
Distilled Mineral Tap Boiled
2788 42.1 30.1 28.1
3044.33 45.97 32.87 30.68
3.28 217.53 304.25 325.91
3.41 223 318 341
3.7 2.5 4.3 4.4
g: Conductivity with EC meter, g´: Conductivity with cell probe.
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be seen in Table 4, the resistance value is the highest for distilled water (2788 X) and lowest for the boiled water sample, which is about 28.1 X. The resistivity parameter is decreasing in the same order while for the DW is about 3044.33 X m and for BW is decreased to about 30.68 X m. Comparison of the Tables 3 and 4 reveals two important points. First, as expected the measured resistance values are different for the long and short probes while the resistivity of the water samples is independent of the length of the cylindrical probe and very similar for the two probes. For example for the mineral water sample resistivity for the long probe measurement is 45.86 X m and for the short probe is 45.97 X m. Second, and perhaps the most important one, is that there is a good agreement between the results obtained with the cell probe and those of the EC meter. For instance compare the conductivity results for the mineral water in which the relative deviation is about 2.5%. Such small deviation is because measurements are not exactly at the same sample temperature. For the water samples the conductivity parameter results derived from the experimental measurements are shown in Fig. 8. As can be seen from data labels on the graph bars this factor for the long probe for DW is the lowest value of 3.30 lS/cm while for the short probe cell correspondingly is 2.28 lS/cm. For both probes the conductivity factor is increased for the tested samples and for the MW is 218.05 (for short probe 217.53 lS/cm), for the TW is 305.27 lS/cm (for short probe 304.25 lS/cm) and for the BW is 336.69 lS/cm (for short probe 325.91 lS/cm). Considering the results for the long and short probes it is noted that such a parameter depends on the sample type and hence independent of the probe cell length. As a result, a good agreement is observed for the conductivity values derived from the measurements performed with two cell probes. In the next study permittivity is determined from the conductivity, g, as determined in the previous section. From Maxwell’s equation we can write
r H ¼ jxeE þ J;
ð12Þ
where the current density is related to electric field by Ohm’s law
J ¼ gE:
ð13Þ
By plugging Eq. (13) into Eq. (12) we can write
r H ¼ ðg þ jxeÞE ¼ jxe er j
g
xe
E ¼ jxe ~er E;
ð14Þ
and by defining the relative permittivity one can write
~er ¼ er j
g
xe
ð15Þ
;
and in the closed form as
~er ¼ e0 je00 ;
ð16Þ
where permittivity includes the real imaginary part. By using Eq. (15) the imaginary part of the permittivity is determined and the results for different tested samples are listed in Table 5. The relative imaginary part is shown and in the last column the imaginary part of the permittivity is listed. In Table 6 for the short probe different parameters similar to those of the long probe are listed. Similar to result of ´, is the lowest for the distilled Table 5, the conductivity, g water (3.28 lS/cm) and the highest value for the boiled water sample, which is about 325.91 ls/cm. To compare conductivity for the long and short probe let us compare the results for the mineral water. The mineral water conductivity for the long probe is 218.05 ls/cm while for the short probe is 217.53 ls/cm, which is similar to that of long probe. This agreement indicates that the conductivity just depends on water type and is independent of the cell length. In a similar way in Table 6, the relative imaginary part for the short cell probe is shown and in the last column the imaginary part of the permittivity is given. As can be seen in Table 6, the imaginary part, which is related to the conductance factor of the sample, is increasing respectively for indicated samples.
Table 5 Imaginary permittivity obtained with the long cell probe. Water sample
Rs (O) T = 15 °C
g´(lS/cm) T = 15 °C
e00r (Im)
Distilled Mineral Tap Boiled
1389 21 15 13.6
3.30 218.05 305.27 336.69
5928.505931 392128.3209 548979.6492 605492.2602
e00 (Im) 107 (F/m) 0.524 34.703 48.584 53.586
g´: Conductivity with long cell probe.
Table 6 Imaginary permittivity obtained with the short cell probe.
Fig. 8. Obtained electrical conductivities for the long and short probes.
Water sample
Rs (O) T = 15 °C
´ (lS/cm) g T = 15 °C
e00r (Im)
Distilled Mineral Tap Boiled
2788 42.1 30.1 28.1
3.28 217.53 304.25 325.91
5907.241562 391196.8997 547155.7966 586099.2696
g´: Conductivity with short cell probe.
e} (Im) 107 (F/m) 0.523 34.621 48.423 51.870
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As indicated in that report the thickness of the water sample and the applied oscillator voltage level affect the measured electrical parameters. For the reported measurement the dielectric permittivity is given for the sample thickness of 3.93 mm and the applied oscillator voltage of 1 V. However, as indicated [18,19], the permittivity of the sample depends on the test frequency, which is 1 kHz in our measurements. From [19] a typical value of permittivity is reported for the pure water sample. Comparing our results with the given value the observed deviation in permittivity is because of the higher impurity and conductance effect of our tested samples. Considering the results shown in Fig. 9 and by comparing the results listed in Tables 5 and 6 it is noticed that the imaginary part results obtained with the long and short probes are almost similar which, leads to the fact that the imaginary part of the permittivity is independent of the cell probe length. Fig. 9. Comparison of the imaginary part of the electrical permittivity for the long and short probes.
As a last study in Fig. 9 for different water samples the imaginary permittivity parameter results derived from the experimental measurements are plotted. As can be seen in Fig. 9, from data labels on the graph bars this factor for the long probe for DW is the lowest value of 0.524 107 F/m while for the short probe cell is 0.523 107 F/m. For both probes the permittivity factor is increased for the tested samples and for the MW is 34.703 107 F/m (for short probe 34.621 107 F/m), for the TW is 48.584 107 F/m (for short probe 48.423 107 F/m) and for the BW is 53.586 107 F/m (for short probe 51.87 107 F/m). Considering the results for the long and short probes it is noticed that such the imaginary part of the permittivity only depends on the sample type and hence independent of the probe cell length. As a result, a good agreement is observed for the conductivity values derived from the measurements performed with both probes. Considering the permittivity factor of the free space, which is e0 = 8.85 1012 F/m, and for pure dielectric water that is about 80e0 (compare 0.00708 107 F/m with 0.523 107 F/m) the imaginary part of the permittivity component is the dominating factor. This is as a result of the high conductivity effect observed for the tested water samples in this investigation. In 2004, the electrical properties of water for the frequency range of 5 Hz–13 MHz is reported by Rusiniak [18,19] using a non-invasive cell probe arrangement. The dielectric permittivity, conductivity, and dissipation factor have been measured for the temperature range of 20–90 °C for the distilled water. Considering data given in that report the relative permittivity of about 1000 and conductance value of 6 104 S (see Fig. 2 of [19]) is reported at 1 kHz and room temperature (20 °C). Comparing the given results [19], and our results it is concluded that in the invasive arrangement most of the contribution is due to the imaginary part of the permittivity, which is in the order of 5928.5 (for the short probe 5907.2) for our case. Comparing the relative permittivity it is noted that at such a frequency and temperature the imaginary part is higher with respect to the dielectric one by a factor of about 5.9.
5. Concluding remarks By implementing the equivalent circuit method; electrical parameters for different water samples are measured, by using the long and short cell probes. Variations of the series and parallel capacitance values as well as resistance, and the dissipation factor are given for different water samples. In another measurement the electrical conductivity of different samples are measured by an EC meter and also the cell probes. Imaginary part of the permittivity is determined at frequency of 1 kHz from electrical conductivity results for different water samples. Concluding outlines of the reported measurements are as follows: (a) The series equivalent circuit is a proper method to investigate the resistance and capacitance of the water samples. The series resistance value is highest for DW and the lowest for the BW. (b) Application of two cell probes with different cylindrical length shows the series capacitance and resistance values depend on the cell length. Our results show that capacitance is directly increased by increasing the length and resistance is inversely proportional to the cell length. (c) Electrical conductivities for different water samples are determined here from the experimental measurements using the long and short cell probes. Obtained conductivities for the different water samples are compared where the lowest conductivity is obtained for the distilled water and the highest one for the boiled water. Obtained conductivities with the cell probes are compared with the EC device results and a good agreement is observed. (d) From conductivity and test frequency the imaginary part of the permittivity is obtained for different water samples. For both probes the permittivity factor is increased for the tested samples and for the DW is lowest and for the BW the highest. (e) Considering the conductivity and the permittivity results for the long and short probes it is noticed that such parameters only depends on the sample type and hence independent of the cell probe length.
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(f) Imaginary part of the permittivity is much higher than the real part, thus the reported method is a very effective way to study the electrical conductivity of different water samples and dilute electrolytes. (g) Our results show that the reported method can be effectively used to study the electrical parameters of different water samples and dilute electrolytes.
Acknowledgments This work was supported in part by the Sharif University of Technology research program. The author gratefully acknowledges the grant devoted to this research. References [1] S.M. Huang, R.G. Green, A.B. Plaskowski, M.S. Beck, Conductivity effects on capacitance measurements of two-component fluids using the charge transfer method, J. Phys. E: Sci. Instrum. 21 (1988) 539– 548. [2] E.D. Tsamis, J.N. Avaritsiotis, Design of a planar capacitive type senor for water content monitoring in a production line, Sens. Actuat. A 118 (2005) 202–211. [3] T.S. Light, S. Licht, A.C. Bevilacqua, K.R. Morash, The Fundamental conductivity and resistivity of water, Solid-State Lett. 8 (2005) E16– E19. [4] R.C. Weast, Handbook of Chemistry and Physics, 60 th ed., CRC Press, 1981. p. E-61. [5] H. Golnabi, P. Azimi, Design and performance of a cylindrical capacitive sensor to monitor the electrical properties, J. Appl. Sci. 8 (2008) 1699–1705. [6] H. Golnabi, P. Azimi, Simultaneous measurements of the resistance and capacitance using a cylindrical sensor system, Mod. Phys. Lett. B 22 (2008) 595–610.
[7] C.N. Strizzolo, J. Cinverti, Capacitance sensors for measurement of phase volume fraction in two-phase pipelines, IEEE Trans. Instrum. Meas. 42 (1993) 726–729. [8] F. Reverter, X. Li, G.C.M. Meijer, Characterisation of a liquid-level measurement system based on a grounded capacitive sensor, in: Proceedings of Electronics, 2006, pp. 20–22. [9] F.-X. Niu, X.-S. Cai, J.-Q. Shen, Feasibility study of the capacitance method for wetness measurement, in: Zhongguo Dianji Gongcheng Xuebao, Proceedings of the Chinese Society of Electrical Engineering, vol. 29, 2009, pp. 27–32. [10] A.L. Stott, R.G. Green, K. Seraji, Comparison of the use of internal and external electrodes for the measurement of the capacitance and conductance of fluids in pipes, J. Phys. E: Sci. Instrum. 18 (1985) 587–592. [11] M. Persson, S. Haridy, Estimating water content from electrical conductivity measurements with short time-domain reflectometry probes, Soil. Sci. Soc. 67 (2003) 478–482. [12] Y. Wu, Z. Teng, H. Lin, H. Chi, Automatic liquid level detection method for capillary-gravity viscometer based on capacitance sensors, Chinese J. Sen. Actuat. 22 (2009) 1061–1065. [13] A. Abu-Al-Aish, M. Rehman, Development of a capacitive mass measuring system, Sen. Actuat. A 151 (2009) 113–117. [14] L. Cheng, H.-J. Zhang, Q. Li, P.-H. Chen, Study on the soft capacitive sensing weight mechanism, Chinese J. Sen. Actuat. 19 (2006) 2388– 2390. [15] C.-T. Chiang, C.-S. Wang, Y.-C. Huang, A low-cost CMOS integrated sensor transducer implemented as a capacitance-to-frequency converter for capacitive measuring, in: Proceedings of IEEE Instrumentation and Measurement Technology Conference, 2007, art. no. 4258153. [16] H. Rodjegard, A. Loof, A differential charge-transfer readout circuit for multiple output capacitive sensors, Sens. Actuat. A 119 (2005) 309–315. [17] Technical information at web site: http://www.gwinstek.com.tw. [18] L. Rusiniak, Dielectric properties and structure of water at room temperature. New experimental data in the 5 Hz–13 MHz frequency range, Phys. Chem. Earth A 25 (2000) 201–207. [19] L. Rusiniak, Electric properties of water. New experimental data in the 5 Hz–13 MHz frequency range, Acta Geophysica Polonica 52 (2004) 63–76.
Contents lists available at SciVerse ScienceDirect
Measurement journal homepage: www.elsevier.com/locate/measurement
Measurements of the electrical parameters for different water samples H. Golnabi Institute of Water and Energy, Sharif University of Technology, Tehran, Iran
a r t i c l e
i n f o
Article history: Received 21 July 2010 Received in revised form 18 July 2011 Accepted 21 July 2011 Available online 29 July 2011 Keywords: Water Cell probe Electrical conductivity Resistivity
a b s t r a c t The resistance and capacitance values of the water samples are measured by using two different cell probes (length 10 cm and 5 cm) and a measuring module. Measured conductivities for the different water samples are compared where the lowest conductivity is obtained for the distilled water (3.28 lS/cm) and the highest value is for the boiled water 325.91 lS/cm. Using the measured series resistance values, and by knowing the frequency (1 kHz), the imaginary part of permittivity value is also determined. The imaginary part of the permittivity for the distilled water with the long cell probe is about 0.524 107 F/m (for the short probe is 0.523 107 F/m) while for the boiled water sample is the highest value of 53.58 107 F/m (for the short probe is 51.87 107 F/m). Imaginary part of the permittivity factor for the given samples from measurements with the long and short probes are compared. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction Physical and chemical properties of water result from strong attraction that hydrogen atoms have for each other in water molecules. For many applications water solution is grouped into ultra pure, pure, and regular water depending on the percentage of impurities. Although pure water is a poor conductor of electricity, but natural impurities found in water can transform it into a relatively good conductor. Conductivity effects on capacitance measurements of the two-component fluids using the charge transfer method are given [1]. In another study [2] design and performance of a planar capacitive sensor for water content monitoring in a production line are reported. The fundamental conductivity and resistivity of water is described [3]. More details about physical and chemical properties of the water solution can be found [4]. Salts and other contaminates in water can dissociate into components called ions. Ions in water are considered as impurities especially when referring to pure water, while in other aqueous solutions such as sodium hydroxide, the ions define the actual chemical deposition. In general, the electrical conductivity
E-mail address: [email protected] 0263-2241/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.measurement.2011.07.017
of the solution has been one of the important physical quantities in this respect and many probes and devices such as conductive sensors have been devised. Design and performance of a cylindrical capacitive sensor to monitor the electrical properties of different liquids are described by author [5]. In the following work a new method for the simultaneous measurements of the resistance and capacitance of waters using a cylindrical sensor system is introduced [6]. In another study the details of the capacitance sensor systems for measurement of phase volume fraction in two-phase pipelines are given [7]. Another study considers the characterization of a liquid-level measurement system based on a grounded capacitive sensor [8]. A feasibility study of the capacitance method for wetness measurement is reported [9]. In another design consideration, the comparison of the use of internal and external electrodes for the measurement of the capacitance and conductance of fluids in pipes is given [10]. In practice, many probes are used to measure conductivity of the solutions at the given concentration and temperature. Capacitance sensors for measurement of phase volume fraction in two-phase pipelines are discussed [7]. Persson and Haridy [11] have been able to estimate water content from electrical conductivity measurements with the short time-domain reflectometry probes. Capacitor
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sensors can have many applications. Development and applications of different capacitance sensors and measuring systems are reported in recent years. In terms of applications, an automatic liquid level detection method for capillary-gravity viscometer based on capacitance sensors is reported [12]. Development of a capacitive mass measuring system is reported [13] and a study on the soft capacitive sensing weight mechanism is reported [14]. Many attempts have been also made to develop or improve the capacitance measuring circuits. For example, in a report by Chiang et al. [15] a low-cost CMOS integrated sensor transducer implemented as a capacitance-to-frequency converter for capacitive measuring is described. In another report a differential charge-transfer readout circuit for multiple output capacitive sensors is described [16].
On the other hand, if the identical electric field were produced by electrostatic charge, Q, on the two metallic conductors, then by Gauss’ law (assuming very long conductors) we can write
2. Electrical conduction
which, is a relation between the equivalent resistance of the medium and the effective capacitance of the electrostatic problem. It is also evident that the quantity e/g has the time dimension and it is called the time constant or relaxation time, tc, of the medium, so one can write
Consider a homogeneous, isotropic medium characterized by conductivity g and permittivity e. Steady-state conduction problem may be solved in the same way as electrostatic Laplace’s equation. Consider two separate metallic conductors in a homogeneous, isotropic, and ohmic medium of moderate conductivity, g, like a salt solution. If the metallic conductors are maintained at the potentials U1 and U2, then the current flow, I, between two electrodes is given by
I¼
U1 U2 ; R
ð1Þ
where R is the resistance of the medium. Such a current may be considered as the steady-state current in a medium without a source of electromotive force. Now consider the produced electric current in the inhomogeneous medium. Let us consider a conduction object composed of ohmic material, but which is not necessarily as before homogenous, so that the conductivity g is independent of the local electric field but vary from point to point in the medium. For this case instead of a constant conductivity factor, g, we must consider g(x, y, z). Suppose two points on the boundary of the conducting object are maintained at the potentials U1 and U2, respectively. The current lines for such a medium from Ohm’s law follow those of the local electric field (J = gE), and the equipotential surfaces intersects the current lines at right angles are not necessarily parallel to each other for this medium. In this case actually we can consider a large resistance network constructed from many elemental resistors Ri in the shape of short wire segments. According to the resistance formula for a resistor we have
‘i Ri ¼ ; g i Ai
ð2Þ
where gi(x, y, z) is the local conductivity, Ai is the cross-sectional area of the segment, and ‘i is the distance between the equipotential surfaces. In the limiting case where the number of the equipotential surfaces between U1 and U2 becomes very large and the number of elemental resistors becomes correspondingly large, the resistors Ri fill the entire space occupied by the conducting object. Thus such a network has an equivalent resistance R that can be considered in Eq. (1).
I
E n da ¼
S
Q
e
ð3Þ
;
where e is the permittivity of the medium, and in this condition two conductors form a capacitor with the charge value of
Q ¼ CðU 1 U 2 Þ;
ð4Þ
and by insertion of Eqs. (6) and (5) into (4) we can write
e
RC ¼ ; g
tc ¼
e g
ð5Þ
¼ eq;
ð6Þ
where q is defined as resistivity of the medium (X m). Time constant is measure of how fast the conducting medium approaches the electrostatic equilibrium; precisely, it is the time required for the charge in a specific region to decrease to 1/e of its original value. A material will reach its equilibrium charge distribution in a specific application when its time constant is much shorter than the characteristic time required to make the pertinent measurement. For some applications a time constant of less than 0.1 s is sufficient to ensure conductorlike behavior; since most permittivities fall into the range e0– 10e0, this require a material with resistivity q less than 109 or 1010 ohm-m. For high-frequency applications a shorter time constant, and a correspondingly smaller resistivity, is required for the true conductorlike behavior. In fact
tc
1 ; f
ð7Þ
must be satisfied in which f is the highest frequency involved in the experiment. In general the complex permittivity of a medium can be written as
g
e ¼ e0 je00 ¼ e0 j ; x
ð8Þ
where e0 is the real, e00 is the imaginary part of the permittivity and x = 2pf. The condition for a good conductor medium is that the imaginary part to be much larger than the real part, i.e.
g 2
e0 x
1;
ð9Þ
where g is the conductivity. For a good dielectric medium the given ratio must be much less than unity. For the metallic conductive materials the conductivity is high
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(for copper 5.88 107 mho/m or S/m) while for the good dielectric medium the permittivity is high (for a pure distilled water is about 80e0). Generally water molecules are in continuous motion, even at low temperatures and when two water molecules collide, a hydrogen ion is transferred from one molecule to the other. The other molecule that losses the hydrogen ion becomes negatively charged hydroxide ion. The molecule that gains the hydrogen ion becomes a positively charged hydrogen ion and this process is commonly called the self-ionization of water. In fact at room temperature (25 °C), each concentration of hydrogen ions and hydroxide ions is only of the order of 1 107 M, and as a result this dissociation allows a minute electrical current to flow. The current flow is in the range of conductivity of 0.05 lS/ cm at room temperature. It is important to note that the amount of (H)+ and (OH) ions are approximately equal and this solution is described as a neutral solution. In other aqueous solutions, the relative concentrations of these ions are unequal and one ion is increased by one order of magnitude while the other one shows some decrease, but the relationship is constant and the ion product is always constant given by Kw, which is called the ionproduct constant for water. Water is a polar solvent with an uneven distribution of electron, and the application of electric field causes one portion of the molecule to be somewhat positive and another part negative (polarization effect). In an external DC electric field, the dissolved electrolyte substances are free to move and positive charged particles move towards negative electrode while negative charged particles migrate toward the positive electrode. The migration of the charged particles causes the electric current flow in liquid. Such DC polarization can be eliminated by using AC voltage at 60 Hz or higher frequencies and in practice by increasing the cross sectional area of the electrodes. The mechanism of electrical conduction through a liquid is different in comparison with a solid. In solid, when a potential is applied to a solid conductor, the flow of current is instantaneous, and is virtually proportional to the applied potential. In addition, different types of materials conduct electrical charges with different efficiencies. In metals, there are free electrons, which are available for conduction even at a very low temperature. One major difference of a metal with semiconductor and isolator materials is that metal resistance increases as the metal heated because of the decrease in electron mobility. Conversely, the resistance of semiconductors and insulators decreases with increasing temperature because the number of charge carries increases. Therefore, in semiconductor and in particular in insulators, more activation energy is needed to excite electrons to be available to conduct a charge. The conductivity of a solution relates to the total dissolved solid (TDS) and amount of the suspended solids (SS) or insolvable solids in a water sample. Total dissolved solid includes solid particulates such as ions, inorganic substances, salts, and metals. Total solid (TS) is defined as the sum of TDS and SS. In laboratory analysis measurement of these parameters are made by filtering and weighing to determine SS, then drying and weighing to determine TDS. In analysis of water the conductivity
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measurements are classified for the ultra-pure, high-purity and pure water samples, which show accordingly an increase in the conductivity value from 0.053 lS/cm to 10 lS/cm.
3. Experimental arrangement Our experimental system as shown in Fig. 1 includes a sensing cylindrical probe and a measuring module. Fig. 2 shows the block diagram for the two tested cell probes with different effective lengths of 100 mm and 50 mm, respectively. A temperature senor is also used for the temperature monitoring of the liquid sample in the cell. The measuring modules are a LCR (Yuke-816, Good Will Instrument, Gw Instek) meter and a 4-wire test clip as shown in Fig. 1. Two measurement leads as indicated in Fig. 1; are connected to the inner electrode and outer electrode, respectively. Measuring instrument specified as LCR-816 2 kHz high precision LCR meter and a LCR-06A measuring probe [17]. 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 (Kelvin clip). The LCR module operates based on the automatic balanced bridge circuit in which the impedance can be determined for the resistance and reactance values. For the case of capacitance measurement; capacitive reactance (XC) and for the inductance measurement the inductive reactance (XL) are measured and displayed. Reactance (X) measures the imaginary part of impedance (Z), and is caused by capacitors or inductors and admittance is the reciprocal of the reactance, Y = 1/Z. In general, capacitance measures the amount of electronic charge stored between two electrodes of a capacitor. The resistance of the medium to the flow of current as a result of applied voltage; is considered as the resistance factor, R. Conductance, G, is the potential of the flow of the electricity in a medium and is given as the inverse of the medium resistance. Impedance that is neither a pure resistance nor a pure reactance can be represented at any specific frequency by either a series or a parallel combination of resistance and reactance as shown in Fig. 3. Such representation is called the Equivalent Circuit (EC) for the probe. In Fig. 3a the Series Equivalent Circuit (SEC) is shown where Rs, and Cs show
Fig. 1. Block diagram for the measurement system.
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4 mm
(a) 5 mm
Gap (Plexiglass)
Filling Gap
100 mm
Outer Electrode (Aluminum)
Main Electrode Lead 10mm
8mm 18mm 24mm 44 mm
Plexiglas s Base Inner Electrode (Aluminum)
4mm
(b) 5mm
Cap (Plexiglass)
Filling Gap
50 mm Outer Electrode (Aluminum)
Main Electrode Lead
10mm
8mm 18mm 24mm 44 mm
Plexiglas s Base Inner Electrode (Aluminum)
Fig. 2. Block diagram for the two tested cylindrical probes. (a) Long probe with an effective length of 100 mm, and (b) short probe with the length of 50 mm.
the series resistance and capacitance parameters. Fig. 2b shows the Parallel Equivalent Circuit (PEC) whereas Rp, and Cp respectively show the parallel resistance and capacitance parameters. Depending on the function selection; series capacitance (Cs) and parallel capacitance (Cp) can be measured by the LCR module. Resistance can be also obtained from the series resistance (Rs) or parallel (Rp) in
diagrams shown in Fig. 3. The component of the primary display of the LCR module depends on which equivalent circuit (EC) is chosen. In normal condition, the component manufacturers specify how a component is to be measured (usually series) and at what frequency. Normally for low value of inductance (<10 lH, SEC method) and capacitance (<10 pF, PEC method) and high measurement frequency of
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4. Measurement results
Fig. 3. Circuit diagram for the probe under study. (a) Equivalent series circuit, and (b) equivalent parallel circuit.
the order of (100 kHz) are recommended. For measuring resistors lower than 1 kX, SEC method and high frequency (1 kHz) are suggested. Four combinations of two parameters can be measured and displayed that could be parameters L (Inductance) and Q (quality factor), C (capacitance) and D (dissipation factor is inverse of quality factor), C and R (resistance) or R and Q. Usually determination of C and R pairs is the goal in our experimental measurements. In this configuration meter displays the C, R and measurements can be performed in either series or parallel equivalent circuit. The accuracy for C and R measurements is about 0.05% (basic) plus another error term that is defined from a given formula [17]. For the cell probe a cylindrical geometry as shown in Fig. 2 is chosen and aluminum materials are used as the capacitor tube electrodes. The diameter of the inner electrode is about 18 mm and the inner diameter of the outer electrode is about 24 mm and has an overall diameter of about 44 mm. Two cell probes are constructed with the similar structures with the effective length of 100 mm and 50 mm, which are referred to as the long and short probes, respectively. The radial gap between the two tube electrodes for filling medium is about 3 mm. The cylindrical gap volume measured when filled with water for the long sensor (10 cm-length) is 20 cc and for the short one (5 cm-length) is 10 cc. The distilled water used in this experiment is produced by an apparatus operating based on the heating and boiling/condensation technique. The mineral water is purchased as bottled water and normally same brand from the single producing company is used. Tested tap water is the regular refined drinkable municipal city (Tehran) water, and the boiled water is the tap sample type boiled, similar to the water sample types used for the tea or coffee making. Salt water solutions are prepared by dissolving small amount of the regular grade salt in distilled water. To analyze the electrical condition of the tested water liquids, another device is used to measure the electrical conductivity (EC) and the total dissolved solid (TDS) density of the water samples in this experiment. The EC of different water liquids measured using conductive meter (Sension5). The conductive meter is a contacting style conductivity sensor in which its plane electrodes are in direct contact with the solution being measured. It provides functions for EC and TDS measurements at a test temperature. Electrical conductivity values in the range of near zero to199.9 mS/cm can be measured with a resolution of about 0.1 lS/cm and TDS in the range of near zero to 50,000 mg/L can be measured with a resolution of about 0.1 mg/L. The specified accuracy of the Sension5 device for EC is about ±0.5% of the full range and for TDS is about ±5% of the full scale range.
In experimental measurements, the resistance and capacitance of different water samples are measured simultaneously at a fixed temperature and a test frequency of 1 kHz using either the long or short cell probe. Table 1 shows the electrical parameters obtained with the long sensor and Table 2 indicates the same parameters measured with the short cell probe. In these tables subscript, s, shows the series, p the parallel values, and factor D shows the dissipation factor measured for the effect of the resistance energy loss in the capacitance measurements. The test samples are (DW), mineral water (MW), tap water (TW), boiled water (BW), dilute salt water solution (SW1), and finally salt water solution (SW2). As can be seen in Table 1, among all samples the DW shows the highest value of D (55.1) and on the other hand SW2 shows the lowest dissipation factor D (0.44). As can be seen in Table 2, a similar behavior for factor D is observed for the short cell probe (compare 57.1 for DW with 0.43 for SW2). The high value of dissipation factor D for DW indicates the high degree of the resistivity of this sample in the equivalent circuit measurements. As can be seen in Tables 1 and 2 the factor D is decreased for the given samples and salt water solution (SW2) shows the lowest D factor of 0.43 and as a results the highest conductance. A careful look at Tables 1 and 2 shows that the capacitance value is about twice for the long probe in comparison with the short probe. For the series resistance values the situation is reversed and the resistance values for the long probe are almost half of the short probe values. The measured capacitance values for the two probes are compared in Fig. 4. Different samples including distilled water (DW) mineral water (MW), tap water (TW), and boiled water (BW), dilute salt water (SW1), and salt water (SW2) samples are considered for this investigation. As can be noticed in Fig. 4, DW sample shows a low series capacitance value of 6.3 lF (3.3 lF for the short probe) and the salt water shows the highest value of 32 lF (14.6 lF for the short probe). In general for all the tested samples the series capacitance is higher for the long probe in comparison with that of the short probe. The actual active length of the long probe (10 cm) is twice of the short probe (5 cm) and considering results a factor of about 2 is observed in the capacitance ratio results for the two probes. In Fig. 5 the measured series resistance values for the two probes are compared. Different tested samples are as before distilled (DW) mineral water (MW), tap water (TW), and boiled water (BW), dilute salt water (SW1),
Table 1 Electrical parameters obtained with the long cell probe. Sample
Rs (X)
Rp (X)
Cs (lF)
Cp (lF)
D
DW MW TW BW SW1 SW2
1389 21 15 13.6 3.5 2.2
1390 23.1 17.7 16.3 11.1 13.4
6.3 23.53 25 26.15 30.83 32.02
0.002083 2.21 3.8 4.36 21.11 26.7
55.1 3.1 2.3 2.2 0.67 0.44
s: Series equivalent circuit, p: Parallel equivalent circuit.
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Table 2 Electrical parameters obtained with the short cell probe. Sample
Rs (X)
Rp (X)
Cs (lF)
Cp (lF)
D
DW MW TW BW SW1 SW2
2788 42.1 30.1 28.1 7.1 4.6
2788.9 46.7 35.9 33.8 24.2 95.6
3.32 11.35 11.96 12.47 14.43 14.8
0.000981 1.13 1.95 2.13 10.20 12.5
57.1 3.0 2.3 2.2 0.64 0.43
s: Series equivalent circuit, p: Parallel equivalent circuit.
Fig. 6. Comparison of the series and parallel resistances of samples for the long probe.
Fig. 4. Comparison of the electrical capacitances of samples for two probes.
Fig. 5. Comparison of the electrical resistances of samples for two probes.
and salt water (SW2). As indicated in the inset of Fig. 5, for presentation of all the results for the series resistance in one figure, the measured value of DW is divided by ten to be comparable with the other results. As can be seen in Fig. 5, result for the DW sample shows the highest series
resistance value of 2788 X (1389 X for the short probe) and the salt water (SW2) shows the lowest value of 2.2 X (4.6 X for the short probe). In general for the long probe measurement the series resistance is higher for the DW in comparison with those of the other samples. Same behavior is observed for the short cell probe measurements. In comparing the results of the short and long probe it is noted that the series resistance values for the long probe for the related samples is almost half of those of the short probe. The actual active length of the long probe (10 cm) is twice of the short probe (5 cm) and considering results a factor of about 1/2 is observed in the series resistance ratio results for the two probes. Fig. 6 shows a comparison of the series and parallel resistances of the tested samples for the long probe. As indicated in Fig. 6, for presentation of all the results for the resistance values in one figure, the measured value of DW is divided by ten to be comparable with the other results. As usual tested samples are the distilled water (DW) mineral water (MW), tap water (TW), boiled water (BW), dilute salt water (SW1), and salt water (SW2). As can be seen in Fig. 6, for the distilled water sample the value of the measured series resistance is 1389 X while for the parallel resistance is 1407 X. For the case of the distilled water sample the relative deviation is about 1.27%. For the next sample such a deviation is increased, and finally for the SW2 such a deviation is the maximum value of 83.58% (compare series resistance 2.2 X with parallel 13.4 X). The result of this study is the important point that for the DW both the series and parallel EC methods can be used, however for other samples, in particular, salt water electrolyte solution one must be careful in choosing the measuring method for a correct resistance measurement. In Fig. 7 a comparison of the series and parallel resistances of the tested samples for the short probe is shown. Tested samples as before are distilled water (DW) mineral water (MW), tap water (TW), boiled water (BW), dilute salt water (SW1), and salt water (SW2). As shown in the inset of Fig. 7, for presentation of all the results for the resistance
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in one figure, the measured value of DW is divided by a factor of ten to be comparable with the other results. As can be seen in Fig. 7, for the distilled water sample the series resistance is 2788 X while for the parallel resistance is 2788.9 X. For this case the relative deviation is about 0.032%. For the next sample such a deviation is increased, and finally for the SW2 such a deviation is the maximum value of 95.18% (compare series resistance 4.6 X with parallel 95.6 X). Similar to the case of the long probe, the result of this study leads to the fact that for the DW both the series and parallel EC schemes can be used, however for other samples, in particular, salt water electrolyte solution one must be careful in the selection of the correct method of the resistance measurement. Considering the previous finding that the series method gives precise results for the water samples in the next
Fig. 7. Comparison of the series and parallel resistances of samples for the short probe.
studies only electrical parameters are derived for such samples. In the next investigation the electrical conductivities of different water liquids are determined from the measured series resistance value Rs for the long cell probe. The results for different water samples are listed in Table 3. As described before for all the water samples both the SEC and PEC provide reliable results. Therefore in this section a more precise measurements are reported for such samples. From the series resistance value the resistivity for the cylindrical probe is determined from the relation
q ¼ 2pRL=Lnðb=aÞ;
ð10Þ
where L is the cell length, b the radius of the outer cylinder and, a, is the radius of the inner electrode. From given series resistivity the electrical conductance is obtained from
g 0 ¼ 1=q;
ð11Þ
and listed in Table 3. Using the EC meter the electrical conductivity for the sample samples are also measured and given in Table 3. As can be seen in Table 3, the resistance value is the highest for distilled water (1389 X) and the lowest for the boiled water sample, which is about 13.6 X. Correspondingly, the resistivity parameter is decreasing in the same order while for the DW is about 3033.41 X m and for BW is decreased to about 29.7 X m. The conductivity determined form Rs measurements of different samples is obtained and compared with the ones measured in Table 3. For a better comparison the relative errors as result of the direct measurements with EC meter and the one obtained with the cell probe are indicated in the last column of the Table 3. As can be seen in Table 3, the relative error for two measurement methods is at maximum about 4.0% that is acceptable for such measurements. In a similar method, the electrical conductivities of the same liquid samples are determined from the related measured series resistance value Rs for the short cell probe. The results of electrical parameters for different water samples are listed in Table 4 for the short probe. As can
Table 3 Electrical conductivities obtained with the long cell probe. Water sample
Rs (O) T = 15 °C
q (X m) T = 15 °C
g´ (lS/cm) probe T = 15 °C
g (lS/cm) EC T = 20.6 °C
Relative error (g g´)/g (%)
Distilled Mineral Tap Boiled
1389 21 15 13.6
3033.41 45.86 32.76 29.70
3.30 218.05 305.27 336.69
3.41 223 318 341
3.3 2.2 4.0 1.3
g: Conductivity with EC meter, g´: Conductivity with cell probe.
Table 4 Electrical conductivities obtained with the short cell probe.
Water sample
Rs (O) T = 15 °C
q (X m) T = 15 °C
g´ (lS/cm) probe T = 15 °C
g (lS/cm) EC T = 20.6 °C
Relative error (g g´)/g (%)
Distilled Mineral Tap Boiled
2788 42.1 30.1 28.1
3044.33 45.97 32.87 30.68
3.28 217.53 304.25 325.91
3.41 223 318 341
3.7 2.5 4.3 4.4
g: Conductivity with EC meter, g´: Conductivity with cell probe.
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be seen in Table 4, the resistance value is the highest for distilled water (2788 X) and lowest for the boiled water sample, which is about 28.1 X. The resistivity parameter is decreasing in the same order while for the DW is about 3044.33 X m and for BW is decreased to about 30.68 X m. Comparison of the Tables 3 and 4 reveals two important points. First, as expected the measured resistance values are different for the long and short probes while the resistivity of the water samples is independent of the length of the cylindrical probe and very similar for the two probes. For example for the mineral water sample resistivity for the long probe measurement is 45.86 X m and for the short probe is 45.97 X m. Second, and perhaps the most important one, is that there is a good agreement between the results obtained with the cell probe and those of the EC meter. For instance compare the conductivity results for the mineral water in which the relative deviation is about 2.5%. Such small deviation is because measurements are not exactly at the same sample temperature. For the water samples the conductivity parameter results derived from the experimental measurements are shown in Fig. 8. As can be seen from data labels on the graph bars this factor for the long probe for DW is the lowest value of 3.30 lS/cm while for the short probe cell correspondingly is 2.28 lS/cm. For both probes the conductivity factor is increased for the tested samples and for the MW is 218.05 (for short probe 217.53 lS/cm), for the TW is 305.27 lS/cm (for short probe 304.25 lS/cm) and for the BW is 336.69 lS/cm (for short probe 325.91 lS/cm). Considering the results for the long and short probes it is noted that such a parameter depends on the sample type and hence independent of the probe cell length. As a result, a good agreement is observed for the conductivity values derived from the measurements performed with two cell probes. In the next study permittivity is determined from the conductivity, g, as determined in the previous section. From Maxwell’s equation we can write
r H ¼ jxeE þ J;
ð12Þ
where the current density is related to electric field by Ohm’s law
J ¼ gE:
ð13Þ
By plugging Eq. (13) into Eq. (12) we can write
r H ¼ ðg þ jxeÞE ¼ jxe er j
g
xe
E ¼ jxe ~er E;
ð14Þ
and by defining the relative permittivity one can write
~er ¼ er j
g
xe
ð15Þ
;
and in the closed form as
~er ¼ e0 je00 ;
ð16Þ
where permittivity includes the real imaginary part. By using Eq. (15) the imaginary part of the permittivity is determined and the results for different tested samples are listed in Table 5. The relative imaginary part is shown and in the last column the imaginary part of the permittivity is listed. In Table 6 for the short probe different parameters similar to those of the long probe are listed. Similar to result of ´, is the lowest for the distilled Table 5, the conductivity, g water (3.28 lS/cm) and the highest value for the boiled water sample, which is about 325.91 ls/cm. To compare conductivity for the long and short probe let us compare the results for the mineral water. The mineral water conductivity for the long probe is 218.05 ls/cm while for the short probe is 217.53 ls/cm, which is similar to that of long probe. This agreement indicates that the conductivity just depends on water type and is independent of the cell length. In a similar way in Table 6, the relative imaginary part for the short cell probe is shown and in the last column the imaginary part of the permittivity is given. As can be seen in Table 6, the imaginary part, which is related to the conductance factor of the sample, is increasing respectively for indicated samples.
Table 5 Imaginary permittivity obtained with the long cell probe. Water sample
Rs (O) T = 15 °C
g´(lS/cm) T = 15 °C
e00r (Im)
Distilled Mineral Tap Boiled
1389 21 15 13.6
3.30 218.05 305.27 336.69
5928.505931 392128.3209 548979.6492 605492.2602
e00 (Im) 107 (F/m) 0.524 34.703 48.584 53.586
g´: Conductivity with long cell probe.
Table 6 Imaginary permittivity obtained with the short cell probe.
Fig. 8. Obtained electrical conductivities for the long and short probes.
Water sample
Rs (O) T = 15 °C
´ (lS/cm) g T = 15 °C
e00r (Im)
Distilled Mineral Tap Boiled
2788 42.1 30.1 28.1
3.28 217.53 304.25 325.91
5907.241562 391196.8997 547155.7966 586099.2696
g´: Conductivity with short cell probe.
e} (Im) 107 (F/m) 0.523 34.621 48.423 51.870
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As indicated in that report the thickness of the water sample and the applied oscillator voltage level affect the measured electrical parameters. For the reported measurement the dielectric permittivity is given for the sample thickness of 3.93 mm and the applied oscillator voltage of 1 V. However, as indicated [18,19], the permittivity of the sample depends on the test frequency, which is 1 kHz in our measurements. From [19] a typical value of permittivity is reported for the pure water sample. Comparing our results with the given value the observed deviation in permittivity is because of the higher impurity and conductance effect of our tested samples. Considering the results shown in Fig. 9 and by comparing the results listed in Tables 5 and 6 it is noticed that the imaginary part results obtained with the long and short probes are almost similar which, leads to the fact that the imaginary part of the permittivity is independent of the cell probe length. Fig. 9. Comparison of the imaginary part of the electrical permittivity for the long and short probes.
As a last study in Fig. 9 for different water samples the imaginary permittivity parameter results derived from the experimental measurements are plotted. As can be seen in Fig. 9, from data labels on the graph bars this factor for the long probe for DW is the lowest value of 0.524 107 F/m while for the short probe cell is 0.523 107 F/m. For both probes the permittivity factor is increased for the tested samples and for the MW is 34.703 107 F/m (for short probe 34.621 107 F/m), for the TW is 48.584 107 F/m (for short probe 48.423 107 F/m) and for the BW is 53.586 107 F/m (for short probe 51.87 107 F/m). Considering the results for the long and short probes it is noticed that such the imaginary part of the permittivity only depends on the sample type and hence independent of the probe cell length. As a result, a good agreement is observed for the conductivity values derived from the measurements performed with both probes. Considering the permittivity factor of the free space, which is e0 = 8.85 1012 F/m, and for pure dielectric water that is about 80e0 (compare 0.00708 107 F/m with 0.523 107 F/m) the imaginary part of the permittivity component is the dominating factor. This is as a result of the high conductivity effect observed for the tested water samples in this investigation. In 2004, the electrical properties of water for the frequency range of 5 Hz–13 MHz is reported by Rusiniak [18,19] using a non-invasive cell probe arrangement. The dielectric permittivity, conductivity, and dissipation factor have been measured for the temperature range of 20–90 °C for the distilled water. Considering data given in that report the relative permittivity of about 1000 and conductance value of 6 104 S (see Fig. 2 of [19]) is reported at 1 kHz and room temperature (20 °C). Comparing the given results [19], and our results it is concluded that in the invasive arrangement most of the contribution is due to the imaginary part of the permittivity, which is in the order of 5928.5 (for the short probe 5907.2) for our case. Comparing the relative permittivity it is noted that at such a frequency and temperature the imaginary part is higher with respect to the dielectric one by a factor of about 5.9.
5. Concluding remarks By implementing the equivalent circuit method; electrical parameters for different water samples are measured, by using the long and short cell probes. Variations of the series and parallel capacitance values as well as resistance, and the dissipation factor are given for different water samples. In another measurement the electrical conductivity of different samples are measured by an EC meter and also the cell probes. Imaginary part of the permittivity is determined at frequency of 1 kHz from electrical conductivity results for different water samples. Concluding outlines of the reported measurements are as follows: (a) The series equivalent circuit is a proper method to investigate the resistance and capacitance of the water samples. The series resistance value is highest for DW and the lowest for the BW. (b) Application of two cell probes with different cylindrical length shows the series capacitance and resistance values depend on the cell length. Our results show that capacitance is directly increased by increasing the length and resistance is inversely proportional to the cell length. (c) Electrical conductivities for different water samples are determined here from the experimental measurements using the long and short cell probes. Obtained conductivities for the different water samples are compared where the lowest conductivity is obtained for the distilled water and the highest one for the boiled water. Obtained conductivities with the cell probes are compared with the EC device results and a good agreement is observed. (d) From conductivity and test frequency the imaginary part of the permittivity is obtained for different water samples. For both probes the permittivity factor is increased for the tested samples and for the DW is lowest and for the BW the highest. (e) Considering the conductivity and the permittivity results for the long and short probes it is noticed that such parameters only depends on the sample type and hence independent of the cell probe length.
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(f) Imaginary part of the permittivity is much higher than the real part, thus the reported method is a very effective way to study the electrical conductivity of different water samples and dilute electrolytes. (g) Our results show that the reported method can be effectively used to study the electrical parameters of different water samples and dilute electrolytes.
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