A new system for measuring electrical conductivity of water as a function of admittance

The admittance cell is fabricated in a plastic tube of diameter 1.67 cm and length 9 cm with four silver electrodes (Ag 92.5 g to Cu 7.5 g) fixed inside the tube. The four silver electrodes each of diameter 1.67 cm and 0.6 cm thickness are arranged at equal distances of 1.5 cm apart as shown in figure (1).

Figure (1)

The impedance measurements are carried out at different frequencies ranging from 50 Hz to 100 kHz by filling the tube with one water sample at a time (distilled, mineral, river, rainfall, and tap water). The voltage of the applied sinusoidal signal is about 10 volt rms. The electrical conductivity of the liquid is derived from its impedance Z. The admittance of the liquid is then calculated from the reciprocal of Z.

Two setups were considered; four electrodes and two electrodes with two modes.

In the four electrode setup, the impedance of the water samples is determined by the ratio of the electrical current (I) measured at the two outer electrodes and the measured potential drop ΔV between the two inner electrodes.

In the two electrodes setup, one with two inner electrodes and the other with two outer electrodes, a voltage is applied to two electrode rings immersed in the water sample. Then the resultant current which is related to the small changes in the electric potential across the two electrodes is measured. The impedance is then determined in the same manner as mentioned above (the ratio between I and ΔV). The conductivity of water measured by both setups was compared to the measurements of a commercial conductivity/оC meter (Wagtech international) at room temperature 25 оC.

The impedance and admittance measurements were performed at three different inter-electrode distances for each frequency. The design of the system allowed the use of both the four and two-electrode setup. These two setups and their results are illustrated in subsections A and B.

In the four electrode setup, a relationship between EC values measured by a commercial instrument EC meter and the admittance was established for different water samples at each frequency. Table (1) and Figure (2) show these relationships at frequencies (0.05, 2, 20, 60 and 100 kHz). They can best be interpreted in accordance to the parameters of a linear equation (slope and intercept). The slope represents the distance between the electrodes. Figure (2) assures the correctness of the aforementioned interpretation. In this figure the slopes of the lines at low frequencies are (1.7, 1.66 and 1.56) with correlation factor (R² > 0.99). These slope values approximate the distance between the electrodes (1.5 cm) with error percent (9.3 %). This result is in agreement with that of previous work [7].

Figure (2)

In addition, the unit of the slope according to the figure is cm^-1 which is the unit of the cell constant for any conductivity meter. So the distance between the electrodes can be taken as the cell constant of the four electrode setup. However, at high frequencies (60, 100 kHz) this interpretation is not feasible because the slopes of the lines exceeded the value of (2) with correlation factor (R² > 0.99). This value is rather far from (1.5 cm) the distance between the electrodes.

The other parameter of the linear equation is the intercept value. Ideally the intercept value should be zero. However, experimentally according to figure (2) the intercept values were (3×10^-6, 3×10^-6, and 6×10^-6). These values can be considered as errors attributed to the electrode conductivity. This point was noticed previously in [2].

In this setup two modes were considered; 2-inner and 2-outer electrodes. Table (2) and figure (3) show the results for the 2-inner electrodes. According to the previous interpretation of the slopes and intercept values, the slope values were (1.47, 1.50 and 1.57) at low frequencies with correlation factor (R² ≈ 0.99). The average of these slope values was exactly equal to the distance between the electrodes (1.5 cm). Also at high frequencies (60, 100 kHz) this interpretation is not feasible because the slopes of the lines exceeded the value of (2) with correlation factor (R² > 0.99). According to figure (3) the intercept values were (1×10^-5, 1×10^-5, and 7×10^-6).

Figure (3)

Table (3) and figure (4) show the results for the 2-outer electrodes. The slope values of the lines were (4.012, 4.09 and 4.567) at low frequencies with correlation factor (R² ≈ 0.99). These slope values approximate the distance between the electrodes (4.5 cm) with error percent (6.15 %). However, at high frequencies (60, 100 kHz) the slopes of the lines were (5.759 and 7.93) with correlation factor (R² > 0.98). These values are rather far from (4.5 cm) the distance between the electrodes. The intercept values in figure (4) were small at low frequency and relatively large at high frequency. In general, it seems that the intercept values for the 4 electrodes setup were less than that of the two modes of two electrodes setups. This confirms the point that the effect of the electrode impedance in the four-electrode setup is smaller.

Figure (4)

The influence of the three electrode setups (four, 2-inner and 2-outer) on the admittance measurements of the water samples was studied. Table (4) and figure (5) illustrates that the admittance of the water samples especially at low frequencies is changed depending on the electrode setup. This figure clearly shows that the admittance in the four electrode setup is greater than those of the two electrode setups at the same frequency. This can be attributed to the fact that increasing the number of electrodes makes the area of charge accumulation around each electrode smaller. This means that the charge transfer resistance decreases, which in turns leads to an increase in the admittance. These results agree with those reported in [8, 9, 10].

Figure (5)

The configuration of the electrodes also contributes to the increase in the measured admittance. For the four electrode setup there is no current flow through the voltage measurement electrodes, thus there is no voltage drop across these electrodes. This is illustrated by table (5).

In contrast, for the two electrode setup with two modes (inner and outer), the measured impedance was greater than that of the four electrode setup as shown in table (5). This table shows that the impedance of the two electrode setup is high because the voltage measurement electrode is the same as the current supply electrode thus the voltage that appears between them is affected by the voltage drop caused by the impedance of the electrodes. This result has been reported in [11].

The influence of the distance between the electrodes on the measured impedance can be explained as follows: the larger the distance between the electrodes the larger is the reactance capacitance value of the water sample. This behavior is especially feasible for the 2-outer mode of the two electrode setup. This makes the impedance to be higher, as seen in table (5). The same explanation was given in [12]. Table (5) shows that the four electrode setup is efficient for minimizing the impedance values. Thus the problem of electrode polarization can largely be eliminated for the four electrode setup.

Although the electrode polarization exists in the two electrode setup, it can still be used as an alternative setup as the results it gave were fair and acceptable as shown in figures (3 and 4). The acceptance of the two electrode setup may be due to the large surface areas of the electrodes which lead to a reduction in the electrode impedance.