The commercial value of the Zamzam water (ZZ) has risen as a result of the global high demands by the Muslim faithfuls. To develop an alternative for cheap, fast, and easy quality monitoring, this study presents the ultra-low frequency dielectric spectroscopy analysis for the ZZ. The dielectric permittivity of the ZZ was higher than that of the samples of local wells and bottled water. Similarly, the loss factor of the water was higher than that of others. As a result of the unique balance of dipole molecules and conducting ions in the ZZ water, the dissipation factor of the water was explored to further create a fingerprint of its characteristics among water samples. At 10 kHz, a unique crossover frequency of dissipation factor was recorded for samples of the ZZ and well water. At this frequency, adulterating the ZZ with well water leads to a decrease in the dissipation rate while also shifting the dissipation rate rightwards. A simple ANN-based model, built on the Tan-Sigmoid function, was developed using permittivity (ɛ′), loss factor (ɛ″), dissipation factor (D), frequency (F), and impedance (Z). The model used these variables, obtained at an ultra-low frequency, to spell out the purity level of the ZZ. Overall, the work presented numerically assisted ultra-low frequency dielectric spectroscopy analysis as a cheaper alternative to the material quality analysis.

  • Novel application of low-frequency dielectric characterisation in the study of Zamzam property.

  • A unique dissipation peak was recorded for the Zamzam water, different from other water samples.

  • A simplified Tansig-function model was developed for determining the purity level of Zamzam.

  • An interesting and simplified ANN-based equation procedure was demonstrated.

  • Five parameters of dielectric spectroscopy were identified as important in the detection of water purity level.

complex permittivity

the real part of complex permittivity

the imaginary part of complex permittivity

A

the area of each parallel plate in m2

d

distance between the two parallel plates in m

frequency in Hz

the permittivity of the vacuum

C

capacitance

D

dissipation factor

N

input into the Tansig function

n

output from the Tansig function

Z

impedance

phase angle

R

resistance

x

actual value of the independent variable parameter

y

normalised value of x

ymax

1

ymin

− 1

xmin

minimum value of the independent variable parameter

xmax

maximum value of the independent variable parameter

E

sum of the weighted normalised independent variable

b

bias

W

weight

k

normalised output of the model

kd

denormalised output of the model

obs

observed value

Scal

calculated value

MSE

mean squared error

ZZ

Zamzam water

AC

alternating current

DRS

dielectric relaxation spectroscopy

n

output of the Tansig function

N

input of the Tansig function

L

inductance

ω

2πf

The Zamzam water (ZZ) has been of physical and spiritual significance to global Muslims and, especially, Hajj pilgrims, for ages. The ZZ springs from within the premises of the Holy Mosque in Makkah, Saudi Arabia. The water is routinely transported across many places in Saudi Arabia and overseas. Also, Hajj and Umrah pilgrims, as well as businessmen, transport water in various quantities from the natural source to various places across the world for commercial transactions. So, samples of the water can be found in various packages in the street shops in many cities and towns across the globe, including Nigeria. Muslims use the water for quenching thirst, healing, and spiritual purposes (Shomar 2012; Moni et al. 2022; Islam 2024) because many religious texts specify divine blessings and benefits associated with the water.

Owing to the growing spiritual awareness of the ZZ among Muslims, its commercial value has risen in many places in Nigeria, and the feeling and practice of adulteration have equally been prevalent. The strict legislation on the exportation of the ZZ by Saudi authorities has led to the rise in its adulteration outside the shores of Saudi Arabia (Rasyida et al. 2014). Diluting the water with local water samples or outright packaging of local water as ZZ will definitely alter or replace its physicochemical and other natural characteristics.

According to studies, ZZ is rich in magnesium, calcium, fluoride, and other minerals (Ahmad et al. 2019). While other water samples from local sources may also contain similar minerals, it is believed that the concentrations, polarisability, orientations, and physicochemical characteristics of various local samples in Nigeria, which may be used for the adulteration of the original ZZ, will be chemically and/or physically distinguishable under certain conditions. Thus, this work studies the dielectric characteristics of ZZ purity under various scenarios of adulteration with local water in Nigeria. The technique applied was a non-intrusive and low-cost dielectric spectroscopy, which relies on the unique dielectric property of each material.

Every material has peculiar electrical and magnetic characteristics that can be utilised to estimate its volumetric concentration in a mixture (Gocen & Palandoken 2021). The dielectric permittivity of a material has a relationship with the material's components, which can then be used to monitor changes in the material's contents (Frau et al. 2021). A material is classified as ‘dielectric’ if it has the ability to store energy when an external electric field is applied. Dielectric properties of water can be used to directly monitor water quality in rivers, lakes, and reservoirs after appropriate calibration (Al-Mattarneha & Alwadie 2016). Alternating current (AC) conductivity is extensively used to characterise the electrical properties of various materials to understand the nature of the conduction mechanism of solid materials (Okutan et al. 2005; Darwish et al. 2014). Dielectric relaxation spectroscopy (DRS) of dielectric material provides information about the orientation and translational adjustment of dipoles in the material (El-Nahass et al. 2006). Dielectric permittivity works due to the fact that the electrical energy transferred to a medium is a function of the electric field and the physicochemical properties of the medium (Darwish et al. 2014). The changes displayed by the dielectric permittivity of materials at different frequencies indicate the responses of the different nigrostriatal layers (electronic, atomic, and molecular) (El-Nahass et al. 2006). Thus, the molecular mobility of materials can be investigated using DRS.

Dielectric spectroscopy has been effective, as demonstrated by many authors, in the identification of different kinds and concentrations of organic or inorganic pollutants (Kaya & Fang 1997; Shang et al. 2004). The technique has been applied in many areas of science and engineering. Taylor & Morris (2022) used dielectric spectroscopy to investigate concrete properties, while Kaya & Fang (1997) detected the role of ionic strength and organic liquids in soil using the same technique.

Particularly, the dielectric relaxation losses over a wide frequency range reveal peculiar characteristics of components under analysis. Dielectric spectroscopy has the wide-range frequency over techniques such as light scattering and neutron scattering, providing a large number of dispersion features that are advantageous to modelling (Volkov & Chuchupal 2022). It has also been indicated that combining dielectric permittivity with conductivity provides sensitivity to chemical, physical, and microstructural states of solid and liquid samples (Chelidze et al. 1999; Kyritsis et al. 2000; Saltas et al. 2023).

Parameters of dielectric spectroscopy include dielectric permittivity (ɛ′), dielectric loss factor (ɛ″), dissipation factor (D), resonance frequency (F), impedance (Z), and so on. The ability to measure the parameters ɛ′ and ɛ″ of the response function is one of the edges of dielectric spectroscopy over techniques such as Raman spectroscopy and neutron scattering, which only allow the imaginary part to be determined (Volkov & Chuchupal 2022). Since these parameters can be directly measured using the inductance (L), capacitance (C), and resistance (R) machine, it is particularly desirable to connect these parameters in a mathematical relation with the adulteration or purity level of the ZZ. Thus, this study employs an artificial neural network (ANN) to create a simple mathematical relationship among these dielectrical parameters, which can then be readily employed to determine the purity level of the ZZ at any local outlet.

ANN is a numerical modelling technique with the ability to detect and extract relationships, both linear and nonlinear, among interplaying variables in complex scientific systems and processes. Details of ANN architectures and applications can be found in Wang & Fu (2009), Khashei & Bijari (2014), and Abidoye & Das (2015). Simplifying the work of Abidoye et al. (2018), this work utilises the Tan-Sigmoid Transfer function (tansig) as a connection for the relationship among parameters of the dielectric spectroscopy and the purity level of ZZ. In this work, the Tansig function is expressed in a simpler version of the ANN-based equation of Abidoye et al. (2018). Generally, a tansig transfer function determines the output of the neural network layer from its net input. Tansig (N) generates its output (n) according to the following expression (Vogl et al. 1988):
(1)

The function takes/produces input/output between 1 and −1.

Tansig (N) takes one input, N (of S by the Q column vector), and returns each element of N squashed between −1 and 1. The Tan-Sigmoid function was found useful in modelling cardiac abnormality (Adnan et al. 2018); energy system (Tarafdar et al. 2018), and so on.

In the literature, the technique of DRS is usually found where there is a wide gap in the dielectric permittivity values of the samples in the mixture (Ávila et al. 2013). The technique was employed to determine the concentration of phosphate and nitrate in water (Harnsoongnoen 2021), volumetric fractions in water–ethanol mixture (Gocen & Palandoken 2021), glyphosate in water from herbicide (Méndez-Jerónimo et al. 2024), chlorine concentration in water (Abdelgwad & Said 2015), and so on. Most studies involving the technique are presented in the microwave frequency range. Only a very few exceptions are encountered. Among the few radio frequency demonstrations of DRS was the work of Shah et al. (2015). The authors applied DRS to distinguish coconut water and distilled water. However, the authors did not investigate the presence of water adulterants in coconut samples, nor did they develop a simplified equation for generic application. Furthermore, none of these applications of DRS can be found in the area of closely related substances like similar potable water from different sources. This is likely because of the close values of dielectric permittivity among such materials. Apart from the application of the technique in cases of dissimilar materials, the majority of these earlier investigations did not come up with simplified mathematical expressions to aid quick and easy quantification of the material purity.

So, the following questions arise from the above discussions: 1. Can we apply the low-frequency DRS technique in distinguishing similar materials from different sources like ZZ and well water? 2. What roles does the ionic content of ZZ play in the profile of dielectric permittivity? 3. How does the adulteration of ZZ with similar materials affect the dissipation factor profile? 4. Can a simplified technique be developed to capture the multi-parameter system of DRS to detect the purity level of ZZ?

With a view to answering the above research questions, this study presents the application of low-frequency DRS to closely related materials – ZZ and water from different sources – using a combination of experimental investigations with ANN modelling. This work investigates the dielectric properties of pure samples of the ZZ, local well water, and bottled commercial water. Dielectric properties, such as permittivity (ɛ′), loss factor (ɛ″), dissipation factor (D), frequency (F), and impedance (Z), were measured and interpreted in line with the compositional characteristics of each sample. Effects of adulterating ZZ with well water on dielectric properties were analysed and the resulting shifts in dissipation factor were investigated. An ANN-based equation, simpler than that of Abidoye et al. (2018), was developed to relate the dielectric spectroscopy parameters to the ZZ purity. The Tan-Sigmoid transfer function of ANN was employed to establish a mathematical relationship among interrelating variables of the dielectric spectroscopy and the water system.

A sample of the ZZ was obtained from the tap of the Holy Mosque in Makkah, Saudi Arabia, during the Hajj pilgrimage in June–July 2023. The sample was refrigerated for the storage period prior to experimentation. Well water was taken from a local well in Osun State, Nigeria. Also, the bottled water was purchased from the commercial stable of ‘Mr V’ purified water.

Some physicochemical characteristics of the water samples were determined using a hand-held pH, total dissolved solids (TDS), and electrical conductivity metre.

Dielectric spectroscopy

Dielectric characterisation was performed on the different water samples using an impedance analyser LCR instrument (EAST-TESTER, Guangzhou, China). The measuring range of the instrument was 10 Hz–1 MHz, with an accuracy of ±0.05% and an oscillating voltage of 1 V. Sample cell was made of square acrylic plastic with parallel copper plates as electrodes. Parameters like capacitance (C), impedance (Z), dissipation factor (D), and phase angle () were measured at the frequencies (F). Pure phases of the different water categories listed in Table 1 were tested. Also, blends of the ZZ with well water were tested at various proportions.

Table 1

Physicochemical characteristics of the water samples

ParameterZamzamWell waterBottled water
pH 7.77 6.02 6.04 
Temp (°C) 27 27 27 
Electrical conductivity (μS/cm) 665 130 
TDS (ppm) 317 58 
ParameterZamzamWell waterBottled water
pH 7.77 6.02 6.04 
Temp (°C) 27 27 27 
Electrical conductivity (μS/cm) 665 130 
TDS (ppm) 317 58 

The following relationships were employed to extract parameters of interest. The complex permittivity comprises real and imaginary ( parts, as expressed in the following equations (Darwish et al. 2014):
(2)
(3)
(4)

where is the real part of the complex permittivity () called dielectric permittivity. The imaginary part, , is the dielectric loss factor. ‘A’ is the area of the plate that serves as the electrodes, ‘d’ is the distance between the two parallel plates, , where is the frequency. is the permittivity of the vacuum. The capacitance at a set frequency is C(ω).

Dissipation factor (D) represents the energy loss per unit energy stored over a charge/discharge cycle:
(5)
(6)
where is the phase angle

ANN modelling

Following a similar procedure espoused in the work of Abidoye et al. (2018), this work presents an improved but simplified Tan-Sigmoid function model to detect the purity level of ZZ at the locality of consumption. As said earlier, the function takes input in the range of −1 to 1. Therefore, the mapminmax function was used in MATLAB to normalise the input variables between the required range (‘1’ and ‘− 1’). The input variables are ɛ′, ɛ″, D, F, and Z. The mapminmax function is expressed in the following equation:
(7)
where is the actual value of the parameter of interest among the independent variables and y is the normalised of any independent variable (ɛ′, ɛ″, D, F, and Z). ‘ymax’ is 1, and ‘ymin’ is −1. ‘min’ and ‘max’ are the minimum and maximum values of the parameter of interest, x, respectively.
The normalisation process was followed by weight and bias assignment at the hidden layer, based on the number of neurons present. Thus:
(8)
where is the nth sum of the weighted nth normalised independent variable () based on the ith neuron. ‘’ is the bias from the ith neuron. ‘j’ is the last count of neurons in the hidden layer.
To develop the tansig function for the detection of adulteration in ZZ water, Equation (8) is inserted into (1):
(9)
The procedure was followed by weighting at the output layer. Thus, the normalised output (k) becomes the following equation:
(10)
where ‘W0,i’ is the value of the weight at the output layer (o) associated with the ith neuron, and ‘bo’ is the outputlayer bias.
Finally, the output layer is normalised based on the ‘ymax’, ‘ymin’, ‘min’, and ‘max’ values. Thus, the denormalised ‘k’ value (kd) is determined as follows:
(11)
is the predicted value of ZZ purity. The above model is designed for a single-hidden layer ANN configuration, which can be applied to any number of neurons.

ANN configurations

Different ANN configurations were tested to arrive at the best-performing ANN model. But the primary aim is to obtain a simplified ANN-based model using the tansig function. A simplified model will make it easy for users to deploy the equation readily and effectively.

Single-hidden-layer configurations of ANN were designed for tests in this work. The number of neurons at the hidden layer was incrementally tested to arrive at a well-performing and simplified model. Therefore, 1, 2, and 4 neurons were differently tested at the hidden layer. These configurations were ANN[5-1-1], ANN[5-2-1]. and ANN[5-4-1]. The first digit (‘5’) represents the number of input variables (ɛ′, ɛ″, D, F, and Z). The second digit (‘1’, ‘2’, ‘4’) represents the number of neurons at the hidden layer. The last digit (‘1’) represents the number of output variables (ZZ purity)

Accuracy assessments for the models

The performances of the different models were assessed using the following mathematical criteria:

  • (1) Pearson product-moment coefficient of correlation (R)

  • This criterion measures the strength of linear dependence in the relationship between calculated and observed values of the output variable (ZZ purity). The closeness of ‘R’ to 1 indicates the highness of the prediction accuracy. A value of R = 1 indicates a perfect model. ‘R’ is computed as:
    (12)
  • are the averages of the observed and calculated output, respectively.

  • (2) Mean squared error (MSE)

  • This determines the average of the squares of the errors between the observed value (Sobs) and the calculated output value (Scal). It is expressed mathematically as follows:
    (13)
  • where N is the number of data points.

The physicochemical characteristics of the different water samples are shown in Table 1. It was interesting to note from the table that ZZ was slightly alkaline (pH of 7.7), signalling the high level of dissolved minerals, as evident from its highest TDS value (317 ppm) in the list. ZZ is rich in magnesium, calcium, fluoride, and other minerals (Ahmad et al. 2019). Moni et al. (2022) reported a pH of 8 for ZZ, which is very close to the value observed in this study. According to Dinka et al. (2015) and Biswas & Mosley (2019), the alkalinity level of water rises with the level of dissolved and particulate components. So, it is interesting that the high level of dissolved minerals in ZZ does not elevate the alkalinity value beyond normal. It can also be observed that ZZ has the highest electrical conductivity value (665 μS/cm). This can also be attributed to the high dissolved minerals in the water.

Moni et al. (2022) reported TDS and electrical conductivity (EC) values of 371 ppm and 718 μS/cm, respectively, for ZZ. These values are very close to the measurements in this study (317 ppm and 665 μS/cm) and point to the accuracy and consistency of the ZZ contents.

Figure 1 shows the error bar plots for the ZZ and well water samples. The figure shows that the measurement was very consistent. The error bars were so small they were invisible at most points except at the lowest frequency (10 Hz) for ZZ.
Figure 1

Error bar plots for (a) the ZZ and (b) well water.

Figure 1

Error bar plots for (a) the ZZ and (b) well water.

Close modal

In fact, nothing was visible in the case of well water. This pointed to the accuracy of the instrument and the care taken in these measurements.

Figure 2 is the plot of the dielectric permittivity plot for the three water samples.
Figure 2

Dielectric permittivity of the ZZ, well, and bottled water.

Figure 2

Dielectric permittivity of the ZZ, well, and bottled water.

Close modal

Figure 2 shows that the dielectric permittivity of all water samples decreases as frequency increases. The values of ɛ′ in ZZ range from 10 Hz to 1 MHz. For the well water, ɛ′ ranges from to for the same frequency range and from to for the bottled water. The results are in agreement with the report of Shah et al. (2015) and Vaja & Rana (2023). Shah et al. (2015) reported ɛ′ for distilled and coconut water from 20 Hz to 2 MHz. They reported ɛ′ for distilled water in the range (of 20 Hz) to (of 2 MHz). Vaja & Rana (2023) reported ɛ′ for distilled water in the range of at 20 Hz to at 1 MHz. Their results agreed largely with those reported in this work. A slight difference may be seen in the water content as a result of the geographical location of their water source (India). Also, the difference of one order of magnitude between their ɛ′ ( at 20 Hz for Vaja & Rana (2023)) and the current result for ZZ ( at 10 Hz) can be traced to the frequency difference at the starting point. It is known that ɛ′ decreases with frequency. So, the difference of 10 Hz (10–20 Hz) might be responsible for the one order of magnitude difference. Furthermore, the results agreed at the higher end of the frequency (1 MHz) as they remained in the same order of magnitude (.

Permittivity indicates the level of energy stored in the medium during an electromagnetic cycle. At lower frequencies, the water dipoles have enough time to orient in line with the applied electromagnetic field (Angulo-Sherman & Mercado-Uribe 2011; Darwish et al. 2014) and thus, are able to store more of the energy as expressed in high values of ɛ′. But, as the frequency increases, there is not enough time for the orientation of dipoles owing to the higher speed of passage. Thus, the materials store less energy at higher frequencies. The dielectric permittivity of the ZZ is higher than that of the well and bottled water at most frequencies. The values virtually coincide for all water samples at higher frequencies. This implies that the ZZ could store more electromagnetic energy than ordinary water. This could be attributed to the presence of vital minerals in the ZZ, giving the water molecular polarisation a tendency to orient in line with the electromagnetic wave passing through it. It could also be observed in the figure that the dielectric permittivities are linear, under a log–log plot, at lower frequencies till 1 kHz. It starts to become nonlinear near 10 kHz. Thus, the permittivity of the water samples is directly proportional to the frequency of the field at lower frequency values.

Figure 3 shows the loss factor in the water samples at various frequencies. The loss factor is inversely but linearly (log–log) proportional to the frequency of the applied electric field. It could be seen that the water of the Zamzam also maintains the highest magnitude in the loss of electromagnetic energy across the medium, while the least energy loss was recorded in the bottled water. The same bottled water recorded the lowest energy storage, as shown in Figure 2. The values of ɛ″ in ZZ range from at 10 Hz to at 1 MHz. For the well water, ɛ″ ranges from to for the same frequency range and from to for the bottled water. The results can be reasonably compared with those of Shah et al. (2015) and Vaja & Rana (2023). Shah et al. (2015) reported ɛ″ for distilled water from at 20 Hz to 8.42 at 2 MHz, while Vaja & Rana (2023) reported approximately at 20 Hz to 1 at 2 MHz for distilled water. The results of these authors can be compared with current results in this work. The authors reported lower ranges of the loss factor because of the distilled water used, which tends to contain fewer ions and therefore results in reduced conduction and lower ɛ″ (Jansson et al. 2010; Abdelgwad & Said 2015). In fact, the figure shows that the loss factor reduces with the concentration of dissolved ions in the water samples. Thus, the distilled water (reported by the authors) is expected to possess a lower loss factor.
Figure 3

The loss factor of the different water samples.

Figure 3

The loss factor of the different water samples.

Close modal

In the same vein, the lowest loss factor in bottled water can be traced to the low TDS (3 ppm), and low conductivity (μS/cm), which shows the non-conducting nature of its constituents. The bottled water sample does not have many mineral contents and so does not have many conducting molecules, thereby minimising its energy loss value while also affecting its energy storage similarly. This is also connected to the low electrical conductivity in the bottled water sample. As for the ZZ, the high loss factor could be attributed to the presence of various minerals, most of which are polar in nature, leading to high orientation ability under electromagnetic waves, while others are simply ionic, leading to loss of electromagnetic energy. The high TDS of the ZZ further shows magnitudes of various dissolved minerals in the sample that may be of various characteristics, which will give the water samples the observed values of the TDS and electrical conductivity. The loss factor in the well water was in the middle and could be connected to the moderate TDS and electrical conductivity in the sample. This shows that most of the content of the well water samples is relatively easily oriented under an electric field and can save more energy than losing or conducting it away.

According to Jansson et al. (2010), the Maxwell–Wagner–Sillars phenomenon dominates at low frequencies, whereby the dipoles align with the applied field and the ionic pairs migrate to the electrodes. Thus, the loss factor is higher at lower frequencies, especially where minerals and ions are present, as in ZZ. However, the ionic effect reduces at higher frequencies owing to fast-changing electrode polarities under AC. The dipoles also respond, albeit ineffectively, at higher frequencies, obeying Maxwell–Boltzmann statistics (Angulo-Sherman & Mercado-Uribe 2011). Thus, the loss factor reduces with frequencies similar to the dielectric permittivity.

Abdelgwad & Said (2015), though carried out in the microwave frequency range, reported a rise in loss factor with an increase in chlorine concentration in water, attributed to the increase in ion concentration that promotes conduction in the medium. Thus, the loss factor is higher where more conducting ions are present. However, the author shows that the permittivity decreases with an increase in chlorine concentration. Gocen & Palandoken (2021) show that ethanol in water reduces the permittivity of water while the loss factor rises and falls at lower and higher frequencies, respectively. It should be noted that these authors conducted their investigations at microwave frequency ranges for mixtures of different substances in water. However, the pure samples in this work reflect similar patterns of dielectric permittivity and the loss factor.

Particularly, the ZZ could be seen as a liquid of complex ions and molecules, which makes its permittivity and loss factor higher than others. Shah et al. (2015) pointed out that high-mineral solutions with diverse species of components tend to possess high ɛ′ and ɛ″ which agrees with the current results on ZZ, having the highest ɛ′ and ɛ″ among the water samples. At 20 Hz, the authors reported ɛ′ values of 3.36 and 1.02 for coconut water and distilled water, respectively. Coconut water with higher mineral content possesses higher ɛ′. On the other hand, the authors also reported values of loss factor of 7.47 and 2.07 for coconut water and distilled water, respectively, at 20 Hz. This shows coconut having higher ɛ′ and ɛ″ than distilled water because of various dissolved minerals. Thus, the current study found results that are consistent in scope with earlier findings.

Figure 4 shows the impedance profile of the different water samples. The impedance refers to the resistance of materials to current flow under AC fields. Here, the bottled water shows the highest impedance. This can be attributed to the very low mineral content of the bottled water. It can also be noticed that the impedance of the bottled water remains fairly unchanged until a higher frequency value of 50 kHz is reached, where the impedance starts to nosedive to a low value in a free-fall pattern. This shows that the high frequency of the electromagnetic field reduces the inhibition of the materials to AC. Thus, a high-frequency electromagnetic field can suppress the resistive property of the water. The ZZ has the least impedance to electromagnetic waves. This is connected to the presence of many minerals that permit current flow through the medium. The impedance of the well water was close to that of ZZ owing to its moderate mineral content, as revealed by the TDS reading shown in Table 1.
Figure 4

Impedance profiles of the water samples.

Figure 4

Impedance profiles of the water samples.

Close modal
In Figure 5, the effects of adulteration of ZZ with well water on the impedance values at various frequencies are shown. The addition of well water to the ZZ water raises the impedance value significantly. The impedance value increases as the adulterated water content increases. The well water is generally more resistive, as shown in Figure 4. Thus, its addition to ZZ raises the total impedance of the mixture. The mixture becomes more resistant to the applied field at various frequencies. Well, water was used for adulteration because of its availability and low cost, which may attract illicit acts of the perpetrators. The high price of bottled water will be a discouragement for use in adulteration.
Figure 5

Mixtures of well water with the ZZ.

Figure 5

Mixtures of well water with the ZZ.

Close modal
Figure 6 shows the dielectric permittivity values of the adulterated ZZ with well water. Unlike the impedance, the pure and impure samples are not easily distinguishable in the figure. At a very low frequency (10 Hz), the permittivity value of the pure sample (ZZ) was sandwiched between those of impure samples. They became indistinguishable at moderate and high frequencies. Thus, the impedance profile is more indicative of adulteration in ZZ water. Similarly, Figure 7 shows the loss factor of adulterated ZZ with well water. As shown in Figure 6, the profiles became indistinguishable at moderate and high frequencies. However, the pure ZZ retains the highest value at low frequency (10 Hz).
Figure 6

Dielectric permittivity of adulterated ZZ with well water.

Figure 6

Dielectric permittivity of adulterated ZZ with well water.

Close modal
Figure 7

Loss factor of adulterated ZZ with well water.

Figure 7

Loss factor of adulterated ZZ with well water.

Close modal

Dissipation factor at relaxation frequency

The dissipation factor indicates the ratio of energy loss in a material to the energy stored in it. This characteristic can serve as a distinguishing factor among materials of scientific interest. Figure 8 shows the dissipation factor between pure ZZ, bottled water, and pure well water. At low frequencies (10–200 Hz), the rate of dissipation of electromagnetic energy in ZZ was lower than that of well and bottled water. But, at higher frequencies (>200 Hz), the dissipation became higher in ZZ. It can be observed that there is a turning point at which the dissipation curve reaches the peak and starts to decline. This is referred to as a crossover point. This point occurs at a relaxation frequency (Shah et al. 2015) of 10 kHz in ZZ and well samples. At this point, the dissipation factors of ZZ and well water samples are approximately 63 and 53.2, respectively. Owing to substantial mineral content in ZZ and well water samples, crossover occurs at the same frequency. But for bottled water, the crossover occurs earlier at 1 kHz. This is attributed to the low mineral content in this sample. Furthermore, at its crossover point, the dissipation rate in ZZ exceeds other samples. Thus, the dissipation factor of well water trails that of ZZ by approximately 10 points.
Figure 8

Dissipation factor of the Zamzam and well water samples.

Figure 8

Dissipation factor of the Zamzam and well water samples.

Close modal
The dissipation factor plot for the ZZ samples adulterated with well water is shown in Figure 9. The figure shows that the presence of well water in the ZZ decreases the dissipation rate at the crossover point. In addition, the adulteration continues to shift the dissipation rate rightwards with the influence of adulterated water concentration. Precisely, there are reductions of approximately 7, 8, and 26%, respectively, in dissipation factor values at 3, 18, and 33% dilution of ZZ with well water at 10 kHz. At 33% dilution with well water, the relaxation frequency has been shifted to 100 kHz. Thus, the presence of foreign water in ZZ can be detected by the dissipation value at the relaxation frequency. The finding is in line with reports that shifts in resonance frequency in dielectric spectroscopy could be analysed for the quantification of volumetric fraction of mixtures both in the microwave (Gocen & Palandoken 2021; Hosseini & Baghelani 2021) and radio frequency range (Ávila et al. 2013). These shifts are often reported in the literature at frequencies above ultra high range (see, e.g., Ávila et al. 2013; Gocen & Palandoken 2021; Hosseini & Baghelani 2021). So, it is interesting to present a similar phenomenon for dissipation factors at ultra-low frequency range in this study. At the radio frequency range, Shah et al. (2015) reported unique relaxation peaks for distilled water and coconut water. These occur at separate relaxation frequencies and are dependent on temperatures. Their findings show that material behaviour around relaxation peaks can be used to detect and quantify adulteration and/or contamination.
Figure 9

Dissipation factor of pure and impure ZZ adulterated with well water samples.

Figure 9

Dissipation factor of pure and impure ZZ adulterated with well water samples.

Close modal

Artificial neural network

ANN was used to model the relationship between the parameters of dielectric spectroscopy. The results of the ANN modelling of the ZZ purity are presented in this section. ANN is efficient in capturing the multivariable complex relationship among water quality parameters (M'nassri et al. 2022) and its supply system (Sörensen et al. 2024).

Figure 10 shows that the networks learn the trends in the data very well without significant overfitting. This capability is demonstrated in the different configurations of ANN shown in the figure. Therefore, any of the trained networks has the ability to determine the purity of ZZ.
Figure 10

Performances of different neural network configurations based on the number of neurons at the single-hidden layer: (a) one neuron, (b) two neurons, (c) four neurons.

Figure 10

Performances of different neural network configurations based on the number of neurons at the single-hidden layer: (a) one neuron, (b) two neurons, (c) four neurons.

Close modal
Figure 11 shows the regression results of the ANN configuration with four neurons in the hidden layer (ANN[5-4-1]). The results made it clear that the network was effective and efficient in capturing complex trends among interacting variables of the dielectric spectroscopy and the water characteristics. The regression coefficient (R2) was closest to 100% (1) in all of the cases (training, validation, and testing).
Figure 11

Regression of ANN configuration with four neurons at the hidden layer.

Figure 11

Regression of ANN configuration with four neurons at the hidden layer.

Close modal
Figures 12 and 13 show similar plots for the configurations having two neurons and one neuron at the hidden layer- ANN[5-2-1] and ANN[5-1-1], respectively. The figures show excellent performances of the various configurations with regression coefficients of almost 100% (1). Thus, the good correlation between the interacting variables of the dielectric spectroscopy and the water characteristics makes ANN learning and prediction easy.
Figure 12

Regression of ANN configuration with two neurons at the hidden layer.

Figure 12

Regression of ANN configuration with two neurons at the hidden layer.

Close modal
Figure 13

Regression of ANN configuration with one neuron at the hidden layer.

Figure 13

Regression of ANN configuration with one neuron at the hidden layer.

Close modal
Therefore, since the different configurations perform excellently in capturing the trends among variables of the process, this study chose the simplest configuration (ANN[5-1-1]), having one neuron at the hidden layer, to build an ANN-based equation for the prediction of ZZ purity based on the tansig function. The procedure follows the steps highlighted in the following equation:
(14)

The resulting model is shown in Equation (14). The equation predicts the purity level of the Zamzam water. The model was built on five parameters of dielectric spectroscopy (ɛ′, ɛ″, D, F, and Z) to predict the purity level of the ZZ. The equation was a much simpler modification to the ANN-based equation espoused in the work of Abidoye et al. (2018). This is because the current ANN modelling approach eliminates tables of parameter values that accompany the model equation in the work of the authors. Hosseini & Baghelani (2021) stated that a simple set of equations, based on the analysis of the shift in resonance frequency, like in this work, could quantify the fractional components of mixtures.

The effectiveness of the model is demonstrated in Figure 14. The figure compares the predicted values of ZZ purity with the actual values measured in the laboratory. It could be seen that the model provides good matches for the actual data. This is especially true at the pure (100% ZZ) and fake (0% ZZ) levels. The performance of the model was also significantly higher in the middle range. This makes the model effective for use in detecting adulteration in the ZZ samples upon measuring the included parameters (ɛ′, ɛ″, D, F, and Z). A similar realisation was made by Liang et al. (2024) that ɛ′, ɛ″, and D are useful dielectric variables that are effective in detecting the level of adulterants in material samples.
Figure 14

Actual and Predicted Zamzam purity level using the Tansig-function model.

Figure 14

Actual and Predicted Zamzam purity level using the Tansig-function model.

Close modal

Firouz et al. (2022) and Khaled et al. (2021) also used ANN to model dielectric parameters in detecting adulteration in oil and identification of oil palm disease, respectively. Different ANN configurations were tried by Firouz et al. (2022) to arrive at a satisfactory model for dielectric spectroscopy at radio frequency. However, none of the authors developed a simplified equation that captures relevant parameters of the process that can be easily applied. This work is a great step to fill these gaps in the dielectric spectroscopy method radio frequency for monitoring the quality of potable water samples from different sources.

Overall, it has been shown that a combination of dielectric parameters can reliably be used to determine the purity of liquid samples. The unique source and components of ZZ, with characteristic dielectric properties, prove successful in detecting its purity and adulteration level with similar water but from different sources. While ZZ permittivity and loss factor represent its energy-saving and lossy characteristics, its dissipation characteristic presents the compact behaviour of its component ions and dipole molecules at every frequency as unique and different from similar materials but from other sources. The spectroscopic shift at the crossover point of the dissipation factor with the presence of external components is a unique way to determine the level of adulterants in the ZZ, and the method can be equally applied in material purity characterisation.

The current results and analysis are limited in scope to the frequency range – 10 Hz to 1 MHz. Also, further work is needed to relate the chemical and physical components of ZZ to its observed dielectric characteristics. Since literature reports of ZZ compositions have shown good consistency (see Donia & Mortada 2021; Moni et al. 2022) to the characteristics reported in this work, it is apt to link these constituent compositions and components to its overall dielectrical behaviour and purity. Furthermore, more water samples from rivers, taps, rain, and elsewhere may be investigated as a way of supporting the analysis in this study.

While common investigations utilised dielectric spectroscopy at microwave frequency to analyse mixtures whose components have widely – varying permittivity, this study successfully utilised the technique in distinguishing closely related materials – ZZ from well water, and bottled water samples. The dielectric permittivity (ɛ′), loss factor (ɛ″), dissipation factor (D), frequency (F), and impedance (Z) were measured for ZZ, well water, and bottled water. The dielectric permittivity and loss factor are higher in ZZ than in other water samples. Contrarily, the bottled water had higher impedance than others. The results point to the influence of mineral content as the most significant factor affecting the dielectric properties of the water samples. As indicated by its TDS value, ZZ comprises a high proportion of molecular and ionic components, giving it exceptional polarisability and higher permittivity values than common water samples in Nigeria. Similarly, the loss factor of the ZZ was higher than that of others, which was attributed to the presence of conducting ions in its mineral content. The unique relaxation peak value was detected for the ZZ, at which the characteristic dissipation rate was recorded. This occurred at a relaxation frequency of 10 kHz for the ZZ and well water samples. As for bottled water, the peak shifted leftward, which was attributed to its unnaturally low mineral content. The use of well water to adulterate the ZZ decreases the relaxation peak at the relaxation frequency while also shifting the frequency rightwards under the influence of adulterated water concentration. A simple ANN-based model, based on the Tan-Sigmoid function, captured the relationship between key dielectric variables and ZZ purity. Thus, the level of adulteration in ZZ can be easily measured using the simplified model. Overall, the work presented numerically assisted ultra-low frequency dielectric spectroscopy analysis as a cheaper alternative to the material quality analysis.

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.

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