## 3 Results
### Limits of Detection of Water and Isopropanol Admixtures in Gasoline Solutions  
The sensitivity of admixture detection was further enhanced when the quartz glass cuvettes were replaced by the TPX cuvette offering the longest optical paths of \(l=10.00\) mm. We have verified in a separate measurement that despite its thicker 5 mm walls, as compared to the 1.25 mm walls of the quartz cuvettes (Section 2.1), the TPX cuvette was characterized by a much lower transmission loss of \(\sim\)1-5 dB over the whole pulse bandwidth. The corresponding transmission loss of quartz cuvettes was \(\sim\)14-45 dB. The 2\(f\) quasi-optical beam delivery setup was chosen because, only in this case, the Rayleigh lengths of all spectral components of the THz pulse could be sufficiently longer than the propagation lengths in the cuvette. The new set of gasoline samples containing only small concentrations of admixtures was prepared. The corresponding mass fractions of isopropanol and water were 0-2000 ppm and 0-3000 ppm, respectively. The results obtained in this experimental configuration are shown in Figure 10.  
In agreement with previous observations, the measured pulse delays exhibited a linear dependence on both isopropanol and water mass fractions, \(\phi_{1}\). This is confirmed by numerical line fitting to the measured data points represented in Figure 10 by dash-dotted lines. The main difference was the agreement with the model of the refractive index of the mixture. While a fairly good correspondence can be observed for isopropanol-gasoline samples, for which the measured pulse delays points are situated along the continuous red line, representing theoretical calculations, the agreement for water-containing samples cannot be confirmed. All measured points lay below the theoretical line and have substantially shorter TOFs than predicted by the calculations. Moreover, we have observed a reverse trend of decreasing pulse delays with an increasing water mass fraction above the 3000 ppm  
Figure 10: The THz pulse delays measured as the function of admixture concentrations by their mass fractions \(\phi_{1}\) below 3000 ppm. (**a**) For isopropanol: \(\phi_{1}\) = 0, 125, 250, 500, 1000, 2000 ppm; (**b**) for water samples \(\phi_{1}\) = 0, 250, 500, 1000, 2000, 3000 ppm. The solid lines represent theoretical dependence according to the Gladstone-Dale mixing rule given by Equation (11), and the dash-dotted lines represent the numerical fits. Note a good agreement between the theory and measurements in the case of isopropanol-gasoline admixtures and the discrepancy in the case of water-gasoline mixtures. mass fraction of water. All this suggests that a simple, quasi-binary mixture model of the refractive index is not applicable in this case. It is well known that water is not miscible with gasoline. These two fractions will tend to separate depending on their relative concentrations in a mixture and environmental conditions [4; 40; 41]. Water forms complexes with gasoline containing liquid phase water and gasoline-water emulsions. Both fractions tend to separate, and the heavier water fraction sediments at the bottom of the cuvette by the presence of pure gasoline. This is why gasoline becomes a dominant fraction in the remaining volume of the liquid. Eventually, this trend causes the THz pulse to reverse because the incident radiation is exposed to a lower refractive index of gasoline. It is important to note that similar conclusions were drawn for other petrochemicals like diesel or crude oils emulsions as reported in [13; 14; 42; 43; 44; 45]. The fact that for water-gasoline mixtures, the delays of the THz pulses cannot be accurately predicted by ab initio calculations is of minor importance from the practical point of view of water detection. The empirically measured linear relation between \(\Delta t\) and \(\phi_{1}\) can still be used, providing an initial calibration with gasoline samples containing known concentrations of water is made before THz-TDS TOF measurements.