Quantitative and Qualitative Characterization of Liquid Materials - Broadband Reflectometry for Enhanced Diagnostics and Monitoring Applications - page 77

through VNA-based measurements), despite being affected by a higher uncertainty.
The higher uncertainty is most probably due to the fact that the relaxation frequen-
cies of 1,1,1-trichloroethane and of ethyl acetate are much higher than the upper
limit individuated for the optimization of the model (i.e., 4 GHz) and even higher
than the frequency limit of the used TDR instrument (i.e., 15 GHz). In fact, addi-
tional measurements on ethanol (whose f r is in the order of 1 GHz) [12], provided
accurate results for all the four Cole-Cole parameters, thus validating the appropri-
ateness of the proposed procedure. The four Cole-Cole parameters for ethanol and
the related experimental uncertainties are reported in Table 4.10.

Ta b l e 4 . 1 0 Comparison between the reference and the evaluated Cole-Cole parameters (at
20.8 ◦ C) for ethanol. The experimental uncertainties for the evaluated values are also reported

ethanol

parameter reference averaged experimental

value evaluated uncertainty

[12] value

ε s 25 . 04 ± 0 . 04 24.57 0.02

. ± .

ε ∞ 4 481 0 027 4.15 0.05

f r (GHz) 0 . 856 ± 0 . 004 0.92 0.01

β 0 . 00 0.00 0.00

4.4.2 Experimental Results for Vegetable Oils

When the proposed procedure was first applied to vegetable oils, the resulting val-
ues of the dielectric parameters were affected by a relatively high uncertainty. Ad-
ditionally, the obtained results were rather different from the data available in the
literature. In particular, the values of the relaxation frequencies were systematically
overestimated.
The reason for this discrepancy could be mostly attributable to some intrinsic
properties of the oils: these characteristics make the minimization over the four
Cole-Cole parameters 4 rather troublesome. In fact, oils are known to exhibit a re-
laxation frequency 5 lower than 1 GHz; additionally, their dielectric properties antic-
ipate a low value of the dielectric increment ( ε s − ε ∞ ).

On such bases, to reduce the number of variables to optimize, the values of the
static permittivity were assessed through an alternative method, and the minimization
routine was performed over the remaining three Cole-Cole parameters (i.e.,

β , ε ∞ ,and

ε s of the oils was performed through independent capacitive
measurements carried out with an LCR meter. This strategy was deemed as the best
solution to obtain accurate results over the whole considered frequency range.
4

f r ). The evaluation of the

For vegetable oils, static electrical conductivity is practically zero.

5

As reported in [19], vegetable oils exhibit a first dielectric relaxation at approximately
1 MHz; however, this first relaxation was not considered in the analysis reported herein.