PROCEEDINGS of the23rd International Congress on Acoustics
9 to 13 September 2019 in Aachen, Germany

Acoustic waves in piezoelectric plates in contact with gasoline
Iren KUZNETSOVA1; Anastasia KUZNETSOVA1; Boris ZAITSEV2; Andrey TEPLYKH2
1
2Kotelnikov Institute of Radio Engineering and Electronics of RAS, Russia

Kotelnikov Institute of Radio Engineering and Electronics of RAS, Saratov Branch, Russia

ABSTRACT
We studied the properties of SH0 wave in LiNbO3 plate which was in contact with gasoline. The
dependencies of phase velocity vs on parameter hf (h is a plate thickness, f is a wave frequency) wereplotted. The influence of various types of gasoline on the wave properties has been studied. In the future it
will be good to investigate influence of viscosity on the investigated parameters. The obtained results
confirmed that it is possible to develop a gasoline identifier based on SH0 wave in YX-LiNbO3 plate. It has
been found that the velocity of SH0 wave in YX LiNbO3 plate decreases with the increase of permittivity ofgasoline or its octane number. In this case the frequency decreases with growing gasoline octane number.

Keywords: gasoline identifier, lithium niobate plate, octane number

1. INTRODUCTION
Recent motor gasolines present as a rule mixtures of components which are obtained by using
various technological processes. Gasolines can contain more than 200 individual differently
structured hydrocarbons depending on the hydrocarbon composition of raw material whose content
and interaction define the gasoline properties. The quality of market gasoline components used in oil
refinery plants is assessed with the use of standard laboratory methods at the values of physical andchemical properties normalized with appropriate documents [1]. Such a procedure requires costequipment and complicated techniques. So the development of a sensor for the express analysis ofgasoline ɚɫquired at gasoline station is quite important. Such a sensor should allow one to identify
gasoline for its real octane number consistency with the gasoline octane number stated by a selling
office. The available papers suggest usually to evaluate the gasoline quality by its viscosity [2]. In
Ref. [3] they show a theoretical possibility of defining the viscosity and dielectric permittivity ofliquid using a quartz torsion resonator. Recently it was suggested to use the self-excited oscillator
the feedback of which contains the delay line based on the plate of Y – X lithium niobate withpropagating acoustic wave with shear – horizontal polarization [4] for realization gasoline identifier.
The liquid container with gasoline under study is placed on the path of acoustic wave. It has beenshown that the frequency oscillation is unambiguously connected with permittivity of gasoline,
which in one's turn is determined by its octane number [4]. In Ref. [5] it was suggested to realize thesensor for express analysis of gasoline octane number based on the lateral electric field excitedresonator. In this paper we discussed the properties of SH0 acoustic waves in structure “piezoelectricplate-gasoline”.

2. THE MEASUREMENT OF THE DEPENDENCE OF THE RELATIVEPERMITTIVITY OF GASOLINE ON ITS OCTANE NUMBER
It is obvious that for the development of the sensor for express analysis of the octane number ofgasoline one needs to know its parameter, which is unambiguously determined by its octane number.
As it has been pointed this parameter is permittivity. The Table 1 contains the region of admissible
values of permittivity for three values of octane number: 80, 92, 95 and their averaged values [6].
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kuziren@yandex.ru
zai-boris@yandex.ru

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Table 1 – Physical parameters of liquids
Octane number

80

92

95

The regions of admissible values of permittivity [6]2 – 2.062

2.08 – 2.115

2.145 – 2.205

Averaged values of permittivity [6]2.031

2.0975

2.175

Measured values of permittivity

2.084

2.148

2.2

The aforementioned grades of gasoline are standard for Russian market. We have measured thevalues of permittivity for these grades, which are also presented in the Table 1. Below the method ofthe measurement is described.
For measuring the permittivity the plane air capacitor with shear dimensions of 20×20 mm2 andwith the gap of 1 mm was fabricated. The capacity of this capacitor in air was measured with thehelp of LCR meter 4285A (Agilent). Then capacitor was immersed into sample of gasoline understudy and capacity was measured again. With the assumption that relative permittivity of the air isequal 1 the sought permittivity of gasoline was determined as ratio of capacity in gasoline andcapacity in air. The obtained data for three grades of gasoline are also presented in Table 1. One cansee that they are close to the values, which are taken from literature. Figure 1 shows the dependenceof measured permittivity of the gasoline on its octane number. It is evident that permittivity ofgasoline insignificantly increases with increase of the octane number.

3. THEORETICAL ANALYSIS
Let us consider the propagation of SH0 wave in a “vacuum – YX LiNbO3 plate – gasoline”
structure. The geometry of the problem is presented in Fig.1. We consider a two dimensional
problem where all field components are assumed to be constant in the x2 direction. To analyze thewave propagation at a fixed temperature we have used the motion equation, Laplace’s equation, andconstitutive equations for piezoelectric media [7]:x2

gasolinex10
YX LiNbO3x3
Figure 1- Geometry of the problem

U w 2U i wt 2wD j wx jwTij wx j

(1)

0,(2)

TijC ijkl wU l wx k  e kij w) wx kDjH jk w) wx k  e jlk wU l wx k,

(3)

(4)
.
Here U is medium density, Ui are components of mechanical particles displacement, t is time, Tij arecomponents of mechanical stress tensor, x j are coordinates, Dj are components of electricaldisplacement, ɋijkl, e ijk, and Hjk are elastic, piezoelectric and dielectric constants, respectively, and ) is2634

electrical potential.
We used the condition of quasistatic approximation:Ei w) wx i ,(5)where ȿi are the components of electric field intensity.
For liquid we have to use the motion equation, Laplace’s equation and constitutive equations in thefollowing form [8]:U lq w 2U ilq wt 2Tijlq

(6)

,lq
Cijkl
wU llq wxk .

wDilq wxiDilq

wTijlq wx j

(7)

0(8)

H lq w) lq wx i(9)Here İlq is permittivity of a liquid.
The mechanical and electrical boundary conditions at the plane x3=0 were written as [9]U 3 U 3lq ; Ti3 Tilq3) ) lq ; D3 D3lq .

(10)
(11)

We used gasoline with C||=1.0092 Pa/s and ȡ=800 kg/m3 for the study. Its permittivity changed ina range from 1.2 to 2.2. We considered the experimental case when parameter hf = 720 m/s (h is theplate thickness, f is the wave frequency). We used the material constants of lithium niobate from Ref.
[10]. The SH0 wave velocity for the YX LiNbO3 plate without adjacent liquid was 4413.291085 m/s
at hf = 720 m/s.
Fig.3 shows the fractional change in velocity of SH0 wave in the YX LiNbO 3 plate to decrease
with increasing permittivity of gasoline. The wave phase velocity changes from 4413.29 m/s up to4400.14 m/s with the increase of İlq from 1.2 to 2.2 when both surface of plate are electrically open.
Analysis has also showed that the presence of gasoline does not lead to noticeable attenuation of SH0wave (10-4 dB per wavelength).
Permittivity of gasoline

1.2

1.4

1.6

1.8

2.0

2.2

ǻV/V (%)

0-0.1

-0.2

-0.3
Figure 3 - Fractional change of SH0 wave velocity in the “gasoline – YXLiNbO3 plate-vacuum” structure
versus permittivity of gasoline at hf = 720 m/s

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4. CONCLUSION
We have theoretically studied the influence of various types of gasoline on the phase velocity ofSH0 wave in YX-LiNbO3 plate. In the future it will be good to investigate influence of viscosity on
the investigated parameters. The obtained results confirmed that it is possible to develop a gasoline
identifier based on SH0 wave in YX-LiNbO3 plate. It has been found that the velocity of SH0 wave inYX LiNbO3 plate decreases with the increase of permittivity of gasoline or its octane number. In thiscase the frequency decreases with growing gasoline octane number.

ACKNOWLEDGEMENTS
Work is done under goverment task of Kotelnikov IRE of RAS.

REFERENCES
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