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

Study of shear-horizontal waves in structure “piezoelectric-viscousand conductive liquid”
Iren KUZNETSOVA1; Vladimir KOLESOV1; Vladimir ANISIMKIN1; Zhenghua QIAN2; Feng ZHU2;
Alena GORBUNOVA3
1

Kotelnikov Institute of Radio Engineering and Electronics of RAS, Russia
23Nanjing University of Aeronautics and Astronautics, China

M.V. Lomonosov Moscow State University, Physical Dept., Russia

ABSTRACT
Recently it has been found that velocity of shear-horizontal surface acoustic waves initially increase as theconductivity of the layer located on the surface of the piezoelectric medium increases. At a certain value ofconductivity the velocity of such waves reaches a maximum and with a further increase in conductivity
begins to decrease. The same effect was found for conductive liquid and shear horizontal wave inpiezoelectric media. In this work the influence of viscosity of a liquid on the magnitude of this effect istheoretically studied. It was found that for Bleustein-Gulyaev wave in cadmium sulfate as the viscosity of aliquid increases the value of above effect decreases and at a certain value of viscosity it disappears. We
used a liquid characterized by low permittivity as 2.5. The results obtained can be useful in thedevelopment of sensors for biological liquids.
Keywords: Bleustein-Gulyaev wave, CdS, viscous and conductive liquid

1. INTRODUCTION
It is well known, that the change of electrical and mechanical boundary conditions leads to thesignificant changes of the acoustic wave parameters [1]. This effect is very useful for developmentof various acoustic sensors. One type of such sensors are devices that work in contact with a liquid[2]. The biological sensors can be implemented based on such devices. The waves with ashear-horizontal polarization are usually used for the design of such sensors [3]. These waves arecharacterized by a weak emission of acoustic energy in a liquid medium [4]. One of these types ofwaves are the Gulyaev-Blustein waves [5]. It has recently been shown that when the conductivity ofa fluid changes in contact with a piezoelectric, an anomalous resistive-acoustic effect (ARAE)
occurs [6].
This effect consists in increasing the velocity of the acoustic wave as the conductivity of the layer
located on the surface of the piezoelectric medium increases [7]. When a certain value of theconductivity of the contacting medium is reached, the velocity of the Bleustein-Gulyaev wave
reaches a maximum, and with a further increase in conductivity begins to decrease. This effect has
the most value for potassium niobate due to its high level of piezoactivity [7].
It is necessary to note that very often the biological liquids are characterized by various value ofviscosity. From this point of view, it has interest to study how viscosity can influence on value of
aforementioned anomalous resisto-acoustic effect [8].
In this paper, the influence of the viscosity of a liquid on the magnitude of this effect in cadmium
sulfide is studied.

2. THEORETICAL ANALYSISThe propagation of Bleustein-Gulyaev wave in a structure “YX cadmium sulfide - conductive andviscous liquid” has been analyzed. The geometry of the problem is presented in Fig.1.
12kuziren@yandex.ru
qianzh@nuaa.edu.cn637

x2

conductive+viscousx1

liquid0

CdS

x3
Figure 1- Geometry of the problem
For theoretical analysis the equation system consisting of elastic medium motion equation (1),Laplace’s equation (2), and piezoelectric crystal state equations(3), (4) were used [9]U w 2U i wt 2wD j wx jwTij wx j

(1)

0,(2)

Tij

C 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 ) iselectrical potential.
We used the condition of quasistatic approximation:

Ei w) wx i ,(5)where ȿi are the components of electric field intensity.
It is necessary to write the equation system for viscous conductive and isotropic liquid in
Maxwellian representation [6, 10, 11]:

U lq w 2U ilq wt 2wTijlq wx j,*lq
C ijklwU llq wx kTijlq

(6)
(7)

.

*lq
Cijkl

are liquid density and its complex elastic constants, respectively. The nonzero
Here ȡlq andcomponents of the liquid elastic constants in matrix form are given by
*

*

*lq
C11lq C 22
C 33lq C11lq  jZK 11lq*
*lq *C12lq C13lq C 23
C12lq  jZK 12lqlq *lq *lq *lq
CCCjZK 44445566.

(8)

where K11 and K 44 are longitudinal and shear components of viscosity, Ȧ is angular frequency of thelqlq

wave, and j = (-1)1/2 is the imaginary unit. K 12 K 11  2K 44 .
Due to the liquid is not only viscous but also conductive we have to write the Poisson equation andthe charge conservation equation:

638

lqlq

wDilq wx i

G lqlq(9)

wJ ilq wx i  wG lq wt

(10)

J lq

Here Dlq , įlq, and i are the components of electrical displacement, space charge density, andcomponent of the current density, respectively.
The constitutive equations for liquid areH lq w) lq wx i(11)V lq w) lq wx i  d lq wG lq wx i(12)

Dilq
J ilq

Here İlq , ılq, and dlq are permittivity, bulk conductivity, and diffusion coefficient of liquid.
The mechanical and electrical boundary conditions at the plane x3=0 were written asUi)

U ilq ; Ti 3) lq ; D3

Ti 3lqD3lq ; J 3lq(13)0(14)The above equations with the boundary conditions have been solved by the method described in [5].

3. RESULTS AND DISCUSSION
We calculated the dependency of the phase velocity of a Bleustein – Gulyaev wave in YX
cadmium sulfide crystal on a bulk liquid conductivity for different values of a liquid viscosity. We
found that anomalous resisto-acoustic effect exists for all investigated values of the liquid viscosity;i.e. the velocity of the Bleustein-Gulyaev wave rises, reaches its maximum, and then falls as theliquid bulk conductivity grows. The analysis shows that the value of positive change in the phasevelocity due to ARAE ('V/V)+ max increases with increasing the liquid viscosity. The corresponding
dependence is presented in Fig. 2.
0.35
0.35

('V/V)+max (%)

0.30
0.30
0.25
0.25
0.20
0.20
0.15
0.15
0.10
0.10
0.05
0.05
0.00
0-310
1.E-06

1.E-05

1.E-04-210
1.E-03

1.E-02

1.E-01-110
1.E+00

1.E+01

1.E+021
1.E+03

Shear viscosity of liquid (kPa x s)
Figure 2- Dependence of the value of positive change in the phase velocity of Bleustein-Gulyaev
wave in YX CdS due to ARAE versus shear viscosity of liquidPreviously [8, 12] it was shown that for strong piezoelectric like potassium niobate the value of
positive change in the phase velocity due to ARAE ('V/V)+ max decreases with increasing the liquidviscosity. Previous analysis shown that the increasing the liquid viscosity leads to reducing the639

Bleustein-Gulyaev electric field penetration depth [8]. In connection with this increase in the liquid
conductivity has a weak effect on the BG wave localization depth for strong piezoelectrics, which inturn leads to a decrease and then disappearance of the anomalous resisto-acoustic effect. But for
weak piezoelectric like CdS increase in the liquid conductivity has a strong effect on the BG wave
localization depth, which in turn leads to a increase of the anomalous resisto-acoustic effect.

4. CONCLUSION
The influence of the liquid viscosity and conductivity on the characteristics of Bleustein-Gulyaev
waves was considered. It has been found that the value of positive change in the phase velocity due
to anomalous resisto-acoustic effect increases with increasing the liquid viscosity for weakpiezoelectrics. This could be explained by the fact that the increasing the liquid viscosity leads toreducing the Bleustein-Gulyaev electric field penetration depth. In connection with this increase in
the liquid conductivity has a strong effect on the BG wave localization depth in weak piezoelectrics,
which in turn leads to a increase of the anomalous resisto-acoustic effect. Obtained results can beused to better understand the fundamental physics of the propagation of weakly inhomogeneous
piezoective waves. Also it can be used for development of acoustic liquid viscosity sensors

ACKNOWLEDGEMENTS
Work is supported by the grant #18-57-7802 from Russian Basic Research Foundation.

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