Simulation of the Interaction between Liquids and the

4 downloads 0 Views 133KB Size Report
In this paper, the simulation and the time response for a solution flows between two interdigital transducers. (IDT) will be deduced. The flow of the solution ...
26th NATIONAL RADIO SCIENCE CONFERENCE (NRSC2009)

K08 March 17-19, 2009, Faculty of Engineering, Future Univ., Egypt

Simulation of the Interaction between Liquids and the Shear Horizontal Surface Acoustic Wave (SH-SAW) Mohamed A.A. Eldosoky Dept of Biomedical Eng, Faculty of Engineering, Helwan university e-mail: [email protected] Abstract In this paper, the simulation and the time response for a solution flows between two interdigital transducers (IDT) will be deduced. The flow of the solution causes perturbation that is shown as a frequency shift and an attenuation in the signal generated between the pair of the interdigital transducers. The time response of these perturbations show the effect of the different parameters in determining and distinguishing between the different solutions, where the steady state values are not sufficient for identifying the solutions. The proposed simulation shows acceptable results as compared to the experimental results. Keywords: Interdigital transducer, Surface acoustic wave.

1. Introduction Surface acoustic wave is a kind of acoustic waves that propagates on the surface of a piezoelectric substrate. The devices of the surface acoustic waves are used as gas and liquid sensors. Many kinds of these waves will be generated depending on the characteristics of the used substrate [1],[2]. Shear horizontal surface acoustic wave (SH-SAW) is a kind of these waves that is more sensitive for detecting the characteristics of the liquids flowing between the interdigital transducers (IDTs) [3]. SH-SAW sensors have been used for several applications, such as identification of the nature of the spring water and the chemical solutions [4],[5]. The general configuration of the SAW sensor consists of two interdigital transducers, one for generating and transmitting the wave and the second for receiving it. These IDTs with the fingers shape are on a piezoelectric substrate as shown in Figure 1. As changing the medium between these IDTs, a corresponding perturbation will be done [6],[7]. This perturbation may be summarized in either the frequency shift (the shift in the velocity) or in the attenuation of the transmitted signal or in the both. From these perturbations, we can extract the mechanical properties (such as the density and the viscosity) and the electrical properties (the conductivity and the permittivity) of any materials [8],[9].

Figure 1: The configuration of SAW sensor 26th NATIONAL RADIO SCIENCE CONFERENCE, NRSC’2009 Future University, 5th Compound, New Cairo, Egypt, March 17 – 19, 2009

1

26th NATIONAL RADIO SCIENCE CONFERENCE (NRSC2009)

K08

2

March 17-19, 2009, Faculty of Engineering, Future Univ., Egypt

Identification of the solutions is an important application of the shear horizontal surface acoustic waves (SHSAW). In [5],[10],[11], the investigators detect the responses of some solutions experimentally. These responses depend on flowing the solutions with the same flow rate for a certain time until the steady state case then pure water is injected after these solutions for a long time for determining the fall response. These solutions are KCl, NaCl, and LiCl. Depending on the electric parameters of these solutions, the time responses of these solutions will be deduced experimentally. In this paper, the simulation of these time responses will be proposed. This simulation depends on the combination between the used equation for determining the steady state values for the attenuation and the frequency shifts [12] and the equivalent circuit model for the surface acoustic wave sensor [13]. This proposed simulation will be used in determining the time response of any solution depending on the mechanical and the electrical components not the electrical components only. From this proposed algorithm, we can determine the time response of the solutions with different concentrations and different conductivities. The effect of the used frequency and the flow rate of these solutions can be observed easily than the experiments, where the time of each process reaches to about more than one hour. Especially, the simulated results give acceptable results as compared to the experimental ones.

2. Mathematical Treatment 2.1. Steady state perturbation In this part we discuss the mathematical model of the shear horizontal waves as flowing the liquid between its interdigital transducers. The steady state values of the perturbations due to the electrical characteristics of the liquid will be described by the following relationships [12]: 2 Δv K 2 (σ ω ) + ε 0 (ε rr − ε r )( ε rr ε 0 + ε p ) =− 2 v (σ ω ) 2 + (ε rr ε 0 + ε p ) 2

(1)

(σ ω )( ε rr ε 0 + ε p ) K2 Δα =− k 2 (σ ω ) 2 + (ε rr ε 0 + ε p ) 2

(2)

Where Δ v and Δ α are the velocity shift (the frequency shift) and the attenuation of the signal, respectively. v

k

2

K is the electromechanical coupling coefficient. the liquid sample, respectively. reference liquid,

σ

and ε rr are the conductivity and the relative permittivity of

ε 0 is the dielectric constant of free space. ε r is the relative permittivity of the

ε p is the effective permittivity of the used substrate.

2.2. Equivalent circuit model Here we will discuss the effect of each parameter. At the start of our simulation, the liquid will flow in a tube with length, L between the IDTs. The velocity of the propagation of the liquid depends on the density, the viscosity, the concentration, and the diffusion coefficient of the liquid. T is the transfer time of the liquid to reach the end of this tube. This time, T is function of the mechanical properties and the flow rate of the liquid. The equivalent circuit of the liquid-solid interaction at the steady state case will be deduced as shown in Figure.2. [12]:

26th NATIONAL RADIO SCIENCE CONFERENCE, NRSC’2009 Future University, 5th Compound, New Cairo, Egypt, March 17 – 19, 2009

26th NATIONAL RADIO SCIENCE CONFERENCE (NRSC2009)

K08 March 17-19, 2009, Faculty of Engineering, Future Univ., Egypt

G

i2

Cl

i1 Liquid

i

Solid

Cs

i3 Figure.2: The equivalent circuit for the steady state case for modeling the liquid-solid interaction.

C s = kε p

(3a)

C l = kε rr G = kσ

(3b) (3c)

k is the propagation constant. In the equivalent circuit model, the medium between the IDTs will be simulated as a capacitance C l . This capacitance will be in Farad/m2 (Farad per unit area) and will be expressed by the relative permittivity of the liquid times the propagation constant, k. In the proposed model for studying the time response, as flowing the liquid between the IDTs, the values of C l and G will change with the time and will be rewritten as shown:

Cl (t ) = kε (t ) G (t ) = kσ (t )

(4a) (4b)

As we discussed before, the time response will be determined from three stages: firstly, the water is injected into the tube. Secondly, the fluid is injected behind the water. Finally, the water is injected again after the solution as shown in Figure.3. Tube

l Interdigital transducer

Interdigital transducer L-l

l : the length of the liquid in the tube with length, L

L-l : the length of the pure water in the tube with length, L

Figure.3: Configuration shows the injection of the solution after the pure water at a certain time. 26th NATIONAL RADIO SCIENCE CONFERENCE, NRSC’2009 Future University, 5th Compound, New Cairo, Egypt, March 17 – 19, 2009

3

26th NATIONAL RADIO SCIENCE CONFERENCE (NRSC2009)

K08 March 17-19, 2009, Faculty of Engineering, Future Univ., Egypt - At time, t=0, the fluid will start to flow ( l=0) and the pure water fills the tube between the IDT. Consequently, the perturbation of the attenuation and the velocity shift is null. - During the time, T, the water and the sample liquid share each other in the total conductivity and the total permittivity under the area of the interaction. That is simulated as a capacitance that its value changes with the length of the fluid in it, l, where l is function of the time (l/L = t/T): and so its relative permittivity is equal to

ε (t ) = ε rr .(t T ) + ε r . (1 − t T )

Finally,

(5a)

ε rr in Eqs. (1) and (2) will be replaced by ε (t ) .

For calculating the total conductivity, the total admittance per unit area , G(t) of the liquid-water interaction will be presented the summation of

σl (t) + σ w (t) . Since the conductivity of the pure water is very low around 10-9

and is neglected as compared to the conductivity of the solution. Consequently, the total conductivity will be rewritten as shown: σ ( t ) = σ .t / T (5b) So that the transient response of the frequency and the attenuation perturbation from Eqs.(1) and (2) will be rewritten as functions of the time, t as shown: 2 Δv K 2 (σ ( t ) ω ) + ε 0 ( ε ( t ) − ε r )( ε ( t ) ε 0 + ε p ) (t ) = − v 2 (σ ( t ) ω ) 2 + ( ε ( t ) ε 0 + ε p ) 2

(6)

(σ ( t ) ω )( ε ( t )ε 0 + ε p ) Δα K2 (t ) = − 2 (σ ( t ) ω ) 2 + ( ε ( t )ε 0 + ε p ) 2 k Now, we will study the following cases: -

At t=0, the tube is filled with the water and so σ ( t ) = 0 and ε (t )

(7)

= ε r , and the values of

and Δ α will vanish.

Δv v

k

-

-

For 0