Extensive Journal of Applied Sciences Available online at www.ejasj.com ©2015 EJAS Journal-2015-3-7, 265-273

Effect of the ambient temperature on single bubble sonoluminescence in Deuterated acetone

Maryam Gheshlaghi

Payame noor University, P.O.B. 19395-3697, Tehran, Iran.

Laser and optics research school, Nuclear Science and Technology Research Institute (NSTRL), P.O.B. 11365-8486, Tehran, Iran.

Corresponding author: Maryam Gheshlaghi

ABSTRACT: The effect of gas solution, by using quasi adiabatic model, is studied on the emitted intensity of single bubble sonoluminescence in Deuterated acetone with ambient temperature 273K and 246K. Also the interior temperature and the interior pressure of single bubble sonoluminescence are measured and compared for single bubble sonoluminescence in Deuterated acetone in each of the mentioned temperature, with presence of noble gases: He, Ne, Ar, Kr and Xe. In both ambient temperature, the interior temperature, the interior pressure and the emitted intensity have increased. At ambient temperature 246K, the pressure increases too high while at 273K the emitted intensity increases so much as the molecular weight of the gas increases.

Keywords: Emitted intensity, Interior temperature, Interior pressure, Noble gas, Quasi adiabatic model.

INTRODUCTION

High temperatures, high pressures and light flashes due to Sonoluminescence (SL) are induced in intensive implosion of the gas or vapor bubbles by acoustic cavitation. Values of the mentioned parameters depend on buffer environment and type of the gas inside the bubble (Borissenok, 2008; Moshaii et al., 2008). Due to fast compression of the bubble, an enormous increase in temperature and pressure is noticed at the end of each oscillation cycle and light emission with continuous spectrum from IR to UV is obtained in the stage of bubble collapse. Following Gaitan’s achievement in producing a stable single-bubble Sonoluminescence (Gaitan et al., 1996; Gaitan et al., 1992), several studies have been conducted and different dynamical aspects and equations of Sonoluminescence in liquids with different ambient parameters have been studied (Moshaii et al., 2004; Sadighi-Bonabi et al., 2011). The dynamics of the bubble motion is characterized to a first approximation by the Rayleigh-Plesset equation coupled with the equation of gas pressure. Gas pressure Pa is related to the dynamics of Sonoluminescence and defined as the quasi-adiabatic, hydro chemical and isothermal models. Recently, Sonoluminescence has been used in Deuterated acetone (C3D6O) fluid for achieving the much higher temperatures needed for nuclear fusion inside the bubble (Taleyarkhan et al., 2004; Taleyarkhan et al., 2002). Various features of SBSL in He, Ar and Xe bubbles are investigated in water (Brenner et al., 2002; Moshaii et al., 2008). In this work, a numerical simulation method is proposed for calculating the fundamental parameters of the sonoluminescence in Deuterated acetone for ambient temperature 273K and 246K. Also the influence of all rare gas solutions on single-bubble sonoluminescence radiation is investigated in Deuterated acetone for same temperatures. The time variations of the bubble interior pressure and temperature due to the presence of the He, Ne, Ar, Kr and Xe, are compared. The emitted intensity, which depends on a bubble temperature according to the Bremsstrahlung model are also investigated and compared for the noble gas bubbles. These achievements are discussed in detail.

MATERIAL AND METHODS The Rayleigh-Plesset equation in association with an appropriate boundary equation governs the radial oscillations of the bubble (Lofstedt et al, 1995):

(1 −�̇�

𝐶) 𝑅�̈� +

3

2(1 −

�̇�

3𝐶) �̇�2 = (1 +

�̇�

𝐶) (

𝑃𝑙 − 𝑃∞

𝜌) +

𝑅

𝜌𝐶

𝑑𝑃𝑙

𝑑𝑡 (1)

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266

Where 𝑅, �̇�, �̈�, 𝜌 and C are the bubble radius, the bubble wall velocity, the bubble wall acceleration, the

density of fluid and the speed of sound in the host fluid, respectively. 𝑃𝑙 is the fluid pressure at the bubble wall (Imani et al., 2012) and 𝑃∞ is the fluid pressure (Ohl, 2000) far enough from the bubble:

𝑃𝑙 = 𝑃𝑔 −2𝜎

𝑅− 4𝜇

�̇�

𝑅 (2)

𝑃∞ = 𝑃0 + 𝑃𝑎(𝑡) (3)

Where 𝑃𝑔, 𝜎 and μ in Eq. (2) are the gas pressure at the bubble wall, the surface tension, and the fluid shear

viscosity, respectively. In Eq. (3), 𝑃0 = 1.031 𝑎𝑡𝑚 is an ambient pressure and 𝑃𝑎(𝑡) is an acoustic driving pressure as follows (Toegel et al., 2006):

𝑃𝑎(𝑡) = −𝑃𝑎 sin(𝜔𝑡) (1 −𝜋2|𝜒|2

6𝑅𝑓𝑙2 ) (4)

In Eq. (4), 𝑃𝑎 is the driving pressure amplitude, 𝜔 is the frequency, |X| is the bubble distance from the center of the resonator and Rfl = 3𝑐𝑚 is the resonator radius.

Interior gas pressure, 𝑃𝑔 is defined as:

𝑃𝑔[𝑅(𝑡)] = (𝑃0 +2𝜎

𝑅0

) (𝑅0

3 − ℎ3

𝑅3(𝑡) − ℎ3)

𝛾

(5)

Where 𝑅0 is the bubble initial radius, ℎ =𝑅0

8.86 is the Van der Waals hard core radius for Ar and γ is the effective

polytropic exponent (Hilgenfeldt et al, 1999a, 1999b). To calculate the Van der Waals hard core radius for other

gases, we have estimated this number by 𝑔𝑎𝑠 𝑎𝑡𝑜𝑚𝑖𝑐 𝑟𝑎𝑑𝑖𝑢𝑠

𝐴𝑟 𝑎𝑡𝑜𝑚𝑖𝑐 𝑟𝑎𝑑𝑖𝑢𝑠× 8.86 instead of 8.86 for Ar. The temperature changes

due to the bubble dynamics and the thermal conduction are described through the definition of γ. If the time it takes the bubble wall to oscillate is faster than the time scale of heat conduction through the bubble wall, the collapse will be (nearly) adiabatic and 𝛾 ≈ Γ, where Г=5/3 is the adiabatic exponent for mono-atomic gas. Away from collapse, the heat conduction is faster than the bubble wall motion, so that the bubble is (nearly) isothermal,

with γ=1. For the strong collapses of SL bubbles, using a time-dependent, instantaneous Pe´clet number γ is a

function of �̇�, 𝑅 and the gas temperature (Kwak & Na, 1996; Löfstedt et al, 1993; Sadighi-Bonabi et al., 2009; Yasui, 1997) T:

γ(Pe) = 1 + (Γ − 1)𝑒𝑥𝑝 (−𝐴

𝑃𝑒𝐵) (6)

𝐴 ≈ 5.8, 𝐵 ≈ 0.6 and Pe is the instantaneous Peclet number:

𝑃𝑒 = 𝑃𝑒(𝑡) =𝑅(𝑡)|�̇�(𝑡)|

𝜒𝑔𝑎𝑠(𝑅, 𝑇) (7)

Where γ(𝑃𝑒 → 0) → 1 (isothermal behavior, where thermal diffusion is dominant) and γ(𝑃𝑒 → ∞) → Γ =5

3

(adiabatic behavior, where advection is dominant) (Hilgenfeldt et al., 1999b). In Eq. (7):

χ𝑔𝑎𝑠

(R, T) =25

48Γ−1 (

πagas2 αT

δgas

)

0.5

G(g) (8)

𝑎𝑔𝑎𝑠 , 𝛼, 𝑇 and δgas are gas effective atomic diameter, ideal gas constant, gas temperature and gas molecular

weight, respectively. 𝐺(𝑔) is defined as:

𝐺(𝑔) =1

𝑔(

1

1 + 𝑐1𝑔 + 𝑐2𝑔2 + 𝑐3𝑔3+ 1.2𝑔 + 0.755𝑔2(1 + 𝑐1𝑔 + 𝑐2𝑔2 + 𝑐3𝑔3)) (9)

In which 𝑐1 = 0.625, 𝑐2 = 0.2869, 𝑐3 = 0.115 and:

𝑔 =2𝜋𝑁𝑎𝑎𝑔𝑎𝑠

3 𝑅03

3Κ𝜏𝑚𝑅3 (10)

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267

Na is Avogadro number and 𝜏𝑚 is a gas specific molar volume (Hirschfelder et al, 1954). The bubble temperature is obtained from an excluded volume van der Waals equation of state:

Pg

4𝜋

3(𝑅3 − ℎ3) =

4𝜋

3𝑅0

3𝜏𝑚𝛼 (11)

and regarding the thermal cooling of the gas in the boundary layer, it is given by (Hilgenfeldt et al., 1999b):

�̇� = −[𝛾(𝑃𝑒) − 1]3𝑅2�̇�

𝑅3 − ℎ3𝑇 − 𝜒𝑔𝑎𝑠

𝑇 − 𝑇∞

𝑅2 (12)

Where 𝑇∞ holds for the fluid temperature at infinity. It is assumed that the radiation is a result of three different processes: electron-ion Bremsstrahlung (the light emission from an electron accelerating in the coulomb field of a positive ion), electron-atom Bremsstrahlung (the light emission from an electron accelerating in the coulomb field of a neutral atom) and the radiative recombination of electrons and ions (the process in which an electron is captured in one of the ionic bound states and the emitted photon takes away the excess energy and momentum) which is the inverse process of photoionization (Rybicki and Lightman, 1979). In this model, it is assumed that the pressure and temperature are spatially uniform inside the bubble except at the thermal boundary layer near the bubble wall (Yasui, 1997). All the effects of thermal conduction between the bubble and the fluid, and also the presence of the water vapor as a result of chemical reactions at the bubble wall, are also taken into account. The emitted intensity of the electron-ion and electron-atom Bremsstrahlung collisions are (Yasui, 1997):

𝑃𝐵𝑟,𝑖𝑜𝑛 = 1.57 × 10−40𝑞2𝑁2𝑇0.54

3𝜋𝑅3 (13)

𝑃𝐵𝑟,𝑎𝑡𝑜𝑚 = 4.6 × 10−44𝑞𝑁2𝑇4

3𝜋𝑅3 (14)

q, N and T are degree of ionization, number density of atoms and interior temperature of the bubble, respectively. The degree of ionization, q is:

𝑞2

1 − 𝑞= 2.4 × 1021𝑇3 2⁄ 𝑒−𝜖𝑔𝑎𝑠 𝐾𝑇⁄ 1

𝑁 (15)

With 𝜖𝑔𝑎𝑠 as an ionization potential of the gas and K as the Boltzmann constant. In Eqs. (13)-(15), all the

quantities are expressed in SI units. The emitted intensity yields:

I = re(rrhplankv + PBr,ion + PBr,atom) (16)

In Eq. (16) re, rr, hplankv are escape rate of the emitted photon from the bubble, rate of radiative

recombination and mean energy of the photon emitted by radiative recombination, respectively. (Gheshlaghi, 2015) It should be realized that a group of atoms at a well-defined temperature will have a radiation source function which is the intensity of emitted radiation without taking into account the interaction of the emitted photons and the atoms corresponding to a Planck black body radiation spectrum (Gheshlaghi et al, 2015). The source spectral intensity (energy per unit time, wavelength interval, solid angle, and projected surface area) at wavelength is thus given by Planck’s law:

IλPl[T] =

2hc2

λ5[exp(hc0 λKBT⁄ ) − 1] (17)

h, KB and c0 are the Planck constant and Boltzmann factor and the speed of light in vacuum, respectively.

The emission changes with time according to the temperature changes T(t). By calculating the above equations, the SL bubble properties in Deuterated acetone, such as; the interior pressure, the interior temperature and the emitted intensity are compared for solution of five noble gases at two different ambient temperature individually that are presented in the next section.

RESULTS AND DISCUSSION

In this paper, a computer simulation of the gas bubble radiation is presented and is compared for various noble gas solutions in Deuterated acetone in ambient temperatures 246 and 273K. Therefore at first, the physical properties of Deuterated acetone are calculated in the mentioned temperature. The physical properties of

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Deuterated acetone are summarized in Table 1. The SL bubble is filled with noble gases and the bubble interior pressure, the bubble interior temperature and the emitted intensity are compared for He, Ne, Ar, Kr and Xe in each of the above temperature separately. The noble gases’ parameters are summarized in Table 2 (Flannigan and Suslick, 2005a, 2005b; Tsui, 1999).

Table 1. The physical properties of Deuterated acetone Ambient temperature T(K) 273 246

Density ρ( kg. m−3) 912.10 966.23 Surface tension σ (N. m−1) 0.0290 0.0339 Liquid viscosity μ(Pa. s) 4.42×10-3 47.2×10-3 Speed of sound C(m. s−1) 1004.32 864.79

Table 2. The noble gases characteristics

Noble gas Effective Atomic Radius Molecular Weight Specific Molar Volume (A) (Kg/mol) (mol/m3)

He 1.40 4.0E-3 2.2424E-2 Ne 1.54 2.0E-2 2.2414 E-2 Ar 1.88 3.9E-2 2.2392 E-2 Kr 2.20 8.4E-2 2.2356 E-2 Xe 2.16 1.3E-1 2.2300 E-2

In the present calculation 𝑃0 = 1.01325 × 105𝑃𝑎 is an ambient pressure. To ensure the required conditions for single bubble sonoluminescence, the driving frequency is 30.0 KHz, the driving pressure is 1.3 Pa and the bubble initial radius is 6 micron (Sadighi-Bonabi et al., 2011). The calculated results are shown in Figs.1-6. Figs. 1-3 show the various parameters of SBSL with of Deuterated acetone 273K as host liquid. And Figs. 4-6 show ones for Deuterated acetone 246 K. In all figures, horizontal axis is in terms of dimensionless time (t/T) at first cycle. T is period of the acoustic pressure.

Fig 1. The bubble interior temperature at the collapse time for SBSL Deuterated acetone 273K in the present of He, Ne, Ar,

Kr and Xe

In Fig 1 is seen that the bubble interior temperature maximum at the collapse time for SBSL Deuterated acetone 273K increase from 4600 to 32900K as the noble gas molecular weight increases.

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269

Fig 2. The bubble interior pressure at the collapse time for SBSL Deuterated acetone 273K in the present of He, Ne, Ar, Kr

and Xe

Fig. 2 shows that the bubble interior pressure maximum at the collapse time for SBSL Deuterated acetone 273K increase from 5300 to 36000 atm as the gas molecular weight increases.

(a)

(b) (c)

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270

(d) (e) Fig 3. (a) The emitted intensity at the collapse time for SBSL Deuterated acetone 273K in the present of He, Ne, Ar, Kr and

Xe, (b)-(e) Enlarge (a) for more clarity

Because of the large difference in pain intensity, Fig. 3 has five part. Fig. 3(a)-(e) show that the emitted

intensity maximum at the collapse time for SBSL Deuterated acetone 273K increase from 1.35 × 10−10 to 1.93 𝑤

𝑚2 ⁄ as the gas molecular weight increases.

Fig 4. The bubble interior temperature at the collapse time for SBSL Deuterated acetone 246K in the present of He, Ne, Ar,

Kr and Xe

In Fig 4 is seen that the bubble interior temperature maximum at the collapse time for SBSL Deuterated acetone 246K increase from 7900 to 35970K as the gas molecular weight increases.

Fig 5. The bubble interior pressure at the collapse time for SBSL Deuterated acetone 246K in the present of He, Ne, Ar, Kr

and Xe

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Fig 5 shows that the bubble interior pressure maximum at the collapse time for SBSL Deuterated acetone 246K increase from 68000 to 105700 atm as the gas molecular weight increases.

(a) (b)

(c) (d)

Fig 6. (a) The emitted intensity at the collapse time for SBSL Deuterated acetone 246K in the present of He, Ne, Ar, Kr and Xe for one cycle, (b)-(d) Enlarge (a) for more clarity

Fig 6 is fragmented Like Fig. 3. Fig. 3(a)-(d) show that the emitted intensity maximum at the collapse time

for SBSL Deuterated acetone 246K increase from 2.6 × 10−8 to 11.64 × 10−2 𝑤 𝑚2 ⁄ as the gas molecular weight

increases. The above figures show parameters of SBSL depend highly on the gas type. Tables 3 and 4 show maximum of the various parameters of SBSL Deuterated acetone 273 and 246 K in the present of He, Ne, Ar, Kr and Xe, respectively.

Table 3. Maximum of the various parameters of SBSL Deuterated acetone 273 K in the present of noble gases

Interior temperature Interior pressure Emitted intensity

T(K) P(atm) I(W/m2)

He 4600 5300 1.35E-10 Ne 11600 17000 7.00E-5 Ar 18800 26000 9.20E-3 Kr 29000 34000 0.72 Xe 32900 36000 1.93

Table 4. Maximum of the various parameters of SBSL Deuterated acetone 246 K in the present of noble gases

Interior temperature Interior pressure Emitted intensity

T(K) P(atm) I(W/m2)

He 7900 68000 2.6E-8 Ne 14129 81000 1.5E-5 Ar 19000 90050 4.1E-4 Kr 31500 104000 4.9E-2 Xe 35970 105700 11.64E-2

Figs 7-9 show the change in maximum interior temperature, interior pressure and the emitted intensity of SBSL Deuterated acetone, respectively in two ambient temperature, for various noble gases

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Fig 7. The change in maximum interior temperature of SBSL Deuterated acetone in two ambient temperature, for various

noble gases

Fig 8. The change in maximum interior pressure of SBSL Deuterated acetone in two ambient temperature, for various noble

gases

Fig 9. The change in maximum emitted intensity of SBSL Deuterated acetone in two ambient temperature, for various noble

gases

CONCOLUSION

The effect of the gas solution on the bubble properties for SBSL in Deuterated acetone is investigated. It is shown that for SBSL, by increasing the gas molecular weight, the bubble interior temperature, the bubble interior pressure and the emitted intensity increase. Also, the increment of the gas molecular weight can induce a great difference in the intensity profile. In spite of the mentioned simulation is run by two different ambient temperatures, the above parameters are the same trend. Expect that in ambient temperature 246 K, the interior pressure has

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risen strongly. And the emitted intensity, in ambient temperature 273 K, rises too high. So it seems that the decreasing of ambient temperature can increase the interior pressure, as well as decrease the emitted intensity for SBSL Deuterated acetone.

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