Thermal characterization of nanofluids using laser induced thermal lens technique Achamma Kurian*a, Rajesh B. Kumara and Sajan D. Georgeb$ a Catholicate College, Pathanamthitta, Kerala, India -689645; b Center for Smart Interfaces, TU Darmstadt, Petersenstraße 32, 64287, Darmstadt, Germany E mail: *[email protected] or [email protected] ABSTRACT A laser induced thermal lens technique has been employed to evaluate the dynamic thermal parameter, the thermal diffusivity, of gold nanofluids. Gold nanoparticles were synthesized by citrate reduction of HAuCl4 in water. The UVVIS optical absorption spectra show an absorption peak around 540 nm owing to surface Plasmon resonance band of the gold particles. The thermal diffusivity of gold nanoparticles was evaluated by knowing the time constant of transient thermal lens obtained by fitting the experimental curve to the theoretical model of the mode-matched thermal lens. Analyses of the results show that the nanofluid exhibits lower thermal diffusivity value in comparison to the host medium, water. Further investigations also reveal that the concentration of nanoparticles in the fluid have influence on the measured thermal diffusivity value. Results are interpreted in terms of interfacial thermal resistance around the nanoparticles as well as on the clustering of nanoparticles. Keywords: Thermal lens, gold nanofluids, thermal diffusivity.

1. INTRODUCTION Technological development in microelectronics and optoelectronic industry results in miniaturized systems with high efficiency. However, cooling of these devices often pose technical difficulty in various industries such as microelectronics, transportation, solid state devices, micro and nano channel devices. The conventional approach of increasing the heat exchange area is practically impossible with small scale devices. In the last decade, nanofluids are emerged as potential candidate for heat exchange and transport in micro and nano devices. Nanofluids are solid-liquid composite consisting of nanoparticles (1-100 nm) dispersed in a host media. Though initially nanofluids gained much attention as a nanoengineered coolant, in recent years, there has been a serious controversy about whether nanoparticles in liquid actually enhance the thermal conductivity or not. Many of the experimental studies with well dispersed nanoparticles show modest enhancement in thermal conductivity consistent with Maxwell mean field theory while a few other reports shows substantial increase in the thermal conductivity value. The on-going controversy in this field can be mainly attributed to lack of understanding on the heat conduction mechanism in nanofluids as well as to the experimental methodology employed to measure the thermal parameters. In the last couple of years, non-contact optical techniques have been employed to measure thermal parameters of nanofluids. In this work, we utilize non-contact dual beam modeNanophotonic Materials VI, edited by Stefano Cabrini, Taleb Mokari, Proc. of SPIE Vol. 7393, 73930U · © 2009 SPIE · CCC code: 0277-786X/09/$18 · doi: 10.1117/12.826233

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matched thermal lens technique to measure the thermal diffusivity of nanofluids with different concentration of nanoparticles. Despite a large number of investigations on effect of nanoparticle size, concentration, shape etc. on the thermal conductivity of nanofluid, only a very little number of published works focused on the measurement of thermal diffusivity of nanofluids. However, thermal diffusivity in nanofluids is extremely important in convective heat transport mechanisms. Photothermal techniques based on thermal wave physics has emerged as an effective research and analytic tool for the evaluation of thermal, optical and transport properties of matter in its different states. Amongst various photothermal techniques, the thermal lens technique offers certain advantage such as its response to even small absorption coefficient as well as accurate measurement of thermal parameters. The method is based on the optical measurement of the thermal energy released by a sample subsequently to light absorption and nonradiative relaxation of the excited species. In this method sample is illuminated using a gaussian beam. A part of the incident radiation is absorbed by the sample and subsequent nonradiative decay of excited state population results in local heating of the medium. The temperature distribution in the medium mimics the beam profile of the excitation beam and hence a refractive index gradient is created in the medium. Due to this modification in refractive index, the medium act as a lens, called thermal lens (TL). The thermal lens generally has a negative focal length since most materials expand upon heating and hence have negative temperature coefficient of refractive index. The formation of the thermal lens causes the probe beam to expand and is detected as a time dependent decrease in power at the center of the beam at far field. Most of the currently employed techniques for thermal parameter evaluation are mainly depending upon the heat exchange mechanism or on temperature gradients. However, the thermal lens technique depends upon change in refractive index due to nonradiative deexciation of sample following the optical excitation can offer accurate results. As thermal diffusivity of nanofluids is one of the least explored quantities and have great significance in device fabrication, the present investigation on this parameter using highly sensitive thermal lens technique have great physical and practical significance. Moreover, in this work we also focused on influence of concentration of nanoparticles in the host media and can thus give better understanding about how heat transport mechanism in nanofluids and are affected by concentration of the constituent.

2. THEORY The magnitude of the effective thermal lens produced by propagation of a cw Gaussian laser beam of spot size

ω

is

governed by the steady state balance between laser heating and solvent or matrix heat dissipation. If the beam is suddenly turned on at time t=0, the lens approach to steady state governed by [1, 2]

f (t ) = f ∞ (1 + t c / 2t ),

(1)

and the steady state focal length f∞ of such a lens is derived as

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f∞ =

π kω 2

(2)

PA ( dn / dt )

where k is the thermal conductivity (W cm-1 K-1), P is the laser power (W), A is the sample absorbance, dn/dt is the refractive index change with temperature and tc is the time response to attain the steady state focal length given by

tc =

ω2 4D

.

(3)

from which D can be calculated. The thermal diffusivity in the sample is detected by its effect on the propagation of the probe laser beam aligned with the centre of the lens. The expression relating the intensity as a function of time is given as

⎡ ⎤ θ θ2 I (t ) = I (0 ) ⎢1 − + 2⎥ ⎣ 1 + tc / 2(t ) 2(1 + tc / 2(t ) ) ⎦

(4)

We have modified this equation for cw laser source as

I (t )

⎡ ⎤ θ θ2 = I (0 ) ⎢1 − + 2⎥ ⎣ 1 + tc / 2(t − t0 ) 2(1 + tc / 2(t − t0 ) ) ⎦

−1

(5)

where t0 is the time at t=0, θ is directly proportional to Pth by the relation

θ =

Pth (dn / dT ) λk

(6)

where Pth is the laser power degraded to heat and λ is the laser wavelength. For a given solvent or matrix the experimental parameter of interest is θ, which may be obtained from the initial intensity I 0 and the intensity after the steady state has been established, I ∞ ,so that

θ = 1 − (1 + 2 I )1 / 2 , I=

(7)

I0 − I∞ I∞

The initial slope of the decay curve,

from which the value of

(8)

m=

2θ I 0t c

(9)

tc and hence D is calculated.

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3. SAMPLE PREPARTION 50 ml of 0.01% HAuCl4 solution is heated to boiling and while stirring, a few hundred μl of 1% (by weight) of trisodium citrate solution is quickly added to the auric solution. The solution changed color within several minutes from yellow to black and then to red or purple color depending on the size of the nanoparticles [3,4].

0.300

Absorbance

0.225

0.150

0.075

0.000 300

400

500

600

700

Wavelength nm Figure 1 Absorption spectrum of gold nanofluid having a concentration of 0.1 m M

The color change is slower for larger nanoparticles than for small nanoparticles. The amount of citrate solution determines the size of the nanoparticles. Faster the capping of the nanoparticles by the citrate, smaller the resulting nanoparticles. The sodium citrate first acts as a reducing agent. Later the negatively-charged citrate ions are adsorbed onto the gold nanoparticles, introducing the surface charge that repels the particles. The size of nanoparticles is 60 nm.

4. METHODOLOGY A schematical view of the present experimental set up is shown in Figure 2. Laser radiation at 532 nm wavelength from a Diode Pumped Nd: YVO4 laser is used as the pump beam to generate the thermal lens in the medium. Radiation of wavelength 632.8 nm from a low power (1 mw) intensity stabilized He-Ne laser source is used as the probe beam. The pump beam is intensity modulated using a mechanical chopper. The probe beam is made to pass collinearly through the sample using a dichroic mirror. An optical fiber mounted on XYZ translator serves as the finite aperture. The other end

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of the fiber is coupled to a fast photodetector. The signal output from detector is processed using a digital storage oscilloscope.

C Pump Laser

L1

DM

S

F

OF

L2

DETECTOR SRS Probe laser DSO Figure 2: Schematic diagram of the experimental set up. BS1, BS2- Beam Splitters, C – Chopper, L1, L2 – Lens, DM - Dichroic Mirror, S - Sample, F- Filter, OF- Optical fiber, DSO- Digital Storage Oscilloscope.

Mechanically chopped optical radiation from pump laser is focused using a lens L1 to the sample in a cuvette of 1cm length. The sample holder is placed in a micrometer translational stage and the position of the sample holder is adjusted along the optic axis to obtain the maximum intensity change of the probe beam (one confocal length away from the beam focus). When the chopper allows impinging of pump beam on the sample, it creates a thermal lens within the sample. The probe beam from the He-Ne laser which travel collinearly with pump beam experience a diverging lens and the beam shape expands in the presence of thermal lens. The change in intensity of the probe beam is measured using a fast photodetector using fiber which is fixed on the optic axis of the experimental set up. The TL signal is recorded from which the relative change in intensity and initial slope is measured. The value of θ and tc are determined. From these values, the thermal diffusivity of the sample under investigation is evaluated. In order to eliminate uncertainty in the determination of the beam radius and hence on the thermal diffusivity value, a reference sample of known thermal diffusivity value, water, is employed. By knowing the thermal diffusivity value of reference sample, one can evaluate

tcwater . thermal diffusivity of unknown sample using the equation D = Dwater tc 5. RESULTS AND DISCUSSION The time evolution of TL signal for nanofluids at room temperature is shown in figure 3. The solid curve represents the theoretical fit obtained using the eqn. (5 ) and the points represent the experimental data.

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0.10 0.09 0.08

I(t) arb.units

0.07 0.06 0.05 0.04 0.03 0.02 0.01 0

50

100

150

200

250

time (ms)

Figure 3. Decay curve for gold nanoparticles in water.

Table 1 shows the thermal diffusivity values of the pure distilled water as well as water dispersed with nanoparticles. Contrary to earlier reported studies, the thermal diffusivity value decreases with the addition of nanoparticles and increase in concentration of nanoparticles in the fluid results in corresponding decreases in their diffusivity. In the past, many theories were proposed to explain the enhancement in thermal conductivity beyond Maxwell prediction.

Table 1. Adjustable parameter tc obtained from fits of Eq. (5) to the experimental data and their calculated thermal diffusivity values.

Thermal Diffusivity Concentration (mM)

tc (ms)

(cm 2 /s)

water

52.9

1.43x10-3

0.1

190

0.398x10-3

0.08

127.9

0.591x10-3

0.069

73.8

1.0236x10-3

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A few important theories among them are based on Brownian motion of the nanoparticles [5], fluid convection at the microscales [6], liquid layering at the particle-fluid interface [7], nanoparticle shape [8], cluster agglomeration [9] or a combination of aforesaid mechanisms [10]. However, recent investigations on molecular dynamic simulation reveals that the hydrodynamic Brownian motion has only minor effect on the effective thermal conductivity even for a relatively high dosage of nanoparticles (ca. 3.3 vol%) [11]. Moreover, a rough estimation of diffusivity of gold particles with diameter 60 nm gives a diffusivity of nanoparticles (calculated using Einstein´s formula Dp= kBT/6πµR, where kB is Boltzmann constant, T is temperature at which measurement is carried out, µ is viscosity of the host medium, R is the radius of nanoparticle) as 7.42 x 10-12 m2/s. From the table it is clear that, the heat transport via conduction mechanism quantified by thermal diffusivity value is much faster than the motion of nanoparticle which is quantified by particle diffusivity. A very interesting modeling on transient absorption and thermal conductivity in a simple nanofluid by Mihail Vladkov et.al showed the effective thermal conductivity (thermal diffusivity) depend upon Kapitza resistance [12]. When the Kapitza length, which is the product of thermal conductivity of host liquid and interface thermal resistance, is less than that of particle radius, regardless of the value of thermal conductivity of particles, the effective thermal conductivity of nanofluid will decrease. A decrease in thermal conductivity reflects in reduction in thermal diffusivity value with inclusion of nanoparticles in the mixture. In addition to this, the wettability of dispersed nanoparticles also play a effective role in thermal parameters of the system. The thermal conductivity of partially wetted or non-wetted particles in a liquid exhibit smaller variation compared to the completely wetted nanoparticles. In the case of non-wetting particle, the temperature jump at the solid-fluid interface due to interfacial thermal resistance is high. In the case of large interface thermal resistance, addition of particles reduces the thermal conductivity (thermal diffusivity) of the fluid as the particles act as insulating holes. With the addition of more and more nanoparticles, this effect become more and more dominant and correspondingly the thermal diffusivity value decreases with increase in concentration of nanoparticles.

5. CONCLUSION The thermal diffusivity values of water as well as water dispersed with gold nanoparticles are measured using the dual beam mode matched thermal lens technique. Our studies clearly show that particle size have great influence on whether the inclusion of nanoparticle will increase or decrease the thermal parameters. The commonly considered Brownian motion of the particle has negligible influence on thermal parameters of nanofluids whereas the interface thermal resistance play an important role in studying the effective thermal parameters of nanofluids.

ACKNOWLEDGMENT Financial support received from University Grants Commission on the project entitled “Thermal characterization of nanofluids using optical techniques, F. No. 34-31/2008(SR), India is gratefully acknowledged.

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