Evaluation of acoustical parameters and thermal conductivity of TiO₂-ethylene glycol nanofluid using ultrasonic velocity measurements

2.1 Synthesis and characterization

The TiO₂ NPs were prepared via sol-gel method using Titanium (IV) isopropoxide (TTIP) as a precursor obtained from Sigma Aldrich Company, USA with a stated purity of 97%. TTIP was dropped slowly into the mixed solution of ethanol and distilled water (Merck, Germany) in the stoichiometry ratio of 1:4:1 (TTIP/H₂O/ethanol). The solution was continuously stirred to obtain a white slurry solution for 1 h at room temperature. Nitric acid (Merck, Germany) was used to adjust the pH in the range 2–3. The mixture was dried at 120°C for 2 h to evaporate water and other waste organic material. Finally, the dried powder was sintered at 450°C for 2 h to obtain the TiO₂ nanopowder.

The synthesized TiO₂ NPs were dispersed in EG (Merck, Germany) by employing ultrasonication for 3 h to get a homogenous suspension without any phase separation and sedimentation. It has been noticed that the ultrasonication increases the stability of the suspension. Nanofluids of various concentrations (0.04, 0.05, 0.06, 0.07, 0.08, 0.09, 0.1, and 0.2 wt.%) were prepared without the addition of any surfactant. No surfactant has been used in order to avoid its effects on the surface property of the nanoparticle and also to avoid chemical contamination. The synthesized TiO₂-EG nanofluids of various concentrations are shown in Figure 1.

Figure 1:

The photographic view of TiO₂ NPs in ethylene glycol.

The crystalline structure, phase composition, and average crystallite size of TiO₂ NPs have been identified from the X-ray diffraction patterns obtained using 3000 TT X-ray diffractometer (Serifert Co., Germany) at 293 K, operating at 30 kV and 30 mA with Cu-K_α radiation (λ=1.541 Å) for 2θ value ranging from 10° to 80°. The average particle size and morphology of TiO₂ nanoparticles have been examined using a High Resolution Scanning Electron Microscope (QUNTA FEG 200, FEI Company, Netherland). The digital ultrasonicator (LMCU-2A: 50 W, 40 KHz, Labman Scientific Instruments Pvt. Ltd., Chennai, India) energy is being produced by converting electrical energy into mechanical vibrations by using generator and piezoelectric transducers. UV-visible spectra of the samples have been dispersed in EG under ultrasonication, recorded on a T90+UV-VIS spectrometer (PG Instruments Ltd., Leicester, UK). The values of the band gap energy have been calculated for the different concentrations of TiO₂ nanofluids, and its stability analysis was done with the UV-visible spectrum measurements.

The density was determined using a specific gravity bottle by the relative measurement method. The weight of the sample was measured using the electronic digital balance with an accuracy of ±0.1 mg (Model: ELB 300, Shimadzu Corporation, Japan). The ultrasonic velocity of a pure solvent and their solutions have been measured by using digital ultrasonic interferometer operating at 2 MHz (Model: VCT 70A, Vi microsystem Pvt. Ltd., Chennai, India). The uncertainty was estimated to be 1 ms^-1. All the measurements were carried out at 298.15 K and 1 atmospheric pressure. The uncertainty of the temperature is 0.1 K and that of the concentration was 0.0001 g cm^-3. The velocity and density measurements were repeated several times for accuracy. The errors between experimental values of density and ultrasonic velocity of EG were very close to that of the literature values [28].

From the experimental data of density and ultrasonic velocity of pure solvent and solutions, various acoustical parameters have been calculated using the following standard equations:

1. Adiabatic compressibility β=1U2ρ

2. Free length L_f=Kβ^1/2

3. Acoustic impendence Z=Uρ

where β, U, ρ, L_f, K, and Z are the adiabatic compressibility, ultrasonic velocity, density, free length, temperature-dependent constant, and acoustic impedance of the solution, respectively.

3.1 Structural and morphology studies

The crystal structure of the obtained powder was characterized by powder X-ray diffraction (XRD) analysis. From Figure 2, the highest peak at 25.4° (101), which was indicated as (101) plane anatase phase of TiO₂ pattern and matched well to the Joint Committee on Powder Diffraction Standards data (JCPDS, card no: 21-1272). The pattern confirms its tetragonal (4/m 2/m 2/m) crystal structure with lattice parameters of a=3.7845 Å, b=3.7845 Å, c=9.5143 Å, α=β=γ=90°. The crystalline size obtained from the Scherrer formula is 34 nm. The morphology of the prepared TiO₂ sample was analyzed by HR-SEM, and it is shown in Figure 3. From the HR-SEM image, it has been observed that the synthesized TiO₂ NPs have an average size of 15 nm.

Figure 2:

XRD Pattern of TiO₂ NPs sintered at 450°C.

Figure 3:

HR-SEM morphology of calcinated TiO₂ NPs at 450°C.

Energy dispersive X-ray spectroscopy (EDS) is an analytical technique used for the elemental analysis or chemical composition of a sample. The EDS spectrum of TiO₂ NPs is shown in Figure 4. It has been noticed that there was no trace of any other impurities within the detection limit of the EDS.

Figure 4:

Energy dispersive X-ray spectrometry (EDS) of TiO₂ NPs.

3.2 UV-visible spectral studies

The optical absorbance coefficient α of a semiconductor close to the band edge could be expressed by the following equation:

αhυ=Α(hυ-Eg)n

where α is the optical absorption coefficient, E_g is the absorption band gap, A is a constant, n depends upon the nature of the transitions, n may have values 1/2, 2, 3/2, and 3 corresponding to allowed direct, allowed indirect, forbidden direct, and forbidden indirect transitions, respectively. In this case, n=1/2 for direct allowed transition [29]. The absorption spectra of TiO₂ NPs are shown in Figure 5A. The absorption band edges were estimated around 337, 343, 347, 350, 352, 360, 366, and 389 nm (about 3.68, 3.7, 3.61, 3.55, 3.5, 3.4, 3.37, and 3.2 eV).

Figure 5:

(A) UV-visible absorbance for TiO₂-ethylene glycol nanofluids. (B) Band gap obtained by extrapolating the linear portion of the (αhτ)² vs. hτ curve.

The band gap of the energy could be determined by extrapolation to the zero coefficients, which has been calculated from the above equation. The intercept of the tangent to the plot (αhυ)² vs. hυ in Figure 5B gives a good approximation of the band gap energy for this direct band gap of material. The band gap energies (E_g) of the as-prepared TiO₂ NPs are larger than the value of 3.2 eV for the bulk TiO₂. This could be explained as the band gap of the semiconductors has been found to be dependent on the particle size [30]. The band gap increases with a decreasing particle size, and the absorption edge has been shifted to a higher energy (blue shift) with that of the decreasing particle size. Considering the blue shift of the position of absorption, the bulk TiO₂, the absorption onset of the present samples could be assigned to the direct transition of electrons in the TiO₂ nanocrystals. The values of the band gap validate our crystallite size results according to the smaller crystallite size, which should have been a larger band gap (15 nm, 3.8 eV), and the large crystallite size should have a smaller band gap (15 nm, 3.7, 3.61, 3.55, 3.5, 3.4, 3.37, and 3.2 eV) by increasing and with the increase in concentration of the nanofluid.

In this paper, a brief study regarding dispersion stability has been made with the help of a UV-visible spectrometer. TiO₂ NPs have high UV light absorption characteristics. The stability of the fluids observed in terms of settling time is presented in the Table 1. The nanofluids have been found to be stable for more than 4 days with no sedimentation or phase separation. Hence, the absorbance of the sample was obtained at 390 nm every day and is plotted in Figure 6. It remains constant for up to 4 days (0.2 wt.%) from synthesis, and then starts decreasing, which ensures the stability of the nanofluid for more than 4 days.

Figure 6:

Plot of absorbance vs. time recorded at 390 nm.

3.3 Ultrasonic velocity studies

The velocity of ultrasound is the most significant parameter, and it is the quantum of molecular vibration in the medium through which the wave passes. It gives a quantitative measure of interparticle and intermolecular interactions in the nanofluid sample, in their natural environment, without any dilution. The variation of the ultrasonic velocity with concentration is shown in Figure 7 where it is clear that the velocity of the nanofluid increases with the increase in nanoparticle concentration. The velocity increases from 0.04 wt.% (for 0.036 vol.%) to 0.2 wt.% (for 0.18 vol.%), higher than that of the base fluid at 298.15 K. This enhancement in ultrasonic velocity with the increase in concentration has been attributed to the TiO₂-EG interactions, and it further ensures the dominance of intramolecular interaction over the intermolecular interactions [31]. Moreover, with the particle loading, there was a possibility of increasing the rate occurrence of the Brownian motion of the fluid molecule, along with the increase in surface layer that can persuade an increase in ultrasonic velocity.

Figure 7:

Acoustical parameters of TiO₂-NPs in ethylene glycol at different concentrations. (A) Ultrasonic velocity (U); (B) adiabatic compressibility (β); (C) acoustic impedance (Z); (D) free length (L_f).

As the structural changes affected the compressibility, there was a change in ultrasonic velocity. It was found that there was an increase in acoustic impedance values with an increase in the concentration of particles. Acoustic impedance is almost reciprocal to adiabatic compressibility. The higher value of the acoustic impedance indicates that there is a significant interaction between the particle and base fluid molecules, which might affect the structural arrangement. The interaction between the particles and the base fluid molecules increases the intermolecular distance between the molecules, which in turn causes impedance in the propagation of ultrasonic waves. The decrease in adiabatic compressibility and free length supports the particle and fluid interaction as shown by the ultrasonic velocity and acoustic impedance results. The calculated acoustical parameters are given in Table 2. The variations of ultrasonic velocity, free length, and acoustic impedance with TiO₂ nanofluid are illustrated in Figure 7.

3.4 Thermal conductivity studies

Thermal conductivity values k_exp of TiO₂-EG nanofluids of various concentrations measured at 298.15 K are depicted in Figure 8. The thermal conductivity of EG at 298.15 K was found to be 0.252 W/m K, which is in agreement with the value reported earlier [32]. The effective thermal conductivity of EG has been increased due to the addition of NPs. The increase in the thermal conductivity was proportional to the increase in particle concentration. Figure 8 represents the increase in thermal conductivity of EG due to the addition of NPs. The increase in thermal conductivity was attributed to the fact that the thermal conductivities of metal oxides are several orders of magnitude higher than those of liquids used as base fluids. It was observed that the nanofluid of 0.2 wt.% shows the maximum enhancement of 36.77% than the base fluid. The enhancement in thermal conductivity with nanoparticle loading in the nanofluid has been contributed by various factors such as Brownian motion, micro convection, clustering, and agglomeration [33, 34]. It is vivid from Figure 8 that the thermal conductivity of TiO₂-EG increases from 0.3374 to 0.3474 W/m K with respect to the increase in concentration from 0.04 to 0.2 wt.% with an enhancement of 2.96%.

Figure 8:

Thermal conductivity (k_bm) values obtained through the Bridgman equation.

One of the widely accepted trends in the theory of heat conduction of liquids is based on Debye’s concept. As per Debye [35], the hydroacoustic vibrations (phonons) of a continuous medium (base fluid) are responsible for the heat transfer in liquids. Based on the above heat transfer mechanism, Bridgman has obtained a formula [36], characterized by the direct proportionality between thermal conductivity and from the assumption of the liquid state as a cubic lattice in which molecules have been arranged with minimal distance between their centers and is given by

where N_A is the Avogadro’s number, U is the velocity of the liquid, ρ is the density of the liquid, M is the molar mass of the liquid, and k_B, the Boltzmann’s constant. The above equation is well established [35] for predicting the thermal conductivity of plain fluids used in the present work and to find the k value of EG. As there has been no effort reported, so far, in applying this equation to find out the thermal conductivity of nanofluids, it has been proposed to extend the equation to nanofluids. So, Eq. (1) is being modified by replacing the density and molar mass of a single liquid by those of nanofluids and is given in Eq. (2),

where k_bm is the thermal conductivity value obtained through the modified Bridgman equation, U is the velocity of the nanofluid, ρ_nf is the density of the nanofluid, and M_nf=X_bfM_bf+X_pM_p is the molar mass of nanofluid. X_bf and X_p are the molar fractions of the base fluid and nanoparticle, respectively, whereas M_bf and M_p are the respective molar masses of the base fluid and nanoparticle. The theoretical value of thermal conductivity obtained through the modified Bridgman Eq. (2) is also illustrated in Figure 8.