Long-Term MWCNTs Nanofluids toward Heat ... - ACS Publications

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Long-Term MWCNTs Nanofluids toward Heat Transfer Capability Improvement Bruno Lamas, Bruno Abreu, Alexandra Fonseca, Nelson Martins, and Mónica Oliveira* Mechanical Engineering Department, University of Aveiro, Campus Universitário de Santiago, 3810-193 Aveiro, Portugal S Supporting Information *

ABSTRACT: This study presents the work carried out toward the establishment of a methodology that enables the production of long-term MWCNT-based nanofluids with the highest thermal conductivities. To this end, a parametric analysis of shelf life and heat conduction capacity of MWCNT-based nanofluids is performed. It is intended to ascertain whether the longest term nanofluid is the one with the best heat transfer capability. To successfully quantify the colloidal stability, an innovative technique that allows for nonintrusive measurement of settling velocity during centrifugation is applied, enabling the estimation of the samples’ shelf life. The appropriate inference from the results was ensured through the analysis of six different MWCNT geometries, which were tested at three volume fractions, dispersed in two conventional base fluids. Furthermore, the obtained results were correlated based on the predicted thermal conductivity. It was found that the MWCNT nanofluids showing a lower thermal conductivity enhancement seem to be those which exhibit higher shelf life. It was also verified that the MWCNT diameter is an important factor to explain the long term stability enhancement of the studied nanofluids. Because this parameter seems to produce negligible impact on the thermal conductivity, the application of nanoparticles with a lower diameter ensures a significant increase of the final quality of the long-term nanofluid. In addition, the results suggest that long-term nanofluids showing the higher thermal conductivity may be produced using MWCNT lengths higher than or equal to those in the 5−15 nm range at volume fractions greater than or equal to 0.75%. It is expected that nanofluids produce through this methodology present a useful life ranging from 10 to 50 years. (Al2O3), and carbon nanotubes (CNT).4−21 From experimental results,21,22 CNTs show higher thermal conductivity enhancement compared with the other nanoparticles. According to the ef fective medium theory (EMT), this phenomenon may be explained by their high aspect ratio, which induces greater enhancement compared with spherical particles.3,23,24 From this, it appears that CNTs are the best-suited nanoparticle, for thermal nanofluid engineering. However, it remains extremely difficult to prepare stable suspensions of pristine CNTs. The high ratio of surface-to-volume of these nanoparticles cause strong van der Waals interactions, which induce easy agglomeration.25,26 The CNT aggregates start to behave as micrometer particles and settle down rapidly, causing the clogging of the flow channels and the fast decay of their engineered thermophysical properties.27,28 Among various thermophysical properties of nanofluids, the thermal conductivity is the one gathering more attention from the research community. The latter appears to present an anomalous and unpredictable behavior.29 Moreover, experimental results of several research groups seem to present lack of agreement. This may be explained by the huge variety in the sample production approaches, which results in different microstructural morphologies and stability quality.

1. INTRODUCTION Nanofluids may be seen as the next-generation thermal fluids. With a large number of applications, they can assist in dematerialization of new heat transfer systems and enable improvements on existing ones.1 Nanofluids are formed by dispersing nanoparticles in conventional fluids and present significant improvements in the effective thermophysical properties. The recognition of the greater capacity of heat conduction of solid particles has incentivized its mixture in conventional fluids to improve the overall conduction of the suspension. Theoretical and experimental studies on increasing conduction properties of liquids from suspending millimeter or micrometer sized particles have been performed since Maxwell.2 However, the incorporation of microsized particles present rapid sedimentation due to their high volume. This causes clogging of the flow channel, surface abrasion, increased pressure drop, and fast decay of the effective thermophysical properties projected.2,3 The word nanof luid appears for the first time with Choi et al. in 1995,4 reporting an advanced class of heat transfer fluids engineered by the suspension of metallic nanoparticles in conventional fluids. The results reported present a highly stable dispersion of nanoparticles in the base fluid with exciting improvements in the effective thermal conductivity at remarkably low nanoparticle volume fractions. The most common nanoparticles used for nanofluid engineering are copper (Cu), cupric oxide (CuO), alumina © XXXX American Chemical Society

Received: February 4, 2013 Revised: May 14, 2013

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dx.doi.org/10.1021/jp401271c | J. Phys. Chem. C XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry C

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Production of CNT-based nanofluids may be achieved through the use of surfactants or covalent functionalization of the CNT surface.30,31 Despite increasing the wettability of the CNTs, the use of surfactants influences the final properties of the mixture as they form an interface between the two phases.8,32 Moreover, the use of surfactants limits the application of the nanofluids since they easily degrade at higher temperatures, leading to nanoparticle agglomeration or the formation of foams.32,33 Therefore, the most promising dispersion technique involves the covalent functionalization of the CNTs, such as attachment of carboxyl groups on the side walls of the CNTs.29,30,34−36 However, this process may also lead to degradation of the CNT length.31 According to several authors,29,30,32 it is essential to ensure long-term stability for the development of reference nanofluids with the highest thermal conductivities, preferably without dispersing agents or stabilizers. Recently, Lamas et al. suggested that the dispersion of covalently functionalized multiwalled carbon nanotubes (MWCNT) through a short period of sonication enables the production of reliable long-term nanofluids.37 It was found that the nanoparticle geometry, volume fraction, and base fluid are the main factors governing the stability of MWCNT-based nanofluids. Their results indicate that it may be possible to develop nanofluids with stably engineered thermophysical properties. When tailoring MWCNT nanofluids, one is always interested in engineering their overall heat transfer capability. This tends to rely upon their thermal conductivity enhancement. Moreover, to ensure the applicability of MWCNT nanofluids, their thermophysical properties may also endure, and this definitely depends upon the nanofluid colloidal stability. Therefore, once the colloidal stability is assessed, it seems necessary to ascertain whether the most stable nanofluid is the one with the best heat transfer capability or whether a compromise may be required. The following study aims at establishing this connection and, therefore, suggests ways to produce MWCNT nanofluids with higher overall quality.

Table 1. Nanoparticle Designation and Their Geometric Properties

a

MWCNT designationa

average aspect ratio

average volume [μm3]

D50-80 L10-20

231

0.0498

D60-100 L5-15

125

0.0503

D60-100 L1-2

19

0.0075

D20-40 L10-30

667

0.0141

D20-40 L5-15

333

0.0071

D20-40 L1-2

50

0.0011

nanoparticle manufacturer

ash [wt %]

purity [wt %]

Cheaptubes Inc. Shenzhen NanoTech Port Co., Ltd. Shenzhen NanoTech Port Co., Ltd. Cheaptubes Inc. Shenzhen NanoTech Port Co., Ltd. Shenzhen NanoTech Port Co., Ltd.

95

97

97

95

97

97

D = MWCNT diameter in nm; L = MWCNT length in μm.

and thermophysical properties of the selected base fluids are described.39 Table 2. Base Fluid Designation and Their Thermophysical Properties39 designation

DW, vol %

EG vol %

ρ [kg/m3]

μ [Pa·s]

DW+30%EG DW+60%EG

70 40

30 60

1044.55 1085.11

0.002 0.005

The nanoparticle concentration is another control parameter selected for this study. Three different MWCNT volume fractions (Ø) were analyzed, namely, 0.25%, 0.75%, and 1.5%. Lamas et al.16 found that the viscosity of MWCNT-based nanofluids appears to increase considerably for 1.5% volume fraction. Since the viscosity is an important parameter in practical heat transfer processes, this volume fraction was selected as the upper limit in the present study. Table 3 summarizes all the considered control factors for the present study and their respective degrees of f reedom.

2. MATERIALS AND METHODS The studied fluids are described herein, as well as the applied method for nanofluid production. A description of the experimental procedure and of the performed analysis regarding all the prepared samples is also described in detail. 2.1. Materials. The manufacturer and geometric properties of the selected MWCNTs for the present study are described in Table 1. These particle descriptions may be summarized by two diameter distributions, D < 50 and D > 50 nm. These are full crossed with three length distributions, L = 1−2, L = 5−15, and L > 15 nm. The diameter and length distributions are used for the designation of each MWCNT type in a quite obvious way. The nanoparticle sizes were chosen in order to cover a broad interval both in diameter and in length to enable appropriate data interpolation and further analysis. Although the particles were achieved through different manufacturers, all the carbon nanotubes were produced by catalyzed chemical vapor deposition (CCVD). According to the Stokes law,38 the density (ρ) and viscosity (μ) of conventional fluids are the main parameters governing the sedimentation behavior of suspensions. Therefore, two aqueous solutions (DW) of ethylene glycol (EG) at volume fractions of 30% and 60% were selected as base fluids. This choice is in accordance with their importance to several applications of heat transfer fluids. In Table 2, the designation

Table 3. Control Factors and Their Range of Settings for the Experiment control factor

MWCNT

Ø [%]

base fluid

level 1 level 2 level 3 level 4 level 5 level 6 degrees of freedom

D50-80 L10-20 D60-100 L5-15 D60-100 L1-2 D20-40 L10-30 D20-40 L5-15 D20-40 L1-2 5

0.25 0.75 1.50

DW+30%EG DW+60%EG

2

1

Applying a full factorial design of experiments to the identified control factors, a total of 36 samples is obtained. 2.2. Nanofluid Preparation. The MWCNTs used in this study were covalently functionalized through the method described by Esumi et al.34 The pristine MWCNTs were refluxed at 413 K in nitric and sulfuric acid at 1:3 volume ratio for 30 min, followed by washing with DW until no signs of acidity were found, and dried in an oven at 373 K for at least 72 h to remove excess water. Other authors20,35,40 applied this B



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Figure 1. SEM of pristine MWCNTs (at left) and covalently functionalized MWCNTs (at right).

through the sample is registered in a gradient color picture. The instability behavior along with the entire height of the samples is registered and it can be easily observed from Figure 2.

method for MWCNT functionalization and suggested good dispersion results. The functionalized MWCNTs were dispersed in 50 mL of base fluid with a stirrer combined with ultrasonication to improve the dispersion of the MWCNTs into base fluid.16 In Figure 1 is depicted scanning electron microscopy (SEM) images, of pristine MWCNTs (at left) and covalently functionalized MWCNTs (at right). In this, it is perceptible that the pristine MWCNTs are highly entangled and, in contrast, the covalently functionalized MWCNTs are well dispersed. Furthermore, it seems that the tubular structure integrity was maintained after the chemical treatment. Nevertheless, it should be noted that this does not indicate that the size distribution of the final MWCNTs dispersed in the base fluids is equal to that of the pristine MWCNTs. 2.3. Experimental Apparatus. 2.3.1. Fourier Transform Infrared Spectroscopy. Fourier transform infrared spectroscopy (FTIR) was performed in the functionalized MWCNTs for the identification of the functional groups attached to the MWCNT surface after functionalization. The FTIR measurements were performed in a Bruker Tensor-27 spectrometer in the range of 400 to 4000 cm−1. The final spectrum is the mean of three measurements with a resolution of 4 cm−1. Each spectrum was collected over 256 scans. Since the MWCNTs detain high absorbance, they were mixed with KBr, and pellets were prepared for the experimental measurements. 2.3.2. Shelf Life Evaluation. It is expected that long-term nanofluids, that is, nanofluids with higher shelf life, exhibit negligible variations with time in the respective engineered thermophysical properties. It is recognized that these properties are related to the concentration of suspended nanoparticles in the conventional base fluid. Therefore, the average settling velocity of nanoparticles in a fluid at rest may be used to quantify the stability of nanofluids. Measurement of the settling velocity of the MWCNT-based nanofluids was achieved through the stability analyzer LUMiSizer 6120 kindly provided by Dias de Sousa SA. According to this methodology, fluid samples are subjected to different centrifugal fields (RCF = centrifugal acceleration/ earth acceleration), which will accelerate the particle settling process,41 and a calibrated NIR light beam intensity is continuously measured by a CCD sensor after intersecting the fluid sample. In each time step, a light transmission profile

Figure 2. Schematic illustration of the measuring principle of the stability analyzer (adapted from ref 41).

Furthermore, change of the light transmission profiles with time enable the calculation of the settling velocity for each RCF. If the deposition/particle decay velocity is proportional to the RCF, the settling velocity for gravity condition (RCF = 1) could be extrapolated, and the shelf life of each sample could be predicted. The samples are tested at a controlled temperature of 298 ± 1 K at three proportional centrifugal force fields, described in detail in Table 4. The particle decay/deposition phenomenon is measured by a near-infrared (NIR) light (865 nm wavelength). As it will be seen further ahead, the particle decay/deposition Table 4. Stability Analyser Measuring Conditions for Each Sample

C

test no.

rpm

RCF [g]

time step [s]

total time [h]

no. profiles

1 2 3

1990 2800 4000

575 1150 2300

200 100 50

14 7 3.5

255 255 255



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3. RESULTS AND DISCUSSION 3.1. FTIR Analysis. The FTIR spectra of the functionalized MWCNTs are shown in Figure 3. The spectra are vertically

rate is proportional to the RCF, proving that the selection of these does not affect the final results. 2.3.3. Thermal Conductivity Prediction Models. There are a number of different predictive models for the thermal conductivity behavior of nanofluids. These essentially diverge in the heat transfer mechanism on which they are based. According to classical models based upon the effective medium theory, thermal diffusion is the only physical mechanism ruling heat conductivity. More recent models also include the Brownian motion, the nanoscale layer concept, percolation, agglomeration, and other complex mechanisms.24,29,42−46 Nevertheless their additional complexity, namely, through the consideration of different heat transfer mechanisms, shows a significant lack of agreement with available experimental data.29,30,47 Therefore, in this study, the classical predictive model of Nan et al.24 for carbon nanotube-based nanofluids was selected. This model, based on the effective medium theory, accounts with the MWCNT geometry and volume fraction and with the interfacial thermal resistance that was shown experimentally by Huxtable et al.48 Although there are recognized differences among the existing prediction models, they all appear to describe a thermal conductivity enhancement with increasing nanoparticle volume fraction and respective aspect ratio. It is believed that the results will not be disguised by the selection of a specific model, since this study intends to evaluate the trend for the thermal conductivity enhancement with the nanoparticle geometry and volume fraction variation. Furthermore, some authors49,50 suggested good agreement of this model with experimental results. The model of Nan et al. for CNT-based effective thermal conductivity, keff, can be expressed as keff =

3 + ϕ(β11 + β33) 3 − ϕ(β11)

k bf

Figure 3. FTIR spectra of studied pristine and functionalized MWCNTs.

shifted to better reading. It is well-known that the covalent functionalization of the MWCNTs with concentrated acids introduced some functional groups on their sidewalls.34,35,51−55 All samples exhibit a peak near 1630 cm−1, which represents the carbon skeleton (CC),55 showing that the integrity of the MWCNTs is not affected by the chemical treatment. The peaks at 1210 cm−1 are associated with C−O stretching of phenolic and carboxylic groups, and the peak at 1710 cm−1 corresponds to CO stretching of the same groups.35,51−55 These results reveal the good quality of the functionalization procedure. 3.2. Shelf Life Evaluation. As mentioned previously, the stability analyzer LUMiSizer 6120 accelerates the phase separation of the colloids at different rates proportional to the selected RCF. The phase separation is registered in a transmission profile, which is used to calculate the settling velocity for the respective RCF. In Figure 4, the transmission

(1)

where kbf is the base fluid thermal conductivity and β11 =

c 2(k11 − k bf ) c k11 + k bf

(2)

β33 =

c k 33 −1 k bf

(3)

The parameters kc11 and kc33 are, respectively, the equivalent thermal conductivities along transverse and longitudinal axes of a thin interfacial thermal barrier layer on the MWCNT surface and can be expressed as: c k11 =

c k 33 =

kp 1+

2a k k p D k bf

Figure 4. Evolution of transmission profiles of sample 1 at 2300 G. (4)

profile of the sample 1 when subjected to a RCF of 2300 G is shown. It should be noted that the transmission profiles for the remaining RCF are proportional to the presented one (RCF = 2300 G), as verified previously.37 In Figure 4, 255 profiles are represented, measured with a 50 s interval (Table 4). The bold profiles, which are spaced at about 20 min, reveal a settling velocity constant over time. In addition, because the shape of the transmission profiles is constant and equally spaced, it indicates that the suspension is composed of monodisperse particles,41 an important requirement to ensure thermophysical property homogeneity.29 This behavior may indicate that the functionalization process and the

kp 1+

2a k k p Ll k bf

(5)

where D and L are the diameter and length of the CNT in nm, kp is the thermal conductivity of the nanoparticle, and ak is the Kaptiza radius defined by ak = R kk bf

(6)

where Rk is the Kapitza resistance with 8 × 10−8 m2K/W. D



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Figure 5. Representation of the linear regression of the sedimentation velocity obtained for some of the samples.

Figure 6. Settling velocity at gravity field (RCF = 1) for the studied samples.

Figure 7. Estimated shelf-life time for the studied samples.

application of the ultrasonication for the MWCNT dispersion in the base fluid broke the MWCNT aggregates, as previously stated from Figure 1. Nevertheless, it should be noted that this does not indicate that the size distribution of the final MWCNTs dispersed in the base fluids is equal to that of the pristine MWCNTs. The behavior described here for sample 1 was observed for all the remaining tested samples. Through linear regressions, as represented in Figure 5 and further described in ref 37, the constant of proportionality between the RCF and phase separation rate for each sample was found. In these regressions, a null ordinate at the origin (y = mx) was considered, since it is assumed that no sedimentation occurs if the force field is null. The constant of proportionality of each sample enables the extrapolation of the results to the remaining conditions, that is, to the gravitational force field (RCF = 1). The results are shown in Figure 6:

The sample holders used in the stability analyzer LUMiSizer 6120-133 had a total height of 22 mm. Thus, it was possible to predict the average time required to attain complete settling of each sample, designated herein as shelf life. The estimated shelf life, represents, therefore, the time required for the MWCNTs to go from the top to the bottom of the container (according to the test conditions). The results are shown in Figure 7. The results obtained suggest that it is possible to produce nanofluids with long shelf life, ranging from nearly 5 to 70 years. Moreover, for the analyzed concentration, MWCNTbased nanofluids are characterized by hindered settling. The latter corresponds to a significant decrease in the settling velocity of immersed particles, with increasing hydrodynamic interparticle interactions. From Figure 8, it is possible to visualize the transition of the microstructure of these nanofluids through the increase of the nanoparticle volume fraction. The transition through the various stages seems to enhance the number of interparticle E



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Figure 9 presents the statistical average impact of each control factor on the shelf life. In general, the MWCNTs with smaller diameter (D < 50) present higher shelf life. In addition, as previously seen, the increase of MWCNT length also produces higher shelf life, except for the smallest nanoparticle studied (D20-40 L1-2). In all samples studied, it was found that the increase on the MWCNT volume fraction leads to higher shelf life. 3.3. MWCNT-Based Nanofluids Thermal Conductivity Prediction. Figure 10 presents the predicted thermal conductivity enhancement through the model selected in section 2.3.3. As previously postulated, the nanofluids prepared with D20-40 L1-2 appear to exhibit thermal conductivities significantly lower than those of other nanoparticles. Moreover, the calculated results suggest that the thermal conductivity increases with the volume fraction and length of the nanoparticle, as expected. Figure 11, presents a statistical analysis of the heat conductivity data aiming the investigation of the parametric average impact of selected factors on the nanofluid thermal conductivity. As expected, a direct proportionality between the conductivity and the MWCNT length and respective volume fraction may be seen. Nevertheless, the difference in the results for the highest lengths, L > 15, may also be due to the slight difference in the real lengths of the MWCNTs D50-80 L10-20 and D20-40 L10-30 (see Table 1), which were combined for the sake of analysis simplification. When testing strictly equal lengths in the predictive model, the trend curves for the two diameters are parallel and nearly coincident. From this analysis, it appears that concerning the effective thermal conductivity, the optimum case happens for the higher volume and MWCNT length, the respective diameter being negligible. Therefore, this study suggests that despite showing good shelf life, nanofluids produced with low length MWCNTs (both L1-2) or 0.25% volume fraction are unsuitable for thermal purposes. When compared with other nanofluids, although they appear to be stable for longer periods, they do not show relevant improved heat transfer effectiveness. Thermal conductivity seems to be independent of carbon nanotube diameter. Yet, the results seem to indicate that the best-suited nanoparticles are those with lowest diameters. Furthermore, for thermal energy systems with expected lifetime ranging from 10 to 20 years, MWCNT-based nanofluids produced with nanoparticles with lengths greater or equal to 5−15 nm and volume fraction above or equal to 0.75% will ensure good effective thermophysical properties during long periods.

Figure 8. Schematic microstructure of a MWCNT suspension: (a) dispersed structure; (b) aggregated structure; (c) percolation-like structure.

collision and electrostatic repulsions, reducing significantly the settling velocity. Furthermore, during sedimentation, the particles displace liquid in the opposite direction to their movement, which affects the motion of the surrounding ones. This behavior has been previously observed by Lamas et al.37,56 In addition, according to the excluded volume theory,57 the interparticle interactions are expected to increase with increasing nanoparticle aspect ratios. In general, this behavior is also observed in the present results, where the nanoparticles with greater length show lower average settling velocities, that is, higher shelf life. However, the MWCNTs that show longer shelf life (D20-40 L1-2) are the shortest, suggesting that other mechanisms may also play an important role. Perhaps, due to their small size, these nanoparticles begin to behave as molecules of the fluid itself, as a colloid. Furthermore, it appears that the settling velocity decreases with increasing base fluid viscosity, as expected. Nevertheless, to improve the interpretation of the results, a factorial statistical analysis is performed, through the estimation of the average impact of each control factor. These are statistically known as main effect58,59 that enables a graphical representation to better elucidate the trends of the variation of just one control factor on the results. As expressed in eq 7, the average impact is the difference between the mean of a control factor level and the overall mean of the observed results. As such, the average impact indicates whether a given control factor contributes positively or negatively to the overall mean of the results. In the present study, a higher average impact indicates an extra enhancement on the shelf life of the nanofluid. In contrast, a negative average impact indicates a poorer enhancement of the shelf life of the nanofluid. average impact = χ ̅ − χc̅ (7) i

where χ̅ is the overall mean of the dependent variable χ (in this case study the shelf life) and χci is the mean of the same dependent variable when the control factor c is at the level i.

Figure 9. Average impact of the MWCNT geometry and volume fraction on the shelf life of the nanofluids. F



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Figure 10. Predicted thermal conductivity enhancement for the studied samples.

Figure 11. Average impact of the MWCNT geometry and volume fraction on the predicted thermal conductivity of the nanofluids.

As a conclusion, the results also suggest that the optimal long-term nanofluid may be produced using MWCNTs with the lower diameter and the higher length (in this case D20-40 L10-30), for volume fractions ranging from 0.75% to 1.5%.

validation. However, all the available prediction models suggest thermal conductivity improvements with rise of the volume fraction and nanoparticle aspect ratio. Therefore, the results suggested in this paper are based on well-established assumptions, and it is possible to assert that they are in full agreement with the available literature.

4. CONCLUSIONS In this research, a methodology was established for the preparation of long-term MWCNT nanofluids, with significant improvements in their ability for heat conduction. To this end, a recent technique was applied for quantitatively measuring the shelf life of the nanofluids. The obtained shelf life results were analyzed against predicted effective thermal conductivities, enabling us to determine the best strategy for the production of high-quality nanofluids. This research suggests that MWCNTs with smaller length and diameter may exhibit shelf life up to 70 years. However, the insignificant improvement in the thermal conductivity obtained by these particles make them of little interest for thermal nanofluid purposes. It was verified that the MWCNT diameter produced a negligible impact on the thermal conductivity enhancement of these fluids. However, this is an important parameter for increasing the shelf life. These results suggest that for fixed MWCNT lengths, MWCNTs with a smaller diameter will produce nanofluids with increased quality. The obtained results further suggest that nanofluids with MWCNT volume fraction less than 0.75% produce both a reduced shelf life and thermal conductivity enhancements. Then typical volume fractions, such as 0.25%, are unsuitable for long-term nanofluid development. This research presents conclusions based on a thermal conductivity predictive model. At the date of the present study, this model continues to be confronted with experimental

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ASSOCIATED CONTENT

S Supporting Information *

Nanoparticle properties and manufacturer information, images of the stability analyzer used in the colloidal stability assessment, and results of the colloidal stability assessment for sample 1. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: +351 234 370 830. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors acknowledge Eng. Pedro Prazeres from Dias de Sousa SA for his assistance with the analytical centrifuge measurements and Dra. Helena Nogueira and Dra. Celeste Azevedo from University of Aveiro for their support with the spectroscopic studies (FTIR). The authors also acknowledge Fundação para a Ciência e Tecnologia (FCT) and Fundo Social Europeu (FSE), for the financial support through the individual grant (SFRH/BD/6445/2009) and through project grants PTDC/EME/MFE/66482/2006 and PTDC/EME-MFE/ 119572/2010 (POPH-QREN program). G



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