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Thermal Conduction and Insulation Modiﬁcation in Asphalt-Based Composites Xiaofeng Zhou1,2,3) , Shengyue Wang1)† and Chao Zhou1) 1) School of Transportation, Southeast University, Nanjing 210096, China 2) School of Energy and Environment, Southeast University, Nanjing 210096, China 3) Department of Fundamental Sciences, Yancheng Institute of Technology, Yancheng 224003, China [Manuscript received January 8, 2012]

The relationship between thermal conductivity and properties of mixing particles is required for quantitative study of heat transfer processes in asphalt-based materials. In this paper, we measured the eﬀective thermal conductivity of asphalt-based materials with thermal conduction (graphite) and insulation (cenosphere) powders modiﬁcation. By taking account of the particle shape, volume fraction, the thermal conductivity of ﬁlling particles and base asphalt, we present a new diﬀerential eﬀective medium formula to predict the thermal conductivity modiﬁcation in asphalt-based composite. Our theoretical predications are in good agreement with the experiment data. The new model can be applied for predicting the thermal properties of asphalt-based mixture, which is available for most of thermal modiﬁcation in two-phase composites. KEY WORDS: Thermal conductivity; Asphalt-based composites; Graphite; Cenosphere; Diﬀerential eﬀective medium formula

1. Introduction Asphalt is a class of complex mixture which is derived from crude oil. It has been a valuable material because it is readily adhesive, waterproof and durable. Asphalt-based materials are asphalt (or aggregates) in which thermal or mechanical functional materials are dispersed[1–6] . By taking account of the advantages of the two both, asphalt-based materials have been applied widely for highway pavement, bridge deck, airport roads and so on[7,8] . Mixing functional materials into asphalt has attracted great interest recently because of their enhanced thermal and mechanical properties such as high temperature rutting, fatigue failure, temperature crack and softening temperature. Several additives have been used to increase the performance of asphalt binders. For instance, it was reported that the thermal conductivity of asphalt-based materials † Corresponding author. Prof., Ph.D.; Tel./Fax: +86 25 83790551; E-mail address: [email protected] (S.Y. Wang).

enhanced with graphite powder (9.0 vol.%) dispersed in matrix asphalt, which resulted in increasing the softening temperature from 45 ◦ C to 82 ◦ C[9] . Thermal conductivity, an important basic heat transfer parameter, is related to most of the thermal and mechanical properties in asphalt-based materials. Many important properties of asphalt-based mixture were determined by the thermal properties and the volume fraction of ﬁlling particles, such as high temperature strength and stability, low-temperature plastic performance and endurance. The quantitative study of heat transfer processes in asphalt-based materials is required on the relationship between thermal conductivity and the properties of mixing particles. In this paper, we study the eﬀects of graphite and cenosphere powders additives on the thermal conductivity enhancement and thermal insulating modiﬁcation in asphalt binders. By taking into account the shape and volume fraction of ﬁlling materials, we would like to present diﬀerential eﬀective medium theory to investigate the eﬀective thermal properties of asphalt-based materials. The purpose of this paper is

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Fig. 1 Polarizing microscopy images of 10 vol.% cenosphere particles (a) and graphite powders (b), which are ﬁlled in the base asphalt

to ﬁnd a general model to predict the thermal properties in asphalt-based materials which include the volume fraction, thermal conductivity and particle shape of ﬁlling materials. 2. Experimental Asphalt was obtained from Wuxi Road Department, Jiangsu, China. Cenosphere particles were supplied in batches by Harbin Thermo-electric Plant. The graphite was obtained from Xingtai Graphite Ore Factory in Hebei province, China. Its particle size <150 μm , carbon content 98.9%, ash content 0.2%, iron content 0.03% by weight. The structure of asphalt and asphalt-based mixture (ﬁlling with cenosphere particles and graphite powders) were examined by polarizing microscopy (NIKON, E600POL). In order to investigate the eﬀective thermal properties of asphalt-based mixture, we chose the volume fraction of cenosphere particles and graphite powders as 1, 3, 5, 7, 9, 11, 13, 15, 17, 20 vol.%. Asphalt was heated to 150±5 ◦ C in an oil-bath heating container until it ﬂowed fully. Then the chosen amount of cenosphere particles and graphite powders is ﬁlled into the heated asphalt and operated under a high rotation speed of 2500 r/min for about 20 min to ensure the well dispersion of additive ﬁlling particles in asphalt. The thermal conductivity of asphaltbased mixture was measured by thermal testing device (ZKY-BRDR). 3. Results and Discussion To observation details of the ﬁlling particles in asphalt-based mixture, a polarizing microscope was employed, and the images are shown in Fig. 1. From Fig. 1(a–b), it could be seen that the 10 vol.% cenosphere particles and graphite powders were ﬁlled in the base asphalt. The cenosphere particles were mainly spherical in shape. In the course of understanding the thermal transport behavior of asphalt-based mixture, we shall

generalize Bruggeman diﬀerential eﬀective medium theory[10] to estimate the eﬀective thermal conductivity of asphalt-based mixture. First, we consider the composites in which randomly oriented spheroidal particles with volume fractions f are embedded in base asphalt with the thermal conductivity Km. Since the embedded spheroids are randomly oriented, the whole asphalt-based mixture will be isotropic. According to the traditional Maxwell– Garnett theory[11,12] , the eﬀective thermal conductivity Ke of asphalt-based mixture can be expressed as, Ke = Km [1 +

f (2βx + βz )] 3

(1)

where βx =

Kx − Km K z − Km ; βz = Km + Lx (Kx − Km ) Km + Lz (Kz − Km )

here Lz [Lx ≡ (1−Lz )/2] is the depolarization factor of spheroidal particles (z denotes the rotational axis)[11] , given by e−p 1 2p3 (−2p + e ln e+p ). if (e ≤ 1) Lz = 1 e 2q 3 (2q − eπ + 2e arctan q ). if (e ≥ 1) √ 2 where √ e is the eccentricity, p= e − 1, and 2 q= 1 − e . Starting with a homogeneous host asphalt, we calculate the change in Ke from Km at f =0 to Ke + ΔKe at Δf , 2βx + βz Δf (2) 3 To carry out further iterations, we simply reply Km by Ke of the new homogenized composites and Δf with Δf /(1 − f ) due to the overlap eﬀect. We arrive at the ﬁnal diﬀerential equation, dKe Ke K x − Ke Kz − Ke = 2 + df 1 − f Ke + Lx (Kx − Ke Ke + Lz (Kz − Ke ) (3) Integrating the above equation and imposing the initial condition that Ke =Km at f =0, we obtain K 3A K + B 3C1 K + B 3C2 m m 1 m 2 1−f = Ke Ke + B1 Ke + B2 (4) ΔKe = Km

X.F. Zhou et al.: J. Mater. Sci. Technol., 2012, 28(3), 285–288.

Fig. 2 Eﬀective thermal conductivity Ke /Km as a function of depolarization factor Lz at volume fraction f =0.05

where A= B1,2 = C1,2 =

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Fig. 3 Ke /Km as a function of Kp /Km for Lz =1/3, 0.1, 0.499, f =0.05

2Lz (−5 − 8Lz − 3L2z ) (2 + 6Lz )(3Lz − 5)

Kz − 3Kx (−1 + Lz ) − 3Kz Lz ± N −10 + 6Lz

N (1 + 8Lz 9L2z ) ± [Kx (−1 + Lz )2 (13 + 21Lz ) + Kz (1 + 5Lz + 47L2z − 21L3z )] N (−10 + 6Lz )(1 + 3Lz ) N = Kz2 (1 − 3Lx )2 + 9L2x (−1 + Lz )2 + 2Kx Kz (13 + 12Lz − 9L2z )

Eq. (4) is the diﬀerential eﬀective medium approximation, which contains not only geometric anisotropy (Lx ) but also anisotropy of physical properties (Kx , Kz ). For spherical inclusions, such as cenosphere particles (see Fig. 1(b), Lz =1/3), and for physical isotropy Kx =Kz =Kp , we can obtain Kp − Ke Kp 1/3 (5) K p − Km Ke In Fig. 2 we investigate the eﬀect of the particle shape on the eﬀective thermal conductivity in asphalt-based mixture. For simplicity, we assume solid particles to be physically isotropic with the thermal conductivity Kx =Kz =Kp . The normalized eﬀective thermal conductivity Ke /Km is plotted as a function of the particle shape for various Kp /Km at the volume fraction f =0.05. We choose the typical six ratios of Kp /Km and Km /Kp which are corresponding to the thermal conduction and thermal insulating in asphalt-based mixture. We ﬁnd that for spherical particles (Lz =1/3), the eﬀective thermal conductivity of the composites achieves minimum. When the granular shape deviates from the spherical one, the eﬀective thermal conductivity will be increased. This can be well understood that since the shape of ﬁlling particle deviates from the spherical one, they can more easily form the conduction path for Kp /Km >1 or thermal barrier for Km /Kp >1. Therefore, the result also indicates that the adjustment of the particle shape is really helpful to achieve the enhancement of thermal conductivity or thermal insulating in asphalt-based mixture. Next we study the dependence of the eﬀective thermal conductivity on the ratio of Kp /Km in Fig. 3. Obviously, when adding high thermal conductivity particles into base-asphalt (Kp /Km > 1), the enhancement of thermal conductivity Ke /Km increases with increasing the ratio Kp /Km . In thermal insulation case (Km /Kp > 1), Ke /Km decreases with decreasing the ratio Kp /Km . The thermal conduction (or thermal insulating) tendency becomes quite dramatic for adding prolate (Lz < 1/3) and oblate (Lz > 1/3) particles. As a result, the thermal conductivity of the constituent and particle shape are the key factors in the thermal modiﬁcation of asphalt-based mixture. We measured the eﬀective thermal conductivity with the ﬁlled cenosphere particles, and graphite powders at chosen volume fraction (1, 3, 5, 7, 9, 11, 13, 15, 17, 20 vol.%) in base asphalt. To further verify the validity of our theory, we compare theoretical results with our experiment data in Fig. 4. For numerical calculations, the thermal conductivity and depolarization factor were taken as 0.09 W/mk, 1/3 for cenosphere particles; 1−f =

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the experiment data. The new model can be applied for predicting the thermal properties of asphalt-based mixture, still is available for most of thermal modiﬁcation in two-phase composites.

Acknowledgements This work is supported by the National Natural Science Foundation of China under grants Nos. 50906073 and 50973018. REFERENCES

Fig. 4 Eﬀective thermal conductivity of asphalt with various volume fractions of graphite and cenosphere powders compared with our numerical results

50 W/mk, 0.3 for graphite particles; 0.8 W/mk for asphalt [13,14] . Our theoretical results were found to be in reasonable agreement with the experiment data. 4. Conclusion In this paper, we investigated the thermal conductivity modiﬁcation with the cenosphere particles and graphite powders ﬁlled in base asphalt. By taken into account the particle shape (depolarization factor), volume fraction, the thermal conductivity of ﬁlling particles and base asphalt, we present a new diﬀerential eﬀective medium formula to predict the thermal conductivity modiﬁcation in asphalt-based mixture. We found that the thermal conductivity of the constituent and particle shape were the key factors in the thermal modiﬁcation of asphalt-based mixture. Our theoretical predications were in good agreement with

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