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The CM factor also depends on the geometry of structures and is expressed differently for cylindrical [38] in (5) and spherical [3] structures in (6) as below: * * ε (5) p − ε * * m f CM (ε p ,ε m ) = * ε m , * * ε p − ε * * m f CM (ε p ,ε m ) = * * (6) ε p + 2ε m , 2.2 Characterisation of the CM factor for MWCNT and polystyrene microparticles The DEP force takes the same sign of the real part of the CM factor, which can be either positive or negative. To explore the ability of DEP force to sort polystyrene microparticles and WMCNTs, calculations of the CM factor for various electric field frequencies were conducted using Equations (1)-(6) for each of these particles suspended in DI water. Because of the significant size difference between MWCNTs and polystyrene microparticles, the geometric factor Γ was also calculated and taken into the consideration. Firstly, the value of Г×Re[f CM ] of MWCNTs was calculated. The relative permittivity of MWCNTs was taken as 2.5 while the conductivity was assumed between 1000 S/m and 150 S/m according to [38, 39]. The diameter and length of MWCNTs were assumed to be 50 nm and 2 μm respectively. The relative permittivity of the DI water is taken 78 and the conductivity is measured as 0.2 mS/m. Figure 1 presents the value of Г×Re[f CM ] as a function of applied electric field frequency, calculated for MWCNTs suspended in deionised (DI) water. Since the value stays above zero for all frequencies considered in this investigation (1 kHz-100 MHz), MWCNTs always experience a positive DEP force. Next, Г×Re[f CM ] of polystyrene microparticles was calculated. This calculation is more complicated than that of MWCNT as the conductivity of polystyrene must be carefully defined. Polystyrene has a very low conductivity, and thus the inherent conductivity of material is zero. However, placing the microparticles in DI water results in the inducing of surface conductance [40]. The total surface conductance can be modelled as two separate components: a conductance due to the movement of charges in the diffuse double layer and another due to charge movements in the Stern layer. As a result, the microparticle has an non-zero effective conductivity σ p , which could be expressed as [41]: 2K (7) S σ p = r where K s represents the surface conductance and r is the radius of the microparticle. K s can be calculated as [41]: r (8) ⎜⎛ 2 2 K = − + − ( − )( + )( ⋅ ) ⎟⎞ S σ m 9σ m 4 ε p ε m ε p 2ε m f 0 2π 4 ⎝ ⎠ Here, f 0 is known as the crossover frequency where DEP force is zero. Therefore, at the crossover frequency the value of K s has a linear relationship with the particle diameter if permittivity of the medium and particles are constant. The surface conductance has been calculated for different dimensions of latex beads [41]. According to the results, the value of K s is found to be 0.25 nS. In this case, the microparticle conductivity is calculated to be 1 mS/m. The relative permittivity of microparticle is assumed to be 2.5. Regarding these values, Г×Re[f CM ] was calculated as a function of frequency and presented in Figure 2. It is evident that in this case, the microparticles experience positive DEP forces below 200 kHz, and negative DEP force above 200 kHz. 98
Figure 1. Г×Re[fCM] vs. frequency for the MWCNTs in DI water; (up): log to log scale; (down): normal scale. By comparing Figures 1 and 2, it is evident that MWCNTs experience strong positive DEP force for frequencies smaller than 1 MHz while polystyrene microparticles experience neutral or moderate negative DEP force for frequencies larger than 200 kHz. As a result, it should be possible to use DEP to separate the MWCNT and polystyrene microparticles, particularly by applying an electric field with frequency in the range of 200 kHz to 1 MHz. In this paper, the used MWCNTs were metallic and their conductivity was assumed to lie in a range between 150 to 1000 S/m and the calculations and simulations were based on this assumption. Semi-conductive carbon nanotubes (CNTs) have also been used in DEP experiments by other groups [42]. However, due to their dielectric properties, they experience negative DEP force at high frequencies. As, the crossover frequencies of polystyrene microparticles and the semi-conductive MWCNTs are different, it is possible to perform DEP separation of these two materials for ranges between the two crossovers frequencies. 99
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The 3 rd VACPS Research Workshop Pr
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Organizing Committee Victorian Asso
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Preface On the occasion of the publ
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Acknowledgements We gratefully ackn
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⎧π0 if j = i and Cx ij k > δij
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As illustrated in Fig.4, the struct
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Definition 2 The probability of tar
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Acknowledgments Xiaobo Deng would l
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