Clausius-Mossotti factor

Figure 1. Real part of the Clausius-Mossotti factor for a solid spherical dielectric particle at various medium conductivities (for Sp = 2.55, o, = 0.01 S/m, and = 78.5). Switch of the sign of Re. K indicates switch between positive and negative dielectrophoresis.

The effective dipole moment is frequency-dependent with the dependence characterized by the Clausius-Mossotti factor ... 

Separating the real and imaginary part of the Clausius-Mossotti factor give a Debye relaxation of the form ... 

Equation (3) shows that the real part of the Clausius-Mossotti factor goes to a low frequency co = 0) limiting value of (o -cr )/(o +2cr ), i.e. it depends on the conductivity of the particle and the medium. At high frequency ( oo) the limiting value is 6p-6m)l Sp+2 m) and the polarization is dominated by the permittivity of the particle and the medium. From Eq. (4), the imaginary part of the Clausius-Mossotti factor is zero at both low and high frequencies at the Maxwell-Wagner relaxation frequency /mw " it has a value of p- m)l pF2 m) - (Jp-(Jm)l... 

GpF2<7m) l2. Both the real and imaginary parts of the Clausius-Mossotti factor govern the movement of particles in AC electric field, but in different... 

DEP force. The frequency dependence and the direction of the DEP force are governed by the real part of the Clausius-Mossotti factor. If the particle is more polarisable than the medium, (Re[/cm] > 0). the particle is attracted to high intensity electric field regions. This is termed as positive dielectrophoresis (pDEP). Conversely, if the particle is less polarisable than the medium, (Re[/cm] < 0), the particle is repelled from high intensity field regions and negative dielectrophoresis (nDEP) occurs. Therefore the real part of the Clausius-Mossotti factor characterizes the frequency dependence of the DEP force, as demonstrated in Fig. 1. 

In practice, it is difficult to measure the DEP force due to the effects of Brownian motion and electrical field-induced fluid flow [3]. Instead, the DEP crossover frequency can be measured as a function of medium conductivity and provides sufficient information to determine the dielectric properties of the suspended particles. The DEP crossover frequency,is the transition frequency point where the DEP force switches from pDEP to nDEP or vice versa. According to Eq. (6), the crossover frequency is defined to be the frequency point where the real part of the Clausius-Mossotti factor equals zero ... 

Figure 1. (a) Diagram of a single shelled spherical particle, representing a cell in suspension, (b) Plot showing the real and imaginary parts of the Clausius-Mossotti factor of the mixture, calculated for different conductivities of the medium. The following parameters for the medium and a cell were used = 8.854 x 10 Fm , = 3 x lo m, [Pg.509]

This frequency, co, dependent factor, K((u), dynamically reflects the polarizability of a particle (subscript p) in a conductive medium (subscript m). The Clausius-Mossotti factor is a ratio of complex permittivities, of the form H = s — ia/oj, where co is the frequency, s is the dielectric constant, and a is the electrical conductivity of the medium. As can be seen, the complex K(ffl) factor has an imaginary component, which is out of phase with the applied electric field, while the real component is in phase [1, 4]. The imaginary... 

This dielectric force pushes particles toward regirms of high field density or low field density depending on whether the Clausius-Mossotti factor is positive or negative, respectively. In other words, if Op < ct then negative dielectrophoretic motion away from sharp points in electrodes or insulator obstacles is observed the converse is true for positive dielectrophoresis, which is rarely observed in DC-DEP due to other electrokinetic forces. For a truly insulating particle, Op = 0, the Clausius-Mossotti factor is simply 1/2, and motion away from high field... 

Fig. 4 Plot of the Clausius-Mossotti factor against frequency for two different solid particles. In the shaded area, one particle experiences positive dielectrophoresis and the other negative dielectrophoresis, enabling separation in this frequency window...

In this equation, the factor, /ay, is called the Clausius-Mossotti factor and describes the... 

The frequency of the applied field, through the real part of Clausius-Mossotti factor... 

In this equation the factor, is called the Clausius-Mossotti factor and describes the frequency dependence of the polarisability. Combining Eqs. (1) and (2) leads to the expression for the dipole in terms of the complex permittivity of the particle and the suspending medium (subscript p and m respectively) ... 

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