Electromechanics of piezoelectric elements

Continuous separation and manipulation of particles and cells using dielectrophoresis

“…Interestingly, yeast cells can form chains when exposed to a non-uniform electric field ( Figure 5.15 (b, c, e and f)). Chain formation occurs as a result of the dipole-dipole interactions, in which two induced dipoles attract each other when aligned with the applied field, but repel each other when aligned perpendicularly to the field [33]. This explains the striking formation of chains in the same direction as the field lines shown in Figure 5.8 (a).…”

“…Due to high frequency, the charged particle keeps stationary, while the neutral particle, after the dipole is re-oriented according to the polarities of electrodes, remains the same direction towards the region of higher electric field. Figure 2.4: Motion of a charged particle and a neutral particle in a non-uniform AC electric field [17] To study the behaviors of a neutral particle in a non-uniform electric field, the estimation of the net force on an infinitesimal dipole that consists of equal and opposite charges (+q and -q) is performed [33]. In the spatial coordinate as shown in Figure 2.5, the location of the charge -q is described by the vector, r , and a distance, d , apart from the charge +q.…”

“…where high-order terms such as 2 , ac E r t , the DEP force acting on a dielectric particle can be determined by using the Maxwell stress tensor formulation [35], or alternatively by using the effective dipole moment method [33]. The results from both methods have been shown to yield the identical DEP force expression [36].…”

“…However, because the latter is much simpler and provides valid predictive results, it is used to derive DEP force here. The method points out that the effective dipole moment of a neutral particle being polarized by an electric field is defined as the moment of an equivalent free-charge point dipole that is immersed in the same dielectric medium and located at the same point of the particle's center [33].…”

“…Assuming that the particle and suspending medium have dielectric permittivities of p ε and m ε , and finite conductivities of p σ and m σ , respectively. The general expression for the complex effective dipole moment of a dielectric sphere with radius a that contains the magnitude and phase information of the effective dipole moment has been given as [33]…”