Dielectrophoretic spectra of translational velocity and critical frequency for a spheroid in traveling electric field

Abstract

An analysis has been made of the dielectrophoretic (DEP) forces acting on a spheroidal particle in a traveling alternating electric field. The traveling field can be generated by application of alternating current signals to an octapair electrode array arranged in phase quadrature sequence. The frequency dependent force can be resolved into two orthogonal forces that are determined by the real and the imaginary parts of the Clausius-Mossotti factor. The former is determined by the gradient in the electric field and directs the particle either toward or away from the tip of the electrodes in the electrode array. The force determined by the imaginary component is in a direction along the track of the octapair interdigitated electrode array. The DEP forces are related to the dielectric properties of the particle. Experiments were conducted to determine the DEP forces in such an electrode arrangement using yeast cells (Saccharomyces cervisiate TISTR 5088) with media of various conductivities. Experimental data are presented for both viable and nonviable cells. The dielectric properties so obtained were similar to those previously reported in literature using other DEP techniques.

Figure 1

A single shelled spheroidal model in ac electric field $\left(\vec{E}\right)$ related with the effective dipole moment vector ${\vec{\mu }}_{\text{eff}\left(k\right)}$. (a) Cross sectional view of the shelled spheroid assigned with dielectric constants and conductivities of the suspending medium (ε_s,σ_s), the cytoplasm (ε_c,σ_c), and the membrane (ε_m,σ_m). (b) Three dimensional view showing three a, b, and c axes along x, y, and z, respectively. The δ is denoted for the membrane thickness.

Figure 2

The top view of the octapair interdigitated electrode with diagrams of electrical setup to operate the electrode. (a) Two orthogonal forces (${\overline{\vec{F}}}_{\text{cDEP}}$ and ${\overline{\vec{F}}}_{\text{twDEP}}$) acting on the spheroid in ±x and ±y directions, respectively. (b) The electrode was driven by the quadrature phase signals split from a function generator through the interjunction unit connected with phase shift unit.

Figure 3

The spectra of Re[CMF] are affected by changing electrical parameters of the spheroidal model, as described in Fig. 1.

Figure 4

Cross-sectional view of the interdigitated electrode, as seen from x-z plane (not to scale), shows forces acting on the cell being levitated above the track.

Figure 5

Curve fittings between experimental and theoretical data of cell translational speeds were plotted as a function of the electric field frequency for the control and dead cells. The conditions are that (a) the conductivities of the suspending medium (σ_s) are changed from 0.01 to 0.10 S m⁻¹ and (b) electric field strengths E of 28–143 kV m⁻¹. For the dead cells of E=28 kV m⁻¹, (c) σ_s=0.01 S m⁻¹ and (d) σ_s=0.04 S m⁻¹, cells’ electrical properties obtained are shown in Table 1.

Figure 6

(a) Curve fittings of critical frequencies of the control and (b) the dead cells as a function of the conductivity of the suspending medium. The theoretical lines were plotted using the parameters shown in Table 1.