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RESEARCH PAPERS: Electrical Effects at the Macro and Micro Scale

An Analytical Method for Dielectrophoresis and Traveling Wave Dielectrophoresis Generated by an $n$-Phase Interdigitated Parallel Electrode Array

[+] Author and Article Information
Hongjun Song

Department of Mechanical Engineering, University of Maryland, Baltimore County, MD 21250hongjs1@umbc.edu

Dawn J. Bennett

Department of Mechanical Engineering, University of Maryland, Baltimore County, MD 21250dawnb@umbc.edu

J. Fluids Eng 130(8), 081605 (Aug 01, 2008) (8 pages) doi:10.1115/1.2956610 History: Received July 19, 2007; Revised February 28, 2008; Published August 01, 2008

Abstract

In this paper, we present an analytical method for solving the electric potential equation with the exact boundary condition. We analyze the dielectrophoresis (DEP) force with an $n$-phase ac electric field periodically applied on an interdigitated parallel electrode array. We compare our analytical solution with the numerical results obtained using the commercial software CFD-ACE . This software verifies that our analytical method is correct for solving the problem. In addition, we compare the analytical solutions obtained using the exact boundary conditions and the approximate boundary conditions. The comparison shows that the analytical solution with the exact boundary condition gives a more accurate analysis for DEP and traveling wave DEP forces. The DEP forces of latex beads are also investigated with different phase arrays for $(n=2,3,4,5,6)$.

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Figures

Figure 1

The schematic physical model of the interdigitated parallel electrode array

Figure 8

The magnitude and vector of the cDEP force and the twDEP force for the four-phase array. The scale on the magnitude plots for both fields are log10. (a) Magnitude of ∇(∣∇ϕR∣2+∣∇ϕI∣2) (b) the vector of ∇(∣∇ϕR∣2+∣∇ϕI∣2), (c) magnitude of ∇×(∇ϕR×∇ϕI), and the vector of (d) ∇×(∇ϕR×∇ϕI).

Figure 9

The comparison of the DEP force at the center plane (y=10μm) with n-phase array (n=2,3,4,5,6). (a) The magnitude of ⟨F⃑cDEP⟩ and (b) the magnitude of ⟨F⃑cDEP⟩.

Figure 10

The distribution pattern of the latex beads: (a) the Initial position of the particles and (b)–(f) the position of the particles with two-phase, three-phase, four-phase, five-phase, and six-phase arrays respectively, at the dimensionless time t#=16. (a) The initial position of the particles, (b) two-phase array, (c) three-phase array, (d) four-phase array, (e) five-phase array, and (f) six-phase array.

Figure 2

The simplified 2D periodic model and boundary condition

Figure 3

The contour plot of the electric field ϕR(x,y) for the two-phase array

Figure 4

The comparison of the distributed electric potential at the bottom boundary (y=0)

Figure 5

The difference value δ=∣ϕR−ϕR*∣ at the bottom boundary (y=0)

Figure 6

The comparison of the electric field ϕR(x,y) at the bottom boundary (y=0)

Figure 7

The comparison of the DEP force near the electrode plane (y∕d=0.1): (a) the x-component of the DEP force and (b) the y-component of the DEP force

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