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RESEARCH PAPERS: Electrical Effects at the Macro and Micro Scale

# Calculation of DEP and EWOD Forces for Application in Digital Microfluidics

[+] Author and Article Information
Patrick M. Young

Department of Aerospace Engineering Sciences, University of Colorado at Boulder, Boulder, CO 80309

Kamran Mohseni

Department of Aerospace Engineering Sciences, University of Colorado at Boulder, Boulder, CO 80309mohseni@colorado.edu

J. Fluids Eng 130(8), 081603 (Jul 30, 2008) (9 pages) doi:10.1115/1.2956606 History: Received June 19, 2007; Revised December 21, 2007; Published July 30, 2008

## Abstract

Two primary methods for electrostatically actuating microdroplets in channels currently exist: dielectrophoresis (DEP) for electrically insulating fluids and electrowetting on dielectric (EWOD) for conducting fluids. In each case, a transverse electric field is used to create an electrostatic pressure, giving rise to the transport of individual liquid slugs. This paper examines the nature of the force distribution for both EWOD and DEP actuated droplets. The effects of system parameters such as contact angle and electrode length on the shape of the force density and its net integral are considered. A comparison of the scaling properties of DEP and EWOD for applications in digital microfluidics is presented. The net DEP force is shown to be strongly peaked when a droplet interface is located near the edge of a charged electrode and reduces to the well-known lumped parameter model in the appropriate limits. The effect of electrode spacing is seen to have an inversely proportional effect on the force experienced by the droplet, and the effect of increasing droplet contact angle is observed to increase the net force on the droplet.

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Topics: Force , Electrodes

## Figures

Figure 1

The (a) EWOD and (b) DEP configurations. H is the droplet and the channel height and L, Le, and Lc, are the droplet, the electrode, and the channel widths. l is the spacing between the hot and grounded electrodes.

Figure 8

Convergence of force calculation as resolution increases. The number of points is in terms of the discretization in the x-direction.

Figure 9

The net horizontal force experienced by the droplet as a function of position. Position is given by the location of the center of the droplet with respect to the center of the electrode. (a) Le=1.8 and L=2.0; (b) Le=2.0 and L=2.0; (c) Le=2.2 and L=2.0; and (d) setup for force calculations in (a)–(c).

Figure 10

Electric potential for various contact angles. The increased gradient from the curvature results in greater net horizontal force.

Figure 11

Increase in net horizontal force as the contact angle θ increases for a droplet with the leading edge placed near the left edge of the electrode near the fringing field

Figure 12

DEP configuration. The gap between the adjacent electrodes is l.

Figure 13

Net horizontal force versus x, for various values of l. The percentage shown indicates the width of the gap with respect to H. P1 and P2 are the same, as shown in Fig. 1. (a) Force versus position. x=−1 when the leading edge of the droplet is flush with the edge of the electrode. (b) Net horizontal force versus nondimensional position (relative to the length of the gap between the electrodes). l2.5% is the length of the gap for l=0.025H and xpeak is the location of the maximum net force.

Figure 7

Example calculation of the electric potential V for a droplet centered under the left edge of an electrode

Figure 6

Representative grid used in computation; not all computational nodes are shown. x0 is the point of maximum clustering.

Figure 5

Boundary conditions used in numerically solving for the electric potential surrounding a dielectric fluid in DEP configuration

Figure 4

Charge distributions (a) and force densities (b) on the leading and trailing interfaces of an EWOD-activated droplet. Contact angle is 0deg. See Ref. 26 for more details.

Figure 3

Example calculation of the electric equipotentials surrounding a droplet in EWOD configuration; the contact angle is 10deg. In nondimensional units, h=1, L=2, and the length of the computational domain=10. See Ref. 26 for more details.

Figure 2

Integration paths used when calculating the force with the Maxwell stress tensor when (a) the droplet interface is far away from the electrode interface and (b) when the droplet interface is near the electrode interface.

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