Calculation of DEP and EWOD Forces for Application in Digital Microfluidics

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.

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.

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.

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.

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

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

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

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

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).

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

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

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

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.