## NUGGET

### Effects of Electric Double Layer on Dielectrophoretic Motion of Particles

T. N. Swaminathan and Howard H. Hu, University of Pennsylvania

Project Goal: Develop theoretical models and computational tools to study of assembly of macromolecules and nanotubes using dielectrophoresis.In an electric field, particles suspended in a liquid with different electric properties become polarized. Under the action of a nonuniform electric field, the polarized particle experiences a dielectrophoretic force, and moves accordingly. By proper design of the electric field, one can manipulate the particles and assembly them into desirable patterns. Our modeling approach uses two-way coupling computing the motion of particles and fluids. At each time step during the motion, the Laplace equation for the electric field, the Navier-Stokes equations with electric Maxwell stress for the fluid, and the particle equations of motion are solved numerically using finite element technique. To account for the effect of the induced electric double layer next to the particle surface, a thin-double-layer model is constructed, where the ion distribution, the electric potential, and the resulted flow within the double layer are solved analytically using the method of matched asymptotic expansions. This analytical solution in the inner layer is then served as interfacial conditions to match the numerical solutions inside the particle and outside the double layer.

(Left) Flow pattern around a particle placed close to a wall located at the right side of the picture in an electric field acting along the wall. (Right) Force on the particle as a function of distance from the wall.

Dielectrophoretic force on a particle were studied in two cases to highlight the effect of the induced electric double layer (EDL). The EDL affects particle motion in two ways: (a) by modified the electric field around it and; (b) by inducing a flow field around the particle surface. The lower frequency dispersion is not captured by the traditional models that don’t account for the effects produced by the double layer.

Variation of force on a cylinder, placed in a non-uniform field, as a function of frequency for three cases; (1) the effect of the double layer excluded (black line), (2) only with the electric field changes of the double layer (blue line) and (3) with both electric and flow effects from the double layer included (red).