  We describe electrophoresis of spherical dielectric particles in a uniformly
aligned nematic medium with a negative dielectric anisotropy. A spherical
particle that orients the liquid crystal (LC) perpendicularly to its surface
moves under the application of the uniform direct current (DC) or alternating
current (AC) electric field. The electric field causes no distortions of the LC
director far away from the sphere. Electrophoresis in the nematic LC shows two
types of nonlinearity in the velocity vs. field dependence. The velocity
component parallel to the applied electric field grows linearly with the field,
but when the field is high enough, it also shows a cubic dependence. The most
interesting is the second type of nonlinear electrophoresis that causes the
sphere to move perpendicularly to the applied field. This perpendicular
component of velocity is proportional to the square of the field. The effect
exists only in a LC and disappears when the material is melted into an
isotropic fluid. The quadratic effect is caused by the dipolar symmetry of
director distortions around the sphere and is classified as an LC-enabled
electrophoresis (LCEEP). The nonlinear electrophoretic mobility of particles in
LCEEP offers a rich variety of control parameters to design 3D trajectories of
particles for microfluidic and optofluidic applications.
