Start-Up Electrophoresis of a Cylindrical Particle with Arbitrary Double Layer Thickness

The start-up of electrophoretic motion of a charged circular cylindrical particle in an unbounded solution of arbitrary electrolytes is analytically investigated. The modified Stokes equation for the transient fluid flow field is solved by using the Laplace transform. Analytical formulas for the time-evolving electrophoretic velocities of the dielectric cylinder are determined for the transversely and axially imposed electric fields, and they can be superimposed linearly for an imposed electric field of arbitrary direction. The transient electrophoretic velocities normalized by their respective steady-state values increase monotonically with an increase in the ratio of the particle radius to the Debye screening length but decrease monotonically with an increase in the particle-to-fluid density ratio, keeping the other parameter unchanged. The normalized electrophoretic acceleration of the particle decreases monotonically with the elapsed time. In general, the electrophoretic velocity of the cylindrical particle is not collinear with the arbitrarily oriented imposed electric field. The effect of the relaxation time for the transient electrophoresis is much more important for a cylindrical particle than for a spherical particle.