Consider a negatively charged spherical particle of
radius a bearing a charge, Qs, suspended in a pure dielectric
fluid (containing no ions). When subject to a uniform
electric field, E~N, the particle will translate under the influence of the electric force acting on it. The induced particle
motion refers to electrophoresis, which has been widely used
to characterize and purify molecules and colloidal particles.
The net electrical force on the charged particle will simply be
F
~
E 5 QSE~N. As soon as the particle starts to move under the
influence of this electric force, it encounters an oppositely
directed fluid drag force.
(a) Under the Stokes flow regime and neglecting the gravitational force and the buoyancy force acting on
the microparticle, derive an expression to calculate the
particle’s steady-state translational velocity.
(b) Based on the above results, explain why electrophoresis
can be used to separate biological samples.
(c) Calculate the translational velocities of two particles
of radius a 5 1 μm and 10 μm using Qs 5 210212 C,
EN 5 1000 V/m, and μ 5 1023 Pa s.