Transient electrophoresis of a charged porous particle

The starting electrophoretic motion of a porous, uniformly charged, spherical particle, which models a solvent-permeable and ion-penetrable polyelectrolyte coil or floc of nanoparticles, in an arbitrary electrolyte solution due to the sudden application of an electric field is studied for the first time. The unsteady Stokes/Brinkman equations with the electric force term governing the fluid velocity fields are solved by means of the Laplace transform. An analytical formula for the electrophoretic mobility of the porous sphere is obtained as a function of the dimensionless parameters kappa a, lambda a, rho p/rho, and nu t/a2, where a is the radius of the particle, kappa is the Debye screening parameter, lambda is the reciprocal of the square root of the fluid permeability in the particle, rho(p) and rho are the mass densities of the particle and fluid, respectively, nu is the kinematic viscosity of the fluid, and t is the time. The electrophoretic mobility normalized by its steady-state value increases monotonically with increases in nu t/a2 and kappa a, but decreases monotonically with an increase in rho p/rho, keeping the other parameters unchanged. In general, a porous particle with a high fluid permeability trails behind an identical porous particle with a lower permeability and a corresponding hard particle in the growth of the normalized electrophoretic mobility The normalized electrophoretic acceleration of the porous sphere decreases monotonically with an increase in the time and increases with an increase in lambda a from zero at lambda a=0.