Transient Electrophoresis in Suspensions of Charged Porous Particles

The start-up of electrophoretic motion in a suspension of uniformly charged, porous, spherical particles within an arbitrary electrolyte solution under a suddenly applied electric field is investigated. The unsteady Stokes/Brinkman equations, modified to include the electric body force, are solved for the fluid velocity field using a unit cell model to account for the particle-particle interactions. An explicit expression for the transient electrophoretic velocity of a porous particle in a unit cell is derived in the Laplace transform domain as a function of the key governing parameters. The transient electrophoretic velocity, when normalized by its steady-state counterpart, increases monotonically with both elapsed time and the ratio of particle radius to Debye length, with other parameters held constant. It generally increases with the ratio of particle radius to permeation length and with porosity, while decreasing monotonically with an increase in the particle-to-fluid density ratio. Similar to its steady-state value, the transient electrophoretic mobility of the suspension is typically a decreasing function of the particle volume fraction. However, under conditions of small elapsed time and large density ratio, the transient mobility may exhibit an initial increase with particle volume fraction.