Unsteady electrophoretic motion of a non-spherical colloidal particle in an oscillating electric field

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Abstract
The oscillatory motion of an electrically charged non-spherical colloidal particle in an oscillating electric field is investigated. The particle is immersed in an incompressible viscous fluid and assumed to have a thin electric double layer. For moderate-aspect-ration spheroids and cylinders, a simple algebraic expression is derived that accurately describes oscillatory electrophoretic particle motion in terms of the steady Stokes resistance, added mass, and Basset force. The effects of double-layer conduction and displacement currents within dielectric particles are included. The results indicate that electroacoustic measurements may be able to determine the ζ-potential, dielectric constant, surface conductivity (and microstructural information contained therein), size, density, volume fraction, and possibly shape of non-spherical particles in a dilute suspension. A simple formula is obtained for the high-frequency electrical conductivity of a dilute suspension of colloidal spheroids with arbitrary charge and dielectric constant; only the added mass and Basset force are required and the requisite parameters are given. The result is needed for electroacoustic measurements but it may also be independently useful for determining the dielectric constant, surface conductivity, volume fraction, and possibly the shape of non-spherical particles in a dilute suspension. Electroacoustic energy dissipation is described for a dilute colloidal suspension. It is shown that resistive electrical heating and viscous dissipation occur independently. Electrical and viscous dissipation coefficients that characterize the order volume fraction contributions of the suspended particles are calculated; the electrical dissipation coefficient is O(1) for all oscillation frequencies, whereas the latter vanishes at low- and high-frequencies. The fluid motion is shown to be a superposition of unsteady, viscous and potential flows past an oscillating particle with no applied electric field. The electro-osmotic flow field is insensitive to particle geometry and qualitatively different from the flow past an oscillating particle with no applied field.