| Summary: | 碩士 === 國立臺灣大學 === 化學工程學研究所 === 95 === The boundary effects on electrophoresis of a spherical or cylindrical colloidal particle with a nonuniform zeta potential distribution in the vicinity of a confining wall at quasisteady state are analyzed. The applied electric field is constant and the electric double layers adjacent to the solid surfaces are assumed to be much thinner than the particle radius and the gap width between the surfaces. The presence of a confining wall causes three basic effects on the particle velocity: (a) the local electric field on the particle surface is enhanced or reduced by the wall; (b) the wall increases viscous retardation of the moving particle; (c) an electroosmotic flow of the suspending fluid may exist due to the interaction between the charged wall and the tangential electric field.
In the first part of the thesis, a study is presented for the electrophoretic motion of a dielectric sphere situated at the center of a spherical cavity when both surface potentials are nonuniform. The Laplace and Stokes equations are solved analytically for the electric potential and velocity fields, respectively, in the fluid phase, and explicit formulas for the electrophoretic and angular velocities of the particle are obtained. To apply these formulas, one only has to calculate the multipole moments of the zeta potential distributions at the particle and cavity surfaces. It is found that the contribution from the electroosmotic flow developing from the interaction of the imposed electric field with the thin double layer adjacent to the cavity wall and the contribution from the wall-corrected electrophoretic driving force to the particle velocities can be superimposed due to the linearity of the problem.
In the other part of the thesis, an investigation of the electrophoretic motion of a long dielectric circular cylinder with an angular distribution of its surface potential under a transversely imposed electric field in the vicinity of a large plane wall parallel to its axis is made, where the applied electric field can be either perpendicular or parallel to the plane wall. Through the use of cylindrical bipolar coordinates, the Laplace and Stokes equations are solved analytically for the two-dimensional electric potential and velocity fields, respectively, in the fluid phase, and explicit formulas for the electrophoretic and angular velocities of the cylindrical particle are obtained. To apply these formulas, one only has to calculate the multipole moments of the zeta potential distribution at the particle surface. It is found that the existence of a nearby plane wall can cause the translation or rotation of a particle which does not exist in an unbounded fluid under the applied electric field.
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