Slow motion of an arbitrary axisymmetric body along its axis of revolution and normal to a plane surface

Hydrodynamics and Brownian motions of a spheroid near a rigid wall

“…The problem of an axisymmetric particle near a boundary has been partially investigated in previous works; 35,36 the method used in those papers (boundary integral method) is different from that used in the present work (see below). Moreover, we compute the complete mobility matrices, whereas only specific configurations were considered in the references indicated above.…”

Motion of a Colloidal Sphere Covered by a Layer of Adsorbed Polymers Normal to a Plane Surface

“…The plane surface can be either a solid wall or a free surface. The momentum equation applicable to the system is solved by using the method of matched asymptotic expansions incorporated with a boundary collocation technique (28,29). Our numerical results for the motion of a particle normal to a plane wall compare favorably with the formulas analytically derived from the method of reflections.…”

Electrophoresis of an axisymmetric particle along its axis of revolution perpendicular to two parallel plane walls

“…When a spheroid with a fixed aspect ratio is located near a first plane wall, the approach of a second wall far from the particle can first increase the electrophoretic mobility to a maximum, then reduce this mobility when the second wall is close to the particle, and finally lead to a minimum mobility when it reaches to the same distance from the particle as the first wall. Although the numerical solutions were presented in the previous sections only for the axisymmetric electrophoresis of a prolate spheroid and an oblate spheroid normal to one or two plane walls, the combined analytical and numerical technique utilized in this work can easily provide the calculations for the corresponding electrophoretic velocity of an axisymmetric particle of other shapes, such as a prolate or oblate Cassini oval (Keh and Tseng 1994). In principle, this method of spherical singularity distribution incorporated with the boundary collocation technique can also be used to investigate the asymmetric electrophoretic motion of a colloidal particle of revolution at an arbitrary position in a slit microchannel (Chen and Keh 2005).…”

“…3, a set of spherical singularities satisfying the boundary conditions in Eqs. 5 and 6 are chosen and distributed along the axis of revolution within a prolate particle or on the fundamental plane within an oblate particle (Keh and Tseng 1994). The electric potential distribution in the fluid phase is approximated by the superposition of the set of the spherical singularities and the boundary condition Eq.…”