Boundary Effects on Phoretic Motions of colloidal Cylinders
Date Issued
2011
Date
2011
Author(s)
Wang, Li-Ju
Abstract
In this thesis, boundary effects on the two-dimensionalcreeping motion, thermophoresis and electrophoresis of cylindrical particles in a continuous medium are theoretically studied. Through the use of cylindrical bipolar coordinates, the transport governing equations are solved to calculate the various velocities of acylindrical particle migrating normal or parallel to a plane wall.
In Chapter 2, an analytical study is presented for the creeping flow caused by a long circular cylindrical particletranslating and rotating in a viscous fluid near a large plane wall parallel to its axis. The fluid is allowed to slip at thesurface of the particle. The Stokes equations for the fluid velocity field are solved in the quasisteady limit. Semi-analytical solutions for the drag force and torque acting on the particle by thefluid are obtained for various values of the slip coefficient associated with the particle surface and of the relativeseparation distance between the particle and the wall. The results indicate that the translation and rotation of theconfined cylinder are not coupled with each other. For the motion of a no-slip cylinder near a plane wall, ourhydrodynamic drag force and torque results reduce to the closed-form solutions available in the literature. Theboundary-corrected drag force and torque acting on the particle decrease with an increase in the slip coefficient for anotherwise specified condition. The plane wall exerts the greatest drag on the particle when the migration occurs normalto it, and the least in the case of motion parallel to it. The enhancement in the hydrodynamic drag force and torque on atranslating and rotating particle caused by a nearby plane wall is much more significant for a cylinder than for a sphere.
In Chapter 3, an analytical study is presented for the thermophoretic motion of a circular cylindrical particle in a gaseous medium with a transversely imposed temperature gradient near a large plane wall parallel to its axis in the quasisteady limit of negligible Peclet and Reynolds numbers. The Knudsen number is assumed to be small so that the fluid flow is described by a continuum model with a temperature jump, a thermal slip, and a frictional slip at the particle surface. The presence of the confining wall causes two basic effects on the particle velocity: first, the local temperature gradient on the particle surface is altered by the wall, thereby speeding up or slowing down the particle; secondly, the wall enhance the viscous retardation of the moving particle. The transport equations governing this problem are solved and the wall effects on the thermophoresis of the aerosol cylinder are computed for various cases. The presence of the plane wall can reduce or enhance
the particle velocity, depending upon the relative thermal conductivity and surface properties of the particle, the relative particle-wall separation distance, and the direction of the applied temperature gradient. The direction of the thermophoretic motion of a cylindrical particle near a plane wall is different from that of the prescribed thermal gradient, except when it is oriented parallel or perpendicular to the wall. The effects of the plane wall on the thermophoresis of a cylinder are found to be much more significant than those for a sphere at the same separation.
In Chapter 4, an analytical study is presented for the steady, transverse electrophoretic motion of a circular cylindrical particle with an arbitrary angular distribution of its surface potential parallel to a plane wall prescribed with the potential distribution consistent with the applied electric field. The electric double layers adjacent to the solid surfaces are assumed to be very thin with respect to the particle radius and spacing between the surfaces. The electrostatic and hydrodynamic governing equations are solved, and the typical electric field line, equipotential line, and streamline patterns are exhibited. The explicit formulas for the electrophoretic and angular velocities of the particle are obtained with the contribution from the electroosmotic flow produced by the interaction between the applied electric field and the thin double layer adjacent to the plane wall. To apply these formulas, one only has to calculate the leading multipole moments of the zeta potential distribution at the particle surface. The existence of a plane wall can cause the translation or rotation of the particle, which does not occur in an unbounded fluid with the same applied electric field. The boundary effects on the electrophoretic motion of a uniformly or nonuniformly charged particle resulting from the parallel plane wall prescribed with the far-field potential distribution are quite different from those produced by a corresponding insulating wall.
In Chapter 5, an analytical study is presented for the electrophoretic motion of a circular cylindrical particle in an electrolyte solution with a transversely imposed electric field near a large plane wall parallel to its axis in the quasisteady limit. The electric double layers at the solid surfaces are assumed to be thin relative to the particle radius and to the particle-wall gap width, but the polarization effect of the diffuse ions in the double layer surrounding the particle is incorporated. The presence of the confining wall causes two basic effects on the particle velocity: first, the local ionic electrochemical potential gradients on the particle surface are altered by the wall, thereby affecting the motion of the particle; secondly, the wall enhances the viscous retardation of the moving particle. The transport equations governing this problem are solved and the wall effects on the electrophoresis of the cylinder are determined for various cases. The presence ofthe plane wall prescribed with the ionic electrochemical potentials consistent with the far-field distributionsreduces the electrophoretic mobility of the particle, which depends upon the properties of the particle–solutionsystem, the relative particle–wall separation distance, and the direction of the applied electric field relativeto the plane wall. The direction of the electrophoretic migration of a cylindrical particle near a plane wall isdifferent from that of the prescribed electric field, except when it is oriented parallel or perpendicular to thewall. The effects of the plane wall on the electrophoresis of a cylinder are found to be much more significantthan those for a sphere at the same separation.
Subjects
Boundary effect
Plane wall
Cylinderical particle
Creeping flow
Slip-flow surface
Thermophoresis
Electrophoresis
Nonuniform zeta potential distribution
Thin but polarized double layer
Type
thesis
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