Boundary effects on Phoretic Motions of Colloidal Spheres:Migration parallel to one or two plane walls

• Main Authors: Chen, Po-Yuan, 陳柏源
• Other Authors: Keh, Huan-Jang
• Format: Others
• Language: zh-TW
• Published: 2003
• Online Access: http://ndltd.ncl.edu.tw/handle/76423571399690876964

博士 === 國立臺灣大學 === 化學工程學研究所 === 91 === Abstract Driven by applying an electrical potential, temperature, or solute concentration gradient, the transport of colloidal particles in a continuous medium is known as the “phoretic motion”. In this work, a boundary collocation method and a reflection method are utilized to calculate the various phoretic velocities of small spherical particles migrating parallel to one or two plane walls. First, in chapter 2, the quasisteady diffusiophoretic motion of a spherical particle in a fluid solution of a nonionic solute located between two infinite parallel plane walls is studied in the absence of fluid inertia and solute convection. The imposed solute concentration gradient is constant and parallel to the two plane walls, which may be either impermeable to the solute molecules or prescribed with the far-field concentration distribution. The particle-solute interaction layer at the particle surface is assumed to be thin relative to the particle radius and to the particle-wall gap widths, but the polarization effect of the diffuse solute in the thin interfacial layer caused by the strong adsorption of the solute is incorporated. The presence of the neighboring walls causes two basic effects on the particle velocity: first, the local solute concentration gradient on the particle surface is enhanced or reduced by the walls, thereby speeding up or slowing down the particle; secondly, the walls increase viscous retardation of the moving particle. Numerical results for the diffusiophoretic velocity of the particle relative to that under identical conditions in an unbounded fluid solution are presented for various values of the relaxation parameter of the particle as well as the relative separation distances between the particle and the two plates. For the special case of diffusiophoretic motions of a spherical particle parallel to a single plate and on the central plane of a slit, the collocation results agree well with the approximate analytical solutions obtained by using a method of reflections. The presence of the lateral walls can reduce or enhance the particle velocity, depending on the surface properties of the particle, the relative particle-wall separation distances, and the solutal boundary condition at the walls. A theoretical study is presented in chapter 3 for the quasisteady osmophoretic motion of a spherical vesicle in a solution located between two infinite parallel plane walls in the limit of negligible Reynolds and Peclet numbers. The applied solute concentration gradient is uniform and parallel to the two plane walls, which may be either impermeable to the solute molecules or prescribed with the far-field concentration distribution. The presence of the neighboring walls causes two basic effects on the vesicle velocity: first, the local concentrations on both sides of the vesicle surface are altered by the walls, thereby speeding up or slowing down the vesicle; secondly, the walls enhance the viscous interaction effect on the moving vesicle. Numerical results for the osmophoretic velocity of the vesicle relative to that under identical conditions in an unbounded solution are presented for various values of the relevant properties of the vesicle as well as the relative separation distances between the vesicle and the two plates. For the special case of osmophoretic motions of a spherical vesicle parallel to a single plate and on the central plane of a slit, the collocation results agree well with the approximate analytical solutions obtained by using a method of reflections. The presence of the lateral walls can reduce or enhance the vesicle velocity, depending upon the relevant properties of the vesicle, the relative vesicle-wall separation distances, and the solutal boundary condition at the walls. In chapter 4, the steady thermocapillary migration of a fluid droplet located between two infinite parallel plane walls is examined in the absence of fluid inertia and thermal convection. The imposed temperature gradient is constant and parallel to the two plates, and the droplet is assumed to retain a spherical shape. The plane walls may be either insulated or prescribed with the far-field temperature distribution. The presence of the neighboring walls causes two basic effects on the droplet velocity: first, the local temperature gradient on the droplet surface is enhanced or reduced by the walls, thereby speeding up or slowing down the droplet; secondly, the walls increase viscous retardation of the moving droplet. Numerical results for the thermocapillary migration velocity of the droplet relative to that under identical conditions in an unbounded medium are presented for various values of the relative viscosity and thermal conductivity of the droplet as well as the relative separation distances between the droplet and the two plates. For the special cases of thermocapillary motions of a spherical droplet parallel to a single plate and on the central plane of a slit, the collocation results agree well with the approximate analytical solutions obtained by using a method of reflections. The presence of the lateral walls can reduce or enhance the droplet velocity, depending upon the relative transport properties of the droplet, the relative droplet-wall separation distances, and the thermal boundary condition at the walls. In chapter 5, the quasisteady thermophoretic motion of a spherical particle in a gaseous medium located in an arbitrary position between two infinite parallel plane walls is studied in the absence of fluid inertia and thermal convection. 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 imposed temperature gradient is constant and parallel to the two plane walls, which may be either insulated or prescribed with the far-field temperature distribution. The presence of the neighboring walls causes two basic effects on the particle velocity: first, the local temperature gradient on the particle surface is enhanced or reduced by the walls, thereby speeding up or slowing down the particle; secondly, the walls increase viscous retardation of the moving particle. Numerical results for the thermophoretic velocity of the particle relative to that under identical conditions in an unbounded gaseous medium are presented for various values of the relative thermal conductivity and surface properties of the particle as well as the relative separation distances between the particle and the two plates. For the special case of thermophoretic motions of a spherical particle parallel to a single plate and on the central plane of a slit, the collocation results agree well with the approximate analytical solutions obtained by using a method of reflections. The presence of the lateral walls can reduce or enhance the particle velocity, depending upon the relative thermal conductivity and surface properties of the particle, the relative particle-wall separation distances, and the thermal boundary condition at the walls. Finally, the four phoretic motions considered in chapters 2-5 are simply compared.