טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentKaynan Uri
SubjectSeveral Problems Concerning the Motion of Small Particles
in a Viscous Liquid
DepartmentDepartment of Applied Mathematics
Supervisors Professor Ehud Yariv
Professor Itzchak Frankel


Abstract

There are two parts to this thesis.

In the first part; Surrounded by a spherically-symmetric solute cloud, chemically active homogeneous spheres do not undergo conventional autophoresis when suspended in an unbounded liquid domain. When exposed to external flows, solute advection deforms that cloud, resulting in a generally asymmetric distribution of diffusio-osmotic slip which, in turn, modifies particle motion. We illustrate this phoretic phenomenon using two prototypic configurations, one where the particle sediments under a uniform force field and one where it is subject to a simple shear flow.

In addition to the Péclet number Pe associated with the imposed flow, the governing nonlinear problem also depends upon α, the intrinsic Péclet number associated with the chemical activity of the particle. As in the forced-convection problems, the small-Péclet-number limit is nonuniform, breaking down at large distances away from the particle. Calculation of the leading-order autophoretic effects thus requires use of matched asymptotic expansions, the outer region being at distances that scale inversely with Pe^(-1) and Pe^(-1/2) in the respective sedimentation and shear problems. In the sedimentation problem we find an effective drag reduction of fractional amount α/8; in the shear problem we find that the magnitude of the stresslet is decreased by a fractional amount α/4. For a dilute particle suspension the latter result is manifested by a reduction of the effective viscosity.


In the second part, motivated by observations of large effective slip over nanostructured surfaces we analyze the hydrodynamic resistance to the rigid-body motion of a cylinder near a slippery wall - perhaps the simplest anisotropic configuration which nonetheless exhibits a non-trivial translation-rotation coupling.

Focusing upon the lubrication limit, the properly scaled resistance-matrix coefficients depend only upon the ratio of the slip length to the cylinder-wall clearance. A distinct feature of a lubrication analysis with slippage is that the pressure field cannot be determined in closed form; nonetheless, the dependence upon the slip length of the resistance coefficients is explicitly obtained. The limit of large slip length, where the wall behaves as a free surface, is elucidated. Considering the companion problem of a slippery cylinder we observe a symmetry relating the two problems.