The Effects of a Planar Wall on the Low Reynolds Number Motion of Solid Particles, Drops and Bubbles

Citation

Ascoli, Edward Paul (1988) The Effects of a Planar Wall on the Low Reynolds Number Motion of Solid Particles, Drops and Bubbles. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/jch2-wy37. https://resolver.caltech.edu/CaltechETD:etd-11062007-130109

Abstract

This thesis focuses on the low Reynolds number interaction of solid particles, deformable drops and bubbles with a rigid plane boundary. In chapters I, II and III we use a numerical technique which employs a boundary integral equation reformulation of Stokes system. In particular, the kernels in the integral reformulation derive from the Green's function corresponding to a no-slip planar boundary. Motion is assumed axisymmetric about the line perpendicular to the plane and through the drop or particle center.

We consider the solid particle case in chapter I. Particle velocity is prescribed and the resultant hydrodynamic force on the particle calculated. The results are discussed in the context of near and far field asymptotic theories as well as existing numerical techniques.

In chapter II deformable drop motion via buoyancy is examined and the time evolution of drop shape is obtained. Interfacial tension is assumed constant. Emphasis is placed on the details of drop "dimpling". In particular, at the initial stages of dimpling, pressure variation normal to the wall is found to be significant in the film trapped between the drop and the wall. Thin-film analytic theories neglect this variation in pressure. The consequences of neglect of this pressure variation are discussed.

In the appendix to chapter II we develop a thin-film asymptotic theory for the buoyancy driven motion of a bubble toward a planar wall. The consequences of this theory are related to the results of chapter II. This work is still in progress, and for this reason it is relegated to an appendix.

Thermocapillarity provides the mechanism for drop motion and deformation in chapter III. Surface tension is allowed to vary with temperature and the drop is placed in a non-constant temperature field. The effects of physical parameters on drop evolution are discussed.

Chapter IV is a digression from low Reynolds number wall effects. Here we examine a numerical technique developed by Ryskin and Leal for generating boundary-fitted orthogonal coordinate grids. Specifically, we present a proof of the existence of a boundary-fitted orthogonal grid for the case when the ratio of "scale factors" is of product form.

Thesis Files