Title

Numerical simulations and theories for wall-bounded flows of suspensions

Date of Award

2008

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Biomedical and Chemical Engineering

Keywords

Bubbly liquids, Multiphase, Multipoles, Kinetic theory, Fluid dynamics, Wall-bounded flows

Subject Categories

Chemical Engineering | Engineering

Abstract

This thesis is concerned with the development of analytical tools for understanding the effect of the presence of walls on the behavior of two-phase systems, such as suspensions of particles in a liquid or gas bubbles dispersed in a liquid. The presence of the walls alters the flow around the particles in a significant way influencing thereby the forces on the particles and the distribution of the particles near the wall. New techniques -- numerical methods for solving detailed hydrodynamic interactions near the walls and kinetic theories -- are developed and applied to three classes of problems.

The first class of problems is concerned with the Stokes flow (vanishingly small Reynolds number) around particles near a wall or in a thin film bounded by a wall and a gas-liquid interface. Image systems are derived for force multipoles of arbitrary orders that account for the presence of a wall, a gas-liquid interface, or both. These image systems are combined with the method of multipole expansions to determine hydrodynamic mobility and resistivity of particles. The usefulness of the method is illustrated by solving a number of problems including chains of particles, radially expanding particles, drops, and bubbles near a wall or in a thin film bounded by a wall and a gas-liquid interface.

The second is concerned with the flow of inertia dominated particulate systems. The particle-wall collisions significantly affect the velocity and spatial distribution of the particles. This makes the problem of prescribing effective boundary conditions for the flows of particulate phase or granular material treated as a continuum a challenging task. A kinetic theory is developed that accounts for the changes in the particle velocity distribution that occur near a wall and the predictions of the theory are compared against the results obtained by the particle-scale numerical simulations.

Finally, the third is concerned with the flows of bubbly liquids under conditions where the bubbles are approximately spherical and noncoalescing and inertial interactions among bubbles dominate. These conditions require that the Weber number, which represents the ratio of inertial to surface tension forces is small while the Reynolds is large. Equations of motion of such ideal flows of bubbly liquids, which have been derived by previous investigators, need to be supplemented with effective boundary conditions. Experimental observations of bubble-wall interactions are used to propose these conditions. The predictions of the theory based on these equations of motion and boundary conditions are compared with the experimentally determined profiles of bubble volume fraction and velocity for flows of bubbly liquids in a vertical pipe at Cornell University. It is shown that there is reasonably good agreement between the theory and experiments.

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