| Summary: | This thesis discusses the development of a numerical tool for studying the permeability
and compressibility of pulp fibres in sedimentation. The purpose is to determine the
functional relationships of permeability and compressibility in the semi-dilute concentration
regime of pulp suspensions.
The first step in the approach to developing this numerical tool involves performing
settling tests and obtaining experimental data by positron emission tomography (PET).
By radioactively labelling select fibres, the mobility of certain fibre fractions can be
detected using PET and changes in concentration throughout the settling suspensions
can be shown over time. These results can be summarized into concentration profiles
that represent a snapshot of the settling fraction at one instant in time.
The next step is to obtain corresponding theoretical concentration profiles by numerical
simulation. The settling process of a suspension in a vertical column is governed
by a time-dependent one-dimensional partial differential equation. This PDE is derived
by assuming the suspension is a superimposed continuous porous medium governed by
permeability and compressibility functions that describe the physical behaviour of the
suspension. The PDE can be solved numerically by suitable discretization of the spatial
domain and stable advancement of the time-dependent solution. Once solved, the
solution to the settling process can again be represented by a series of concentration
profiles.
Since the PDE is governed by permeability and compressibility functions, a good
match between experimental and theoretical concentration profiles reveals the correct
functions for a given fibre fraction within the suspension. For known functional forms
of permeability and compressibility, this reduces to a parameter fitting exercise. The
optimal set of parameters is found by numerically comparing the match between results
using the sum-of-squares method to measure overall discrepancy. Final comparison be tween experimental and numerical profiles reveals a good fit between results and shows
that the parameter fitting procedure is successful in determining the desired functions
of permeability and compressibility. === Applied Science, Faculty of === Mechanical Engineering, Department of === Graduate
|
|---|
