Xiaolin Fan

Date of Award


Degree Type


Degree Name

Doctor of Philosophy


The thesis studies the movement of wood pulp through a rotating disk refiner, by developing continuum and discrete models of the process. An existing continuum model of pulp movement for steady-state refining is first extended to include time-dependent effects, in order to study the dynamic aspects of refining operation. A system of hyperbolic P.D.E.'s is obtained, but it is shown to suffer from numerical instability. Attention is therefore shifted to a discrete model, and a stochastic model treating pulp as discontinuous flocs is developed. The prediction of the residence time distribution of pulp in a refiner is the first test for the model. The model treats pulp as individual flocs moving in three regions inside a refiner: the grooves in the stator, the gap between the plates, and the grooves in the rotor. As the pulp moves through the refiner, it changes regions stochastically. The model calculates the residence time by following each floc individually and then accumulating the results to obtain the distribution of the time. The model is also used to predict the treatment time, that is, the time that pulp spends between the refiner plates. The treatment time distribution shows a non-monotonic rise to a maximum, followed by a non-monotonic decay to zero. Several simple prototype simulations are analyzed to show that the behaviour is not due to errors in the numerical simulation, but is inherent in the class of models used. The model is then extended to a time-dependent one, by keeping track of all flocs in the refiner simultaneously. The fluctuation of the locally averaged densities or pulp inside the refiner are simulated. The trends in the treatment time and the residence time of pulp in the refiner, as well as the correlation between the locally averaged densities and the treatment time are also given. The stochastic model is improved by introducing formulas that calculate the probabilities for flocs to switch regions based on both the locally averaged densities and the densities of pulp flocs averaged over the refining zone. A new set of residence-time and treatment-time distributions calculated using the probability formulas is given. Finally, the relation between the thrust load on the refiner and the plate gap is predicted by considering the forces supported by a single floc, and a mechanism is found to take into account all the flocs collectively.



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