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UBC Theses and Dissertations

On the fluid mechanics of viscoplastic particle suspension fractionation : understanding multilayer spiral poiseuille flow in an annulus Al-Shibl, Mohammad


The focus of the present work is the study of laminar spiral multi-layer viscoplastic flow in annular geometries. The motivation for the present work stems from an interest in utilizing such flow in fractionation of particle suspensions. The work is presented in four studies. In the first study we solve the fully developed condition of the flow analytically. This solution is considered a reliable reference to validate the remaining numerical studies. Also it provides a means to test the stability of the flow. The second study is related to the fractionation of particle suspensions utilizing the solution demonstrated in the first study. We develop fractionation curves of particles of different sizes in fluids with different rheology. We develop a code to simulate thousands of flow cases (a flow case has a unique combination of streams flowrates) of known fluids properties. We predict the fractionation operating window (some range of streams flowrates) needed for successful fractionation. In the third study, we examine the flow in the full annulus geometry including the entrance region of the flow. Here, we estimate the flow entrance length in order to design the length of the mixing zone of the two streams in the continuous fractionation device. We study the effect of Kelvin-Helmholtz and density current instabilities on the flow. In the fourth study, we attempt to design the continuous fractionation device in which we use the results of the first three studies together with the analysis of the constraints imposed by the physical construction of the device. We explore the flow behavior in the exit region of the device and suggest some guidelines to achieve successful fractionation accordingly. Results of this work show that spiral multi-layer Poisuille viscoplastic flow can be stable and the range of stability expands with increasing fluids yield stress. Gravity current instability is evident in density unstable cases and the flow can be stabilized by increasing the fluids yield stress. Kelvin Helmholtz instability was not found on conditions tested. Viscoplastic flow entrance length was found to be shorter than the equivalent Newtonian one for the same range of Reynolds number.

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