The hydrodynamics of individual pulp fibres
Creators: name: Wong, Tze Bun
Publisher: name: University of British Columbia
Year: 2009

description: In order to understand how pulp fibres with different properties (e.g. length, diameter, coarseness, etc.) can be fractionated in hydrocyclones, there is a need to understand the hydrodynamic behavior of individual pulp fibres. Measurements of the settling velocity of fibres in fluids of different density and viscosity can be used to give the drag coefficient of fibres as a function of the Reynolds number. Such measurements can yield Reynolds numbers up to about 0.1. In order to achieve the higher fibre Reynolds numbers present in a hydrocyclone, a novel device, called the rotating tank, was constructed to measure the velocity of fibres in water under the influence of a centrifugal field. The tank is a circular cylinder made of plexiglas, 30.5cm in diameter, and 4.45cm high, with its axis vertical. The tank is filled with fluid and is spun at a constant rate until the fluid is in solid body rotation. Fibres or other objects to be tested can be placed in the tank through a hole along the axis of the cylinder, and centrifugal forces cause the fibres to be flung outwards. A fibre inside the rotating tank is subject to a centrifugal force, a drag force, and a pressure force. The radial equation of motion of a fibre in the rotating tank will be exactly the same as during gravitational settling except the gravitational acceleration is replaced by the centrifugal acceleration. Therefore, high Reynolds numbers can be achieved by using a high rotation speed of the tank. Our rotating tank was tested and found to be capable of spinning at 1500 rpm. The tank has been primarily validated by reproducing Stokes' theory for the drag of a sphere. The tank results were in good agreement (4% error) with Stokes' theory. Further validation of the tank was done with copper wires and nylon fibres, which are similar to wood fibres. The results were in good agreement (&lt;15% error) with the results of other researchers Tests with hardwood kraft and softwood thermomechanical pulp (TMP) fibres in the tank yielded the following results: • The orientation of a fibre settling in the tank depends strongly on its initial orientation. In contrast with a widely-used assumption, most fibres do not orient themselves with their long axis perpendicular to the direction of radial motion. The fibre orientation can be anything from purely perpendicular to purely parallel to the direction of radial motion with the majority of the fibres oriented in the range from 20 to 40 degrees from the perpendicular. • Fibres do not rotate regardless of their orientation. They will maintain their orientation during the entire settling process in the rotating tank. • The settling velocity of pulp fibres is a strong function of their orientation. Fibres settling at an angle of larger than 45 degrees to their direction of motion settle faster than those at smaller angles. The orientation effect becomes more pronounced as the angular acceleration increases. • For hardwood kraft pulp, the plot shows that the settling velocity increases with fibre length but the plot of softwood TMP does not show the same dependence. • The shape of the fibre does not significantly affect the settling rate. Curved fibres and fibres having sharp corners settle at about the same rate as straight fibres. • The kraft and TMP used have on average much larger drag coefficients than any other objects tested under the same conditions. The apparent density and mean diameter are used to plot the drag coefficient against the Reynolds number. The apparent densities for hardwood kraft and softwood TMP are 1329 kg/m³ and 1265 kg/m³ respectively whereas the mean diameters for hardwood kraft and softwood TMP are 22.3 and 33.8 microns respectively. A least square fits from the mean values gives the mean drag coefficient as a function of Reynolds number for hardwood kraft and softwood TMP: