Fiber trapping in low-consistency refining: new parameters to describe the refining process

Fiber trapping in refining has been defined by the fraction f of the bar edges that trap fibers as they cross, and by the number of fibers i trapped under each section of bar. From these parameters, equations were derived to calculate the number of impacts that a fiber undergoes during refining and the maximum force experienced during each impact. Refiner power versus gap was measured for a conical laboratory refiner at maximum peripheral speeds ranging from 4 m/s to 27 m/s and consistencies ranging from 1% to 6% for one softwood kraft pulp. The data were used to calculate relative changes in i and f as a function of consistency and speed. It was found that f was extremely sensitive both to an increase in refiner rotational speed and to a reduction in pulp consistency. A reduction in consistency from 4% to 2% at 20 m/s (3000 rpm) led to a decrease in the trapping fraction, f, by approximately 80%. The number of fibers trapped under each section of bar also decreased, although to a lesser extent. The reduction in fiber trapping greatly increased the forces on the fibers, leading to enhanced fiber shortening and reduced refining efficiency. Application: Fiber trapping is a hidden variable affecting refining efficiency. This paper describes how to estimate relative changes in fiber trapping and shows how fiber trapping impacts the refining process. low-consistency refining july 2008 | TAPPI JOURNAL 15 , (1) peer-reviewed low-consistency refining 16 TAPPI JOURNAL | july 2008 , (2) where CEL is the cutting-edge length per revolution, projected in the radial direction, and  is the rotational speed in revolutions per second. SEL is an empirical parameter which represents the energy transferred per bar crossing per unit length of rotor bar crossing over a unit length of stator bar [12]. The two factors that characterize the refiner action in trapping and treating fibers are the fraction ƒ of the bar that traps fibers and the number of fibers i trapped under the bar edge at each point where a fiber mat is trapped. In the following work, these parameters are combined with the SEC and SEL as described above to characterize refining action on fibers, based on the maximum force applied to the fibers and the number of times this force is applied. This line of reasoning follows that originally developed by Kerekes for the C-factor [7] and later extended to a force-based characterization [12]. To trap a mat one fiber wide requires a refiner-bar segment length equal to the width of a fiber, d w , when projected perpendicularly to the direction of bar motion. Refining-gap measurements indicate that fibers are processed as a mat. Therefore, for each fiber that is in contact with the rotor-bar edge, there will be a number of additional fibers underneath it. Not all bar edges will capture a fiber mat. Here the fraction of the bar that traps fibers will be designated as ƒ, and the number of fiber layers in the mat at each point of trapping will be designated as i. Figure 1 is a schematic diagram of this concept. This diagram shows a segment of rotor bar and of stator bar, each of length x. Fibers have been trapped at five points along the bar, and at each of these points, three fibers have been trapped, for a total of fifteen fibers. From this diagram, ƒ =5d w /x and i=3. The number of fibers per second in contact with the bar edges as they cross is fCEL/d w , and the total number of fibers that are impacted per second is ifCEL/d w . The total number of fibers refined is: