Shear factor: a new way to characterize pulper performance.

Application: The knowledge and use of shear factor [lambda] should permit better control of the energy input to a pulper to minimize the power consumption.

In this paper, we describe the unique shear behavior of structured wood fiber suspensions as compared with classical laminar shear, homogeneous, non-Newtonian fluids. The emphasis is placed on applying a shear factor [lambda] for flowing suspensions in pipes instead of apparent viscosity [[mu].sub.a] which applies strictly to laminar flow.

Shear factor [lambda], which is the ratio of shear stress t to the shear rate, can also be applied at the onset of bulk mixing in a helical pulper. We have applied a procedure to a helical pulper using a bleached kraft pulp in the medium-consistency (mc) range in order to characterize its performance in terms of the effective power consumed.

Procedure to characterize a pulper

According to Metzner and Otto [AIChE 49(3): 3(1957)], the power required to rotate an impeller in a mixing vessel can be expressed as a function of fluid properties and vessel geometry. Using Newtonian liquids, they obtained a characteristic curve when a dimensionless power number was plotted against Reynolds number.

Their method was first developed to determine the power needed to mix a non-Newtonian fluid using the apparent viscosity [[mu].sub.a] of the fluid. For our helical pulper with its specific geometry, the shear factor [lambda] can be determined from an equation based on a generalized Reynolds number Re', with [lambda] used in place of [[mu].sub.a].

Verification of the method

We used a bleached softwood kraft pulp to confirm the method of determining shear factor [lambda] and to compare the results with those of previous workers who used [[mu].sub.a]. Virgin pulp was disintegrated at 5% consistency, thickened, fluffed, and dispersed. Power consumption data were obtained at rotor speeds ranging from 50 to 1000 rpm at seven different consistencies in the range of 1%-11%. The same behavior was observed in all cases and is represented in Fig. 1.

[FIGURE 1 OMITTED]

Shear factor can be used to predict the transition point from swirling flow to tangential-radial-axial flow for mixers. This transition point, previously termed the "fluidization" point for mixers by some workers, corresponds to the sudden reduction in torque and thus power input as the suspension flow changes from pure tangential flow to a combined tangential folding-inward radial bulk motion in the pulper (kneading action). The corresponding values of shear factor [lambda] can then be calculated for the consistencies studied (1% to 10.7%).

Conclusions

The concept of apparent viscosity was originally derived for homogeneous fluids in laminar flow, but fiber suspensions are inhomogeneous and do not flow in laminar shear. By considering the transition flow point where the pulp begins to move tangentially, axially, and radially in a pulper, we can ascribe a shear factor [lambda] that generalizes the apparent viscosity. This coefficient can be determined by the Metzner-Otto method, well known in classical rheology. It is then possible to analyze the mixing characteristics of a fiber suspension from the power consumption in the MC range of 1%-11% and hence to determine the shear factor over the whole range.

The methodology has been applied to a bleached kraft pulp, the average shear stress has been determined, and the value compared well with values given by other researchers. Thus, the use of the shear factor provides a meaningful way to characterize pulper performance.

Fabry and Roux are with the Laboratoire de Genie des Procedes Papetiers, UMR 5518 au CNRS/INPG/EFPG/CTP, Ecole Francaise de Papeterie et des Industries Graphiques, BP 65-38402 Saint Martin d'Heres Cedex, France. Carre is with the Centre Technique du Papier, BP 251 38044 Grenoble, Cedex 9, France. Duffy is a professor in the Dept. of Chemical and Materials Engineering, School of Engineering, University of Auckland, Private Bag 92019 Auckland, New Zealand. Address correspondence to Duffy by email at [e-mail].