Ind. Eng. Chem. Res. 1995,34, 382-391
382
Viscoelastic Properties of High Solids Softwood Kraft Black Liquors Abbas k Zaman and Arthur L. Fricke* Department of Chemical Engineering, University of Florida, Gainesville, Florida 32611
The linear viscoelastic functions of several softwood slash pine kraft black liquors from a two level, four variable factorially designed pulping experiment were determined for solids concentrations from 65% to 81% and temperatures from 40 to 85 "C. At high solids and lower temperatures, black liquors behave like un-cross-linked polymers. The exact level of dynamic viscosity and storage modulus at any given condition is dependent upon the solids composition which will vary from liquor to liquor. The linear viscoelastic functions were described using Cross and Carreau-Yasuda models. Superposition principles developed for polymer melts and concentrated polymer solutions were applied to obtain reduced correlations for dynamic viscosity and storage modulus. The data for dynamic viscosity were shifted over the whole range of temperature, solids concentrations, and frequency, and a single curve for dynamic viscosity behavior of every liquor was obtained. The data for storage modulus did not superimpose into a single curve for the effects of solids concentration. The reduced correlations were used t o estimate the viscoelasticity of the liquors near normal firing conditions and found that black liquors will not have any problem in droplet formation for concentrations up to 81%solids and temperatures above 120 "C. The viscometric and linear viscoelastic functions of black liquors were compared (Cox-Merz rule), and it was shown that at sufficiently low shear rates and frequencies both shear viscosity and the magnitude of the complex viscosity approach zero shear rate viscosity. 1. Introduction
There are many studies that can be cited in reference
to the rheological properties of black liquors, but most of them refer to the shear viscosity of black liquors. However, only two studies (Co and Wight, 1982; Wight, 1985) refer specifically to the linear viscoelastic functions of only one or two black liquors. Black liquors, which are the byproducts of delignification in chemical pulping, are very complex in nature, and their rheological properties are not only affected by temperature, solids concentration, and shear rate, but they will vary from liquor to liquor due to the cooking conditions and type of the wood species. Rheological properties affect a number of important parameters such as droplet formation, drying characteristics, and swelling characteristics in the furnace. In this paper we present results on the rheological properties of several softwood kraft black liquors at high solids concentration in small amplitude oscillatory shear flows, using a series of well-characterized liquors pulped under carefully controlled conditions. The behavior of these liquors have been characterized by means of the complex viscosity q* = 7' - if' determined in oscillatory shear flow at different solids concentrations and temperatures. As was shown earlier (Zaman and Fricke, 1991, 19941, black liquor can be treated as a polymer solution which is due to the fact that the polymeric lignin (main constituent) composes more than 50% of the organic constituents in black liquor. Also, in this work, the concept of the reduced variables methods developed for concentrated polymer solutions was employed to obtain reduced correlations for linear viscoelastic functions of black liquor as a function of temperature, solids concentrations, and frequency. Availability of accurate and reliable data on well-characterized liquors provides a useful tool in developing generalized correlations to describe the linear viscoelastic function of black liquors which will be useful for estimation of viscoelasticity of the liquors near normal firing conditions in the recovery furnace where the 0888-5885/95/2634-0382$09.00/0
Table 1. Pulping Conditions, Lignin Concentration, and Lignin Weight-Average Molecular Weight for Black Liauors Used in This StudvD cook t,h T,K % E A ABAFX013,14 1.333 450.0 13.0 ABAFX025,25 1.333 450.0 16.0 ABAFX043,44 1.000 444.3 14.5
Gig,
% SU g/gsolids
20.0 35.0 27.5
43.46 39.28 43.44
-
M,
6618.0 3910.0 9672.0
t = cooking time; T = cooking temperature; EA = effective alkali; SU = sulfidity; Cfig= concentration of lignin, = lignin molecular weight by HPLC. (I
E
liquors are sprayed to form droplets and then burned to recover the cooking chemicals and produce most of the energy required for the pulping process. Furthermore, it is possible to find an analogy between the shear viscosity and the corresponding dynamic viscosity under linear viscoelastic conditions. Measuring the shear viscosity is difficult at high shear rates due to viscous heating, while the complex viscosity is easier to measure (Dyson, 1970; Barnes et al., 1989). Prior to this study, quantitative evaluation of this analogy has been frustrated by lack of accurate and reliable data on shear viscosity and linear viscoelastic functions of wellcharacterized black liquors. 2. Materials
The black liquors used in this investigation are from a four variable-two level central composite designed experiment for pulping slash pine that was conducted in a pilot scale digester under carefully controlled conditions. The four pulping variables are the cooking time, cooking temperature, effective alkali, and sulfidity. The pulping conditions for these liquors, along with lignin concentration and lignin weight average molecular weight, are summarized in Table 1. Cooks were made a t a liquor-to-wood ratio of 411. The results of pulping can be found elsewhere (Fricke, 1987, 1990; Zaman et al., 1991). The liquors were chosen so that a wide range of behavior might be expected. For rheo-
0 1995 American Chemical Society
Ind. Eng. Chem. Res., Vol. 34, No. 1, 1995 383 logical studies, the liquors must be concentrated to about 85% solids. For this purpose, a pilot scale evaporator was used to concentrate the liquors to about 40-45% solids and then a small scale evaporator which could be used for both concentrating the liquors and studying the vapor-liquid equilibria was used to concentrate the liquors t o about 85% solids. The details of the operating procedure are given elsewhere (Shy et al., 1992). Data have been taken for solids concentrations from 61% to 81% and temperatures from 40 to 85 "C. Special care was taken to maintain very precise temperature control, and the experiments were carried out within a time period that is short compared to the time required for degradation of lignin within the liquor.
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