Ind. Eng. Chem. Fundam. 1986, 2 5 , 483-490
403
Vaneless Disk Fractionation of Slurries Ani1 R. Oroskart and E. Johansen Crosby" Department of Chemical Engineering, University of Wisconsin, Madison, Wisconsin 53706
The use of vaneless disk atomizers for the partial cleaning, screening, and fractionation of wood pulp fibers was investigated. Studies with paper pulp and rayon fibers indicated separation to occur at the disk edge by ejection of dewatered fibers with classification primarily dependent on fiber diameter. Very shallow disks having keen-edged chamfers with lips of extreme widths effected sharp fractionation of rayon fibers. A simple mechanistic model based on fiber inertia and surface forces described the separation process reasonably well and indicated extension to other particle geometries. Mechanical entanglement of irregular particles and flow instabilities limited slurry concentration and processing rates.
Introduction Classification of slurried solids in the process industries on any significant scale is based usually on differences in particle size and/or density and occasionally on shape. Screening techniques augmented by mechanical vibration and/or hydraulic pulsation generally are used to separate particles according to size. Hydraulic schemes based on inertia or relative velocity, supplemented many times by mechanical assistance, commonly are used to separate particles according to density. Sharp fractionation of particles which deviate from three-dimensional symmetry and/or lack rigidity is more difficult. This problem is particularly acute in the processing of wood and paper pulps, whose useful portions are composed of fibers rendered moderately flat and quite pliable by beating and milling. Larger nonpulped and partially pulped wood particles are removed by screening with provisions to preclude blinding and entrapment, while high-density contaminants are separated hydraulically by cyclones. Reasonably successful fractionation of clean fibers according to length by low-pressure screening techniques and hydrocyclones requires concentrations to be as low as 0.1-0.6 wt %, while high-pressure screening permits concentrations to increase to ca. 1.5 wt % (Britt, 1970). Fiber fractionation by suitable control of flow conditions in discrete fluid fields, e.g., the Johnson fractionator (Olgbrd and Axenfalk, 1972),is limited to concentrations below 0.3 wt % . A new technique to clean, screen, and fractionate pulp suspensions of higher concentrations based on the use of a high-speed, rotating, vaneless disk of the design normally used in spray drying has been proposed (Moller et al., 1979). Fractionation is realized by collection of various axial zones of the circular particle cloud near the disk periphery, as shown in Figure 1. These disks resemble an inverted saucer which terminates in a short hooplike skirt whose border is chamfered to produce a sharp edge at the inner surface, as shown in Figure 2. For the processing of sediment pulps containing 3 wt % solids, it generally was found that (i) fine cellulose and clay particles were concentrated near the top of the cloud, (ii) good pulp fiber was concentrated near the middle and upper middle of the cloud, and (iii) sand grains, nonfibrous wood particles, and bark particles were concentrated near the bottom of the cloud. Without exception, the smaller and less dense particles were concentrated near the top of the +Allied Signal Engineered Materials Research Center, Des Plaines. IL 60017-5016. 0196-4313/86/1025-0483$01.50/0
Table I. Estimated Film Thickness near Edge of Rotating F l a t Disk"
rot. speed, rpm 3000 6000 12000 24000
film thickness, pm, at flow rates 18.9 L/min 3.8 L / m h 63 32 37 20 23 12 13 8
"Fluid = water; disk radius = 10 cm. Table 11. Fiber Dimensions of US.-Canada Pulpwoods fiber dimensions type species length, mm diameter, pm hardwood beech 1.2 16-22 0.8 16-30 maple oak (white, red) 1.4 14-22 softwood fir 3.5 30-45 pine 3.6-3.9 30-50 redwood 6.1 50-65
cloud and the larger and more dense particles were concentrated near the bottom. Subsequent studies with other feedstocks (Moller et al., 1980; Duffy et al., 1982) substantiated these results. In this application area, positive results have been indicated at solids concentrations as high as ca. 6 w t % with improved quality of fractionation noted at lower feed rates and higher disk speeds and diameters. The success of this classification scheme for pulp fibers was attributed to the extremely intense shear field that exists within the liquid film passing over the disk surface and to the centrifugal force acting normal to the film near the edge of the disk. The shear field was credited for (i) fiber disentanglement and (ii) preferential migration of the larger particles and fibers away from the disk surface toward the film's free surface. The centrifugal force was considered to promote migration of the larger and denser particles toward the disk surface. Carry-over of the resulting distributions of fiber/particle size and density from the liquid film to the generated particle cloud was credited for the observed fractionation. However, these particlemigration mechanisms seem to counteract each other and separation of pulp fibers from nonfibrous wood particles is not expected. Also, the much denser sand grains, which are most subject to centrifugal forces, are not collected near the top of the particle cloud. In addition, unless it possesses high internal turbulence, the ejected liquid film a t the disk edge is most stable in its smallest dimension and maintenance of fiber/particle stratification in the resulting cloud during its formation and dispersion is not apparent. 0 1986 American Chemical
Society
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Ind. Eng. Chem. Fundam., Vol. 25, No. 4, 1986
1
SLURRY FEED
ROTATING VANELESS DISK
\
WANELESS DISK ATObiZER FEEDRATE = 22 LITER MIN FEED CONCN = 1 6 W T - P E R C E N T ~ . . L I I . I ~ R B ~FA ~R ~ ~ ~ ~ ~ ~ j -
U'MFFRENTIALLY 1I FEED RATE = 22 L I T E R M N FEED CONCN = 3 0 WT-PERCENT DISK SPEED = E. 400 REV'MIN
p)-j likE FRACTIONS
U
4 Figure 1. Axial zone collection of particle cloud near rotating vaneless disk (after Moller et al., 1979).
3co
1
CLOUD
1
J
1
2
3
1 4
I
I
5
-
TOP
I
CLGLD BOTT3t 1
PARTICLE CLOUD FRACTION ZONE NUMBER
Figure 3. Fractionation of OCC pulp.
previously used disk design is optimal.
VANELESS DISK ATOMIZER (COMMERCIAL)
VANELESS DISK ATOMIZER (MODIFIED)
CONICAL aowL WITH HORIZONTAL si 10 and their axes oriented radially, it results that (happel and Brenner, 1983) Fdreg,,= [2TpU,L]/[ln (L/D,) - 0.031 (3) With V , = (7rD,2L)/4 and A, = [TO& + (~D,2)/2],combination of eq 1, 2, and 3 gives D,2w2R(pP- pf)[ln (L/D,) - 0.031 u, = u,
+
8P
(4)
488
Ind. Eng. Chem. Fundam., Vol. 25, No. 4, 1986
Table VI. Estimated Radial Velocities of Rayon Fibers on Rotating Flat Disk" fiber fiber radial vel, m/s, a t disk speeds diameter, length, Km mm 1920 rpm 2740 rpm 4400 rpm 4.26 11.0 54 6 2.10 3.64 9.39 54 3 1.79 0.60 1.54 0.29 18 6 1.35 0.26 0.52 18 3 "Disk diameter = 15 cm; fiber geometry = rigid cylinder.
.
Table VII. Estimated Disk Speeds Required for Rayon Fiber Detachment from WLD" rot. speed of disk, rpm, a t lip angles fiber diameter, pm 67l/? deg 45 deg 22l f deg 3900 54 2510 2880 26 5510 6300 8560 13080 18 8420 9620 "Disk diameter = 15 cm; fiber geometry = rigid cylinder; fiber length = 3 mm.
motion supplies the energy for disengagement. The kinetic energy required in terms of the fiber velocity normal to the film surface is
(u,sin Et = VpPp
2
Combination of eq 4,6, 7, and 8 then interrelates the disk parameters, operation conditions, system properties, and particle geometry and size for a specific fractionation. CONDITIONS AT DISK EDGE
Estimated values of disk speeds required for fiber disengagement are given in Table VI1 and agree closely with the experimental results reported in Table 111.
ANGLE
COMPLETE WETTING
PARTIAL WETTING
PARTICLE DlSENGAGEMENl
Figure 8. Fiber fractionation mechanism.
Contact and wetting of the rotating disk imparts tangential momentum to the slurry, and the resultant centrifugal force radially accelerates the developing film. The liquid is a slurry, considerable tangential slip-especially near the center of the disk-prevails, and momentum transfer at the air-film interface exists. Consequently, the average film velocity will be significantly less than (Hinze and Milborn, 1950) (5)
Predicted values of fiber velocity upon neglect of film velocity are tabulated in Table VI and are in relative agreement with the actual fiber velocities given in Table V. Conditions near the edge of the disk are depicted in Figure 8. The energy associated with fiber displacement from well within to well ouside the film consists of viscous dissipatio resulting from movement to the film surface parallel t the lip and surface energy associated with disengagement from that surface.
2
E, = E ,
+ E,
(6)
For any particle E , = Apy cos /3
(7)
while E, can be safely neglected since fiber displacement is only a few diameters. The radial component of fiber
Discussion The previously reported ability of commercially available vaneless disk atomizers to clean, screen, and fractionate natural fiber slurries was demonstrated for OCC pulps. It also was found that a similar degree of fractionation was possible with an inverted conical bowl having a wide, horizontal skirt. Modification of the commerical disk to allow more orderly deposition of the feedstock on its surface resulted in somewhat improved fractionation. One of the two postulates used to explain the examination of the vaneless disk atomizer as a fractionator of fiber slurries was not supported by these results as no centrifugal force was applied to the liquid film while it flowed over the horizontal skirt of the conical bowl. High-speed still photography indicated that the fibers in slurries fed to the centers of rotating disks tended to orient themselves radially as they were carried outward toward the peripheries. Consequently, the modest tangential slippage of the liquid film relative to the disk would promote only minor rotation of the fibers about their axes with such rotation being necessary for shear-field migration. This low potential for such fiber migration, coupled with predicted film thicknesses of only a few fiber diameters, did not support the other postulate for consideration of vaneless disks as fiber fractionators. Particle cloud classification resulting from favorable air flow patterns induced by disk rotation was found to be insignificant. Only by considerable augmentation of the intensity of this air flow was any improvement in fiber fractionation noted. High-speed still photography and variation of surface conditions a t the edge of the disk demonstrated the manner by which fibers disengaged themselves from the slurry film and established the importance of disk wettability. These results led to the development of the WLD whose design features are present in the commerical vaneless disk atomizers only to a very limited extent. The very narrow, keen-edged chamfer a t the end of the skirt
Ind. Eng. Chem. Fundam., Vol. 25, No. 4, 1986
of the commercial atomizer functions similarly to the wide lip of the WLD, which essentially has no skirt. For the atomizers investigated, the restricted, 3.4-mm width of the chamfer limited the quality of fractionation in the same manner as the reduction in lip length of the WLD. The wide, horizontal, 1.8-mm-thick skirt of the inverted conical bowl may have acted as a wide lip to promote the observed fractionation. However, the upstream edge of the skirt was not sharp and fractionation quality, which may have been enhanced somewhat by the skirt acting as a thin disk, was no better than the commercial vaneless disk atomizer. The systematic study of the effect of the WLD design variables and wettability, major operation conditions except slurry concentration, and fiber dimensions on the separation of rayon fibers indicated that fractionation required an abrupt change in the direction of slurry flow. The disengagement of fibers was dependent upon a balance of their kinetic energy normal to the film surface and surface forces downstream of the point of altered flow direction. As the abruptness of change in flow direction diminished, the quality of any realized fractionation became poorer. This mechanism controlled fractionation as long as stability of the flowing film on the lip surface prevailed. Flow instability introduced turbulence and breakdown of the film. An intense loss of film integrity manifested itself as a major shortening of the lip length or a near elimination of the lip angle and resulted in minimal fractionation. The proposed model based on the postulated energy balance under conditions of stable film flow on the disk lip did not take curvature of the lip edge and fiber acceleration into account. In addition, tangential slippage was ignored in the determination of the body force acting on the fiber and the fibers were considered as rigid right-circular cylinders. This model predicted that separation was much more sensitive to fiber diameter than fiber length, which was supported by experiment. The influences of fiber diameter, disk speed, disk diameter, and lip angle also were predicted correctly. Fiber separation on the basis of density likewise is predicted. Further, the fractionation of fibers whose density is identical with the liquid is indicated. The manner in which fiber wettability influences separation was incorporated and has been demonstrated with OCC pulps contaminated with hot-melt adhesives (Klungness et al., 1984). In addition, the manner in which liquid viscosity influences fiber fractionation was indicated. The model arranged in the form of eq 9 can be used to establish disk design and operation conditions for separation of fibers above and below a given diameter. It also can be used to estimate the potential for fiber separability on the basis of density. This physical model can be extended readily to other geometries. In the case of spheres it is well-known that Fdrag,r
=
3rd)pUm
(10)
and with V , = ( x D P 3 ) / 6and A,, = sDP2it results that
Comparison of eq 9 and 11 suggests that the separation of spherelike particles and inflexible fibers could be accomplished readily. However, fractionation of spherelike particles would require either larger disk radii or operation speeds. Both of these requirements lead to greater film instability which, in turn, would make fractionation more
489
difficult and reduce processing rates.
Summary Those design features of vaneless disk atomizers, found responsible for modest fractionation of wood and paper pulp slurries, were determined to be limited. The previously proposed mechanism, based on preferential fiber/ particle migration in a liquid film because forces of centrifugal effects and conditions of high shear, was found unsuitable. Experimentation with rayon fiber slurries indicated the separation to result from a balance between the kinetic energy associated with fiber motion and the surface energy associated with fiber disengagement, the existence of a very wide lip at the edge of the disk, and the retention of the integrity of the liquid film as it passed over that lip. An approximate performance model based on disk geometry and dimensions, operation conditions, and properties of the slurry components was developed and found to agree reasonably well with experiment. Although the disk may be fabricated of any material, that portion of its surface in contact with the slurry must be perfectly wettable and any contamination that reduces wettability during operation is detrimental to performance. Fractionation will be optimum when the junction between the leading edge of the lip and the disk proper is sharp. The width of the lip must be sufficient to allow adequate partition of the particle cloud zones containing the ejected larger fibers and the residual slurry. The angle between the disk surface at its edge and the lip must be greater than 0 deg; the angle between the plane of disk rotation and the lip must be less than 90 deg. Both the performance model and experimental results indicate that like fibers undergo fractionation primarily on the basis of diameter and not length. Analysis predicts that fiber wettability can be an important factor in vaneless disk fractionation. Separation is predicted for fibers on the basis of density and for particles, in general, on the basis of shape. Although not theoretically predicted, fiber flexibility may play a role in separation. While studies have been limited to fiber slurries, vaneless disk fractionation may be applicable to numerous types of homogeneous and heterogeneous suspensions of solid and, possibly, liquid particles. A limitation to this method of separation is the inherent instability of the liquid film as it flow across the lip surface. The growth rate of instabilities originating on the lip surface increases with film thickness. A t large flow rates these instabilities break away from the film before it reaches the downstream edge of the lip. To increase film stability at the high rates, the system must be operated at low disk speeds, low lip angles, and large disk diameters. However, each of these requirements has a negative effect on the extent of fiber separation. Acknowledgment The authors thank the Forest Products Laboratory, U.S. Department of Agriculture, the Walter B. Schulte Trust, and the University-Industry Program of the University of Wisconsin-Madison Graduate School for financial assistance during the course of this study. The donations of the high-speed disk drive and vaneless disk atomizer by Rockwell International Corp. and the custom-fabricated high-speed disks by Stork Bowen Engineering, Inc., are gratefully acknowledged.
Nomenclature A , = surface area of particle, 1' D,, = diameter of cylindrical fiber or spherical particle, 1
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Ind. Eng. Chem. Fundam. 1986, 2 5 , 490-498
E, = energy associated with particle wetting, m 1"t' E, = energy associated with particle disengagement, m l'/t2 E, = energy associated with viscous dissipation by particle motion, m 12/t2 FdragJr = drag force resisting particle motion in radial centrifugal field, m l/t2 L = length of cylindrical fiber, 1 Q = volumetric flow rate of slurry, 13/t R = disk radius, 1 r = radial position on disk, 1 u, = radial velocity of particle relative to disk, l / t u , = radial velocity of particle relative to fluid, l/t u, = radial velocity of fluid relative to disk, l/t $ = wetting or contact angle between liquid and particle, deg y = surface tension, m/t2 0 = lip or chamfer angle (Figure 8), deg p = liquid viscosity, m/(l t) pf = liquid density, m/13 pp = particle density, m/13
= disk rotation speed, rad/t Literature Cited
w
Britt. K. W., Ed. Handbook of Pulp and Paper Technology; Van Nostrand Reinhold: New York, 1970; Vol. 2, pp 209-223. Dombrowski, N.; Lloyd, T. L. Chem. Eng. J , 1974, 8 , 6 3 . Duffy, G. G.; Pedersen, M. L.; Petersen, J. H. Appita 1982, 35, 512. Freeness of Pulp : T227 os-58; Technical Association of the Pulp and Paper Industry: New York, 1958. Happel, J.; Brenner, H. Low Reynolds Number Hydrodynamics ; Martinus Nijhoff: The Hague, 1983; pp 42, 229. Hinze, J. 0.; Milborn, H. J . Appl. Phys. 1050, 77, 45. Klungness, J. H.; Oroskar. A. R.; Crosby, E. J. Tappi J . 1984, 67, 78. Matsumoto, S.; Saito, K.; Takashima, Y. J . Chem. Eng. Jpn. 1973, 6 , 503. Moller, K.; de Ruvo, A.; Norman, B.; Felsvang, K. Pap. Techno/. Ind. 1979, 20, 110. Moller, K.; Duffy, G. G.; Moller, J. T.; Foghmar, P. Tappi 1980, 63, 89. Olgard, G.; Axenfalk, S. I. Appita 1972, 26, 123. Oroskar, A . R.; Crosby, E. J. US. Patent 4427541, 1984. Rydholm, S. A. Pulping Processes: Interscience: New York, 1965; p 39.
Received f o r review June 16: 1986 Accepted July 24, 1986
Scaling Up Gradient Elution Chromatography Stephen J. Gibbs and Edwin N. Lightfoot" Department of Chemical Engineering, University of Wisconsin, Madison, Wisconsin 53706
The fractionation of biologically active proteins by gradient elution chromatography is critically reviewed in terms of underlying transport theory. Simple, explicit equations are found adequate for data correlation and for extrapolation from isocratic to gradient operation. Improved techniques for parameter estimation are presented, but chromatographic experiments are shown inadequate for this purpose. The ratio of mass- to momentum-transfer coefficients is shown to provide useful insight for design of improved apparatus.
I. Introduction Transient transport/reaction processes in granular beds have long been of central interest to chemical engineers, and they are among the topics treated in the now famous series Chemical Process Principles. Our concern here is with extensions of the fixed-bed separations methods described on p 1086 of Part 111, 1st ed. (1943). More specifically, we wish to provide an overview of gradient elution chromatography, now used extensively for fractionation of protein mixtures, with particular emphasis on the scale-up of laboratory procedures to obtain economical and effective preparative separations. Gradient elution is a variant of differential chromatography (Giddings, 1965) in which the migration velocities of the species to be separated are continually increased by changing the composition of the eluting solvent. This process is useful because the distribution of solute mean residence times in the absence of a gradient, isocratic operation, tends to be in a geometric series. Proper selection of a gradient schedule can, however, modify this distribution to decrease process time and solvent consumption without significant losses in resolution. Salt gradient elution i n ion-exchange chromatography plays a key role in the development of separation processes for biologically active proteins, particularly in pilot stages where substantial amounts of large numbers of possibly interesting proteins must be screened for their commercial potential. Here, gradient elution is accomplished by continually increasing the salt concentration of the carrier buffer. A typical result, illustrated in Figure 1, is to compress the long time periods needed to elute the slowest moving
species and produce a near-uniform distribution of peaks in the chromatogram. This example, as well as the others in our discussion, is taken from our current fractionations (Tien and Kirk, 1984) of a fungal fermentation broth into the order of ten fractions with ligninase activity, i.e., the ability to depolymerize the lignin components of wood. Our experimental procedures are described in Appendix A. The goals of our discussion are to assess the utility of transport theory for description of gradient elution chromatography, for interpretation of laboratory experiments via data analysis, and for design of large-scale processors. We wish to determine what is possible to learn about this process and to what extent our knowledge must remain incomplete. It will be assumed in this discussion that large-scale processes are to duplicate the resolution of laboratory experiments. This will not always be true, but our results will provide a useful limit for more general design procedures. It should also be noted that isocratic operation is included as a special case and that our analysis is not limited to ion-exchange systems. Rather basic arguments in transport theory and the analysis of laboratory data lead us, not suprisingly, to the conclusion that description is much more satisfactory than data analysis and that small-scale chromatographic experiments are not optimal for this latter endeavor. We shall also suggest the use of newly available estimation procedures, applicable directly in the time domain, as superior to the widely used but inflexible method of moments. Finally, we shall recommend a radical restructuring of large-scale chromatographic columns suggested by simple but surprisingly powerful arguments.
0196-4313/86/1025-0490$0lSO/OG 1986 American Chemical Society
