Ind. Eng. Chem. Res. 1994,33, 355-362
355
Centrifugal SPLITT Fractionation: New Technique for Separation of Colloidal Particles Chwan Bor FuhJ Marcus N. Myers, and J. Calvin Giddings' Field-Flow Fractionation Research Center, Department Salt Lake City, Utah 84112
of
Chemistry, University
of
Utah,
A centrifugal SPLITT fractionation system has been assembled for the purpose of extending the capabilities of gravitational SPLITT fractionation to materials in the colloidal size range and to particles of low density. The integrity and capabilities of the system are examined using polystyrene and other latex beads. Fractionation is illustrated using a mixture of latex beads of two different diameters, 0.60 and 1.05 pm. In addition, palladium particles in the size range 0.03-0.3 pm are separated into small and large particle size fractions with diameters below and above 0.15 pm, respectively. Continuous fractionation is then carried out for periods ranging from 7 h to 3 days using a polydisperse poly(viny1 chloride) latex material (0.2-2 pm, cut at 1.1 and 0.7 pm) and a polydisperse nematic curvilinear align phase liquid crystal emulsion (1-10 pm, cut at 2.8 pm). Fractionation is verified by electron microscopy and by size analysis using sedimentation field-flow fractionation. Throughputs are the order of 0.5-1.0 g/h; guidelines are provided to expand this level significantly. Introduction SPLITT fractionation (SF) is a family of techniques designed mainly for the separation of macromoleculesand particles (Giddings, 1985, 1992; Springston et al., 1987; Fuh et al., 1992,1993; Gao et al., 1991). Although these techniques can be used for analytical separations (e.g., leading to the measurement of particle size distributions and the content of oversized particles (Fuh et al., 1992), as well as the measurement of macromolecular diffusion coefficienta (Fuh et al., 1993)),the main strength of SF is related to ita capability for continuous operation and thus the preparative separation of materials in amounts ranging from milligrams to kilograms and above. Separation in SF is accomplished in a thin elongated flow cell or channel of rectangular cross section. A driving force, usually derived from an imposed field, is applied across the major walls of the SPLITT cell perpendicular to the axis of flow. The driving force or field compels particles of different types and sizes to occupy thin laminas located at different transverse positions between the major channel walls. A flow splitter at the outlet end of the channel divides these laminas into different substreams that can be separately collected. The separation process is fast (typicaMy in the range 10 s-10 min) because the transport path for separation is very short, usually constituting only a fraction of the submillimeter channel thickness w. While more than one outlet splitter can be used, the binary separation produced by a SPLITT cell with a single splitter can be rapidly refined by a second separation step in the same or a different SPLITT cell. SPLITT cells can be operated in either equilibrium or transport modes (Giddings, 1985). In the equilibrium mode, particles may start at any cross-sectionalposition. They are soon driven by the field to different equilibrium positions, and thus they occupy different laminas to be separated by the outlet splitter. In the transport mode, all particles enter the cell in a common lamina but are driven into different laminas as a result of their different field-inducedtransport rates. Before reaching equilibrium the differentially occupied laminas are divided by the
* Author to whom correspondence should be addressed.
Current address: Department of Biomedical Engineering, The Cleveland Clinic Foundation, 9500 Euclid Ave., Cleveland, OH 44195-5254. t
outlet splitter and the contents thus separated. The transport mode of separation (as utilized in this paper) requires an inlet as well as an outlet splitter in order to bring particles into the channel confined within a single thin lamina. The thin separation channel and the applied perpendicular field are common features both of SF and of another family of separation techniques, field-flow fractionation (FFF). However, the mechanism of separation is quite different in the two cases. In SF the axis of separation lies along the thin dimension of the channel whereas in FFF the separation axis is the elongated axis of the channel. Thus FFF, while excelling as an analytical separation technique, cannot be run continuously as can SF and is thus not readily adaptable to preparative separations (Giddings, 1986). Various forms of centrifugation and elutriation, along with combinations of these two techniques, are commonly used for the separation of small particles (McEwan et al., 1968;Pretlow and Pretlow, 1979;Lindahl, 1986;Brouwer et al., 1984; Dyrkacz and Bloomquist, 1992). Separation by these methods lacks the speed and flexibilityof SPLITT fractionation, and generally requires batch operation. These techniques are also subject to important hydrodynamic constraints. The sensitivity of conventional centrifugation to convective disturbances requires careful attention (Brouwer et al., 1984). Highest resolution is gained by centrifugation out of a narrow band (rate-zonal Centrifugation). However, a density gradient is generally needed in order to avoid convective instabilities; the gradient-forming material may then require additional steps for removal. As shown here, SF can employ centrifugation out of a narrow band without gradients; the thinness of the channel not only hastens separation but has an anticonvective role as well. When elutriation is used, either with centrifugation or gravity, flow nonuniformities along the separation axis degrade resolution. Such flow-induced degradation is not found in the SPLITT cell configuration. The perpendicular forcesutilized for the implementation of SF have a number of different origins. These include gravitational sedimentation, electrical forces, concentration gradients (for diffusive transport), and hydrodynamic lift forces. Gravitational forces are most convenient and have been used most frequently (Springston et al., 1987;
0S~S-5SS5/94/2633-0355$04.5QIQ 0 1994 American Chemical Society
356 Ind. Eng. Chem. Res.. Vol. 33, No. 2,1994
Fuh et al., 1992; Gao et al., 1991). However, it is often desirable to increase the strength of the driving force, a change not readily carried out when gravity is used. The increase in driving force, when it can be realized, provides a proportionate increase inmaterial throughput (Giddings, 1992). Even more importantly, the effects of weak forces (especially on small particles) can be overwhelmed by Brownian motion, in which case the separation is degraded and separative powers are eventually lost. This degradation becomes serious for gravitational SF as particle size decreases toward 1 pm. For particles with densities close to those of the carrier liquid utilized in the channel, the degradation of separation can be serious for particle diameters of several microns and the throughput can be seriously limited for even larger diameters (Giddings, 1992). In these cases it is desirable to amplify the driving force by installing the SPLITT cell within a centrifuge. When this is done one has the possibility of extending the SF process downward into the colloidal size range. While the resulting technique of centrifugal SF requires a more cumbersome and complex apparatus than gravitational SF, the frequent need to separate colloidal-sizedparticles in many industrial, environmental, and biological settings makes the additional complexity of centrifugal SF worthwhile. We observe that when a material is processed one time through a SPLITT cell with a single wtler splitter, two fractions are produced, one having particles whose transport coefficients exceed the designated cutoff value and the other having particles with transport coefficients smaller than the cutoff value. In thecase of sedimentation SF (either gravitational or centrifugal SF), the critical transport parameter is the sedimentation coefficient s. The value of s correlates strongly with particle size unless the particles exhibit large differences in density. The cutoff value of s, and thus of particle diameter d , can be readily adjustedover wide limits by altering the constituent flowrates and, where possible, the field strength. This controllable binary separation process, exhibiting a sharp cutoff, can be used either to divide a material into two well-defined fractions or to rid materials of particles in an undesirable sizerange. Thus 'undersized" and "oversized" particles can be readily removed in a single pass. Further processing steps can be used with other cutoff diameters to prepare narrow fractions. However, in order to extend this relatively sharp cutoff capability into the colloidal size range, centrifugal driving forces must be used as explained above. (We note that either gravitational or centrifugal SF is intrinsically capable of working with particles that float in their medium as well as those that sink.) Gravitational SPLIlTcellsare relativelysimpledevices although they must be constructed with precision because of the critical alignmentrequirements for placingsplitters evenly within such narrow confines. Several mechanical complications must be faced in proceeding from gravitational SF to centrifugal SF. First and most obviously, the SPLITT cell must be incorporated in a rotor system. Second, special rotating seals must be designed or other provisions made for transferring the fluid substreams between the environment external to the centrifuge and the SPLITT cell within the centrifuge. Third, the precision alignment of inlet and outlet splitters must be maintained despite the enhanced sedimentation forces that tend to distort the splitters. A centrifugal SPLITT system meeting these requirements is described in this paper. We note that a larger centrifugal SF system designed for higher throughputs is
Oullrl I)
I"lPI h'
Figure 1. Schematic diagram of centrifugal SPLITT cell and the continuousseparationoftwo typesof particlesaeeordingtodifferencen in their transport (sedimentation) rates. Channel thickneaa w (normally submillimeter) is exaggerated for clarity of illustration.
under construction in our laboratory. The main purpose of this study is to demonstrate the feasibility of applying centrifugal SF to particulate materials having particles of such small size or low density that gravitational SF is not readily applicable.
Mechanism and Theory of Centrifugal SF The mechanism of transport-based centrifugal SF is illustrated in Figure 1. Inlet and outlet splitters divide the flow space in the SPLITT channel into inner and outer compartments at the inlet and outlet ends, respectively. Thechannelisgenerallyverythin(w V(t)
.'
innov wyk~l(.mr
(5)
The cutoff diameter, based on the condition Fb = 0.5 impoeedoneq6whereeqs3and4areusedforA~,bbeeomes
This diameter can be controlled by varying the field strength G or by varying the constituent flow rates that determine V(t) (see eq 1). In the second case all particles of a size equal to or larger than the cutoff diameter are assumed to sediment to the surface of the inlet splitter before entering the separation region of the SPLITT cell. In this case the retrieval factor F b is approximated by eqs 5 and 9 where the latter is (Springston et al., 1987)
Fb= 1 (for A V > V(U)
(9) In this case the cutoff diameter is that for which AV = V(t), namely d,=
[; 3 " 2
(10)
Experimental Section The centrifugal SPLI'IT cell was constructed as a sandwich of three layers and clamped between two concentric Hastelloy C rings that serve as the channel walls. The structure of the layers is shown in Figure 2. The center (splitter) layer consists of a 127-pm-thick stainless steel sheet from which a rectangular section was removed to form the central one-third of the channel volume. Two identical 127-pm-thick Mylar sheets were cut as shown in Figure 2 and clamped symmetrically on opposite sides of the splitter layer. The volume cut from the Mylar spacers formed the remainder of the channel volume and also the smaller volumes allowing ingress and egress of fluid substreams above and helow the splitter layers. Thus the assembled SPLITT cell has a thickness w = 381 pm; its other dimensions are, excepted as noted, L = 26.7 cm and b = 2 cm. The area of the inlet splitter is 6 cm2. Several variants of the above system were tested. In onecasetheinletandoutlet wereswitched,givinganinlet splitter area of 50 cm2. Some experiments were also done withchannelsofbreadth b= 1.0,1.25,and1.5cm,thefirst and third of these having constituent layers of thickness 254pmandthusacumulativethicknessw = 762pm.These andothervariantswill benoted whenusedtoproduceany of the experimental results reported below. In order to prevent the stainless steel splitter from saggingor otherwise bendingin thecentrifugalfield,small Mylar strips were placed between the splitter and the two walls. The strips were shaped and positioned in such a way that flow disturbances induced at the splitter edges were small. The SPLITT cell and enclosing rings were inserted into a sedimentation FFF system replacing the conventional FFF channel. Thesedimentation FFFsystem isaspecially modified version with rotating seals accommodating two inlet substreams and two outlet substreams. A similar
358 Ind. Eng. Chem. Res., Vol. 33, No. 2, 1994
system was reported earlier in a study of split outlet sedimentation FFF (Jones et al., 1987). The radius of rotation ro of the SPLITT channel in this system is 15.0 cm. Operation was carried out at the ambient laboratory temperature of 23 f 0.3 “C. The carrier used for the latex [polystyrene (PS) and poly(viny1 chloride) (PVC)I and colloidal palladium experiments was 0.1% FL-70 (w/v) detergent (Fisher Scientific, Fair Lawn, NJ) and 0.03% (w/v) sodium azide (Sigma Chemical Co., St. Louis, MO) in doubly deionized water. The carrier for the liquid crystal emulsion experiments was doubly deionized water. The density measured for both carrier liquids was 0.997 g/mL. For the calculation of cutoff diameters, the viscosity was assumed to equal 0.996 cP, which is the value for pure water a t our operating temperature. One Minipuls 2 peristaltic pump (Gilson; Middleton, WI) and one Kontron (Electrolab, London, UK) LC pump Model 410 provided independent flows to the SPLITT cell inlets a’ and b’, respectively. Two liquid chromatography UV detectors with variable wavelength, one a Model SPD-6A detector from Shimadzu (Tokyo, Japan) and the other a Model 750 unit from Applied Biosystems (Ramsey, NJ), were connected to outlets a and b to monitor the particulate content. The collected fractions were characterized using a Model s-450 scanning electron microscope from Hitachi (Tokyo, Japan). The retrieval factor F b of a monodisperse particle population can be measured by injecting a pulse of particles into substream a’ and then measuring the areas A(a) and A(b) of the detector response curves generated by the detectors at outlets a and b, respectively. The applicable equation is (Fuh et al., 1992) Fb
=
V(b) A(b) V(b) A(b) + V(a) A(a)
(11)
For the more realistic case in which polydisperse particulate materials are subject to centrifugal SPLITT fractionation, the measurement of F b for a given particle diameter requires that the size distribution of material eluting both from outlets a and b be measured so that the relative elution of particles of a given size within the distribution (which determines F b for that size) can be determined. In this study the particle size distribution (PSD) was measured by sedimentation FFF. The sedimentation FFF system used for PSD analysis was constructed at this research center with design features similar to those of the Model SlOl apparatus from FFFractionation, Inc. (SaltLake City, UT). Two different FFF channels were used for PSD, both of length 90 cm. For steric mode analysis the other channel dimensions were thickness w = 127 pm, breadth b = 1.0 cm, and void volume Vo = 1.41 mL. The steric mode conditions were rotation rate = 1500 rpm and flow rate V = 7.15 mL/min. For normal mode analysis the other channel dimensions were w = 254 pm, b = 2.0 cm, and V” = 4.9 mL. Power programming was used in the normal mode case with programmingparameters rpm (initial) = 500, V =0.7 mL/ min, p = 8, tl = 19.7 min, and t e = -157.6 min (Williams and Giddings, 1987). These conditions produce a uniform fractionating power F d of 3.5. The monodisperse test particles used in this study were polystyrene (PSI latex beads obtained from Duke Scientific (PaloAlto, CA) and vinyltoluene tert-butylstyrene (VTBS) from Seradyn (Indianapolis, IN). The polydisperse materials included palladium particles provided by Dr. Dan Goia of Degussa Corporation (South Plainfield, NJ), a PVC suspension provided by Dr. Alan Handley from IC1
600
800
rpm
0
200
400
600
800
rpm
Figure 3. Plot of retrieval factor Fb versus rpm for 1.05-pm polystyrene latex beads. The cell, of dimensions w = 762 pmr b = 1.5 cm, and L = 35.5 cm, was operated with the flow rates v(a’) = 0.2, V(b’) = 0.62, V(a) = 0.49, and v(b) = 0.33 mL/min. In part a the splitter area at the inlet is 4 cm2 and eqs 5-7 are applied to obtain the theoretical line. In part b the inlet splitter area is 50 cm2 and eqs 5 and 9 are used.
(Runcorn, Cheshire, UK) and NCAP (nematic curvilinear align phase) liquid crystals provided by Dr. Paul Drzaic of Taliq Inc. (Sunnyvale, CAI.
Results and Discussion Channel/Splitter Integrity. In order to test the integrity of the centrifugal SPLITT system, short pulses (16 pL) of a dilute (0.3 % ) suspension of polystyrene latex beads were run through SPLITT cells having different structures and the results compared to theory. The breadth b of the cells used in these experiments varied from 1.0 to 2.0 cm with thickness w either 381 or 762 pm (see last section), corresponding to an aspect ratio b/w range from 13to 52. Cells with and without Mylar support strips were examined. The inlet splitter area varied from 4 to 50 cm2,the smaller area giving results close to those described by eqs 5-7 and the larger area corresponding more closely to the predictions of eqs 5 and 9. Figure 3 shows the dependence Of F b (obtained using eq 11)on rpm for four different SPLITT cell structures. These experiments were carried out using 1.05pm PS latex beads in a channel of length L = 35.5 cm with b = 1.5 cm, w = 762 pm, and thus an aspect ratio b/w = 20. The flow rates were V(a’) = 0.2, V(b’) = 0.62, V(a) = 0.49, and V(b) = 0.33 mL/min. The results shown in Figure 3a were obtained using a SPLITT cell with a 4-cm2 inlet splitter area; the theoretical line is based on eqs 5-7. The closed triangles, representing data obtained for a cell with Mylar support strips utilized at both inlet and outlet ends and spaced about 0.5 cm apart, show good agreement with theory. The cell without Mylar support strips (open squares) produces results in good agreement with theory up to about 550 rpm. At higher rpms the agreement is poor, suggesting that the positioning of the splitter is disturbed by the higher centrifugal forces. Similar results are shown in Figure 3b, which represents parallel experiments done with a cell having an inlet splitter area of 50 cm2. Although eqs 5 and 9 are used to construct the theoretical line, the results appear to be in bettkr agreement with eqs 5-7. Once again, the splitter integrity appears to be compromised in cells lacking Mylar support strips at rpm values of 550 and higher. Experiments similar to those described above were carried out on a SPLITT cell of still smaller breadth, b = 1.0cm and blw = 13. Even with Mylar support strips, the F b value failed to approach unity at higher rpm’s, giving a result more comparable to that shown in Figure 3 for cells lacking Mylar support strips. This result may be due to enhanced secondary flow in channels of low aspect ratio driven by Coriolis forces (Schure and Weeratunga, 1991).
Ind. Eng. Chem. Res., Vol. 33. No. 2, 1994 359 8.
Original mirturc
(0.60 3nd I .OS p n
131ch head%)
vm
Tm
Figure 4. Plot of retrieval factor F b versus rpm for PS latex beads of 1.05-pmdiameter for part a and 0.60 pm diameter for part b. The cell dimensions are L = 26.1 em, b = 2 em. and w = 381 pm with an inlet splitter area of 6 emz. The flow rate8 were V(a’) = 0.16, V(b‘) = 0.14. v(a) = 0.64,and V(b) = 0.26 mL/min. Table 1. Retrieval Factor Fb of 0.334-rm VTBS at Different rum’s.
8M)
0.08
loo0 1200
0.10
1500
0.14 0.25
0.40 0.44 0.48 0.50
The amect ratio of the channel is 5 2 other dimensions are those reported fir Figure 4. Flow rates: V(ai = 1.8, V(b’) = 1.2. V(a) = 3.0. and V(b) = 6.0 mL/min.
Figure 4 shows the results of similar experiments done with a thinner but broader channel, w = 381 pm, b = 2.0 em, and b/w = 52, using PS latex beads of two diameters, 1.05 and 0.60 pm. Cells with and without Mylar support strips were again used, each having an inlet splitter area of 6 emz. For this set of experiments the flow rates were V(a’) = 0.16, v(b’) = 0.74, V(a) = 0.64, and f4b) = 0.26 mL/min. Theresultsareshown inFigure4 in comparison to the theoretical F b values predicted by eqs 5-7. The agreement of theory and experiment is quite satisfactory for the SPLITT cell with Mylar support strips but is very poor for the cell without support strips. The even worse agreement of the latter results with theory, as compared with the parallel results in Figure 3, is in all likelihood a result of the greater channel breadth and reduced channel and splitter thickness (the latter reduced from 254 to 127 pm), and thus the greater inability of the splitter to maintain its positional stability when subjected to centrifugal forces. AmorerapidtestoftheintegrityoftheSPLI’Msystems described in theprecedingparagraph was carried out using the0.334-pm neutrally buoyant VTBS latex beads. These were run in the presence of a relatively thin transport lamina as specified by the ratio V(t)/V = 0.13, where V is the total flow rate (9.0 mL/min) through the SPLITT channel. (The constituent flow rates were V(a’) = 1.8, V W ) = 7.2, V(a) = 3.0, and V(b) = 6.0 mL/min.) Despite the fact that the transport lamina is thin, the neutral buoyancy of the latex eliminates sedimentation transport across the lamina although there can in principle be some leakage due to diffusion. Therefore if the thin lamina is well formed by properly aligned splitters, F b should be small. This expectation is largely realized at rpm’s up to loo0 for splitters supported by Mylar strips as shown in Table 1. There is still a degradation of channel performance above loo0 rpm and a substantial degradation at evenlower rpm’sfor thechannellacking theMylar support strips. On the basis of the theory describing diffusion in such SPLITT cells (Williams et al., 1992), we calculate that the leakage across the transport lamina due to
11. 001ii.i ,I (iiii1i.r \\.ill)
c.
O L 1 1 1 1 ~ 1II
1 0.7 wm)
TIME (min) TIME (min) Figure 10. Fractionation of PVC latex with a cutoff diameter d, = 0.1 pm. Conditions are rotation rate = 540 rpm; V(a’) = 0.8, fl(b’) = 3.8, v(a) = 2.2, and V(b) = 2.4 mL/min. confirm that the original particle distribution is divided intoamajorsmalldiameter fraction (emergingfromoutlet a) andaminor largediameter fraction (outlet b), thelatter consisting of the ‘oversized” particles. One way of gauging the sharpness of cutoff of the fractionation described by Figures 8 and 9a is by plotting Fb(obtainablefromtheratioofoutletbtoout1etadetector response curves from Figure 9a) versus particle diameter. Such a plot is shown in Figure 9b. This type of plot is described by Snow and Allen as a selectivity plot with Fb being the selectivity (Snow and Allen, 1992). The results of a second run of similar duration with d, = 0.7 pm are shown in Figure 10. The 0.7-pm cutoff is near the peak of the distribution. TO attain the 0.7-pm cutoff the flow rates were changed to V(a’) = 0.8, V(b’) = 3.8, V(a) = 2.2, and V(h) = 2.4 mL/min using a rotation rate of 540 rpm. The results presented in Figure 10 are similar to those given in Figure 8 except that d, has clearly shifted downward (1.1to 0.7 pm) and the detector signal for outlet b representing particles above d, is elevated by the larger particle population exceedingthe smaller cutoff diameter. Theshift in d,and thus the shift in the relative particle populations arealso illustrated in Figure 11,which shows the sedimentation FFF fractograms and the Fb
Sl%I(,,“l)
Figure 12. Particle size distribution curve8 from sedimentation/ steric FFF for liquid crystal emulsion. SPLITT cell is same as reported for Figure 4. Conditions are rotation rate 526 rpm; V(a’) = 0.8, V(b’) = 3.4, v(a) = 3.2. and V(b) = 1.0 mL/min. versus diameter curve derived from those fractograms. We note that the throughput for the case in which d, = 0.7 pm, in which the feedstream again contains 1% solids, is 0.48 g/h. Fractionation of Liquid Crystal Emulsion. CentrifugalSPLITTfractionationwascarriedoutonan NCAP liquid crystal emulsion of relatively low density (1.042 g/mL) in the particle size range 1-10 pm in order to extend theapplicabilityofthistechniquetoaparticulatematerial of quite different character from those described above. Accordingly, continuous SPLITT fractionation was undertaken on this material in a 3-day run a t 526 rpm with flow rates V(a’) = 0.8, V(b’) = 3.4, v(a) = 3.2, and V(b) = 1.0 mL/min. These run conditions correspond to d, = 2.8 pm (based on Ap = 0.045 g/mL) and a throughput for a 1% suspension of 0.48 g/h. The run was unattended and proceeded smoothly for the 3-day period as indicated by the stability of the detector responses from the two outlets (not shown). The steric mode of sedimentation FFF (sedimentation/ steric FFF) was used to examine the PSD of the original emulsion material and of the two fractions collected. For this purpose the sedimentation FFF device was operated at7.15 mL/minandat 1628rpm. Thecalibrationrequired for steric mode operation was provided by polystyrene latex beads run at the same flow rate and the same GAp valueasused fortheanalysisof theliquidcrystal emulsion (Giddings et al., 1991). The results of this analysis are shown in Figure 12a. The relatively steep F b plot shown in Figure 12b provides verification of the efficacy of the fractionation process. Conclusions The above study provides an initial evaluation of centrifugal SPLITT fractionation and demonstrates its effectiveness in fractionating low-density particulate materials extending into the submicron size range and highdensity (metal) particles with cutoff diameters as small as 0.15 pm. We have shown that the SPLITT device can be
362 Ind. Eng. Chem. Res., Vol. 33, No. 2, 1994
operated continuously and unattended for m a n y hours, i n one case for a period up to 3 days. However, much more work is needed i n optimizing the separation and extending i t s range of applicability. It is likely that more work on splitter integrity can f u r t h e r sharpen the separation to yield more cleanly fractionated products. However, the most significant gains are expected to be made b y increasing the t h r o u g h p u t of the system. According to theory (Giddings, 19921, SPLITT cell t h r o u g h p u t is proportional to cell area bL, field strength G, and the density difference times the square of the cutoff diameter Apd,2. In order to extend the technology to smaller diameters and lower Ap's, increases are needed i n bL and in G. Using our present apparatus, the value of bL could be increased by a factor of approximately 2.7 simply b y changing the dimensions of the SPLITT cell cut from the spacers. Further significant gains i n bL require a different channel and rotor system, an example of which is presently being assembled i n our laboratory. The proportionality of throughput to G promises further gains simply b y operating at higher rpm. Once splitter integrity is better assured, higher rotation rates should be possible. Simply b y increasing rpm from 550 (as used commonly i n this work) to 2200, the t h r o u g h p u t is multiplied 16-fold. With such gains, centrifugal SPLITT fractionation should become a highly practical tool for the separation of gram to kilogram quantities of m a n y colloidal materials and of numerous particulate materials of relatively low density. Acknowledgment This work was supported b y Grant CTS-9204086 from the National Science Foundation. Nomenclature a = outlet at cell wall A a' = feed inlet b = outlet at cell wall B b = channel breadth b' = carrier inlet d = particle diameter Fb = fraction of particle retrieved from outlet b G = acceleration L = cell length ro = radius of rotation s = sedimentation coefficient tl, .ta = time parameter of power programmed FFF = velocity of sedimentation V = total volumetric flow rate through cell V(a) = volumetric flow rate exiting outlet a V(a') = volumetric flow rate of feed inlet substream a' V(b) = volumetric flow rate exiting outlet b V(b') = volumetric flow rate entering inlet b' V(t) = volumetric flow rate in transport region w = cell thickness
v
Greek Symbols Ap = particle density minus carrier fluid density 7 = fluid viscosity w = angular velocity
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