INDUSTRIAL AND ENGINEERING CHEMISTRY
2756
In each case the visual detection of the critical yw and no conditions agreed with the photoelectric detection. The permeabilities are probably less correct than those based on rL data, but the agreement is reasonably good. This technique may also be of value because of its simplicity. The critical wetting conditions may be found visually, but in this laboratory, the photoelectric apparatus is considered the more reliable in that the visual perception of the critical wetting conditions requires practice. The detector is far less critical in its dependence on arrangement than the visual technique is upon the judgment of the observer. As instances of this weakness the following will suffice to emphasize the necessity for accepting the limit r L = rc when the liquid mirror first becomes detectably blurred. If the limit is taken when the cake becomes completely dry in appearance the resultant permeabilities will be far below the true value. Tests to demonstrate this gave permeabilities of 1 to 1.2 X for cake No. l., 0.4 to 0.48 X lO'for cake No. 3, and 1.8 x l o + for cake No. 6. For these cakes the permeabilities by other methods are shown to be about twice these values (Figure 7). The discrepancy between the two visual limits may be large
Vol. 44, No. 11
or small depending on the characteristics of the material being tested, the difference being larger for cakes having a slightly gelatinous surface. The photoelectric detector always seems to show the start of the disappearance of a complete liquid layer rather than the full development of a dry diffuse reflecting surface. Conclusions
The results discussed here appear to confirm the form of the equations proposed for the various analyses, and hence for the fundamental Equation 1. The data cover tests of the groups ( r o 2 - T L ~ )n2, ) y, (ro2- T L ~ )in Equations 1 and 2, using various techniques vith water flowing through beds of different materials. Tests on glycerol solutions confirm the viscosity term in Equation I . The agreement between cake permeabilities as in 9and 18-inch hydroextractors confirmed the application of the analysis over a 2:l range of ro. It is thus probable that the relationships and mechanism originally proposed ( 2 ) for the hydroext,ractor flow condition are near the truth.
(Hydroextraction)
Relation between Hydroextraction and FiItration Per meabilities
E
ARLIER work in this laboratorv (1-3) using visual detection of critical i\-etting conditions shon ed large differences between permeability to hvdroextraction and permeability to filtration when testing samples cut from hydroextractor cakes or cakes formed in a filter cell and subjected to stresses similar to those operating in the centrifuge. As part of the investigation to check this anomaly, it was considered necessary to form and test cakes in a cell under both centrifuge conditions and filtration conditions without removal from the cell. It was expected that this uould decide whether the differences in permeability referred to above were due to possible causes such as disturbance of samples in cutting them from centrifuge cakes. differences of cake formation in the hydroextractor and in a filtrr cell, or faulty technique, Studies with a Small Cell
The essentials of the apparatus adopted for this study are illustrated in Figure 8. The cell of 3.8-cm. diameter cross section and 5.08-em. length (Figure 8-4) was carried on a counterbalanced head fitted to a 9-inch diameter centrifuge as carrier, liquid being fed to a tube lying along the axis of rotation and discharging freely from the perforated base of the cell. The cake, B, was held on layers of duck weave cloth, C, xithin the perforated base. The cell x a s sealed by the rubber bung, D ,which carried the feed tube, leaving a free volume. A , filled with the f e d liquid. The carrier which held the cell and feed tube rigidlv t o avoid radial motion is not illustrated. It will be observed from the dimensions of apparatus and cakes (Table V) that the latter were tested under conditions of centrifugal head and stress similar to those acting on cakes in the 9-inch diameter hydroextractor already studied, The cakes were formed by filtration of a slurry through the cell either under a hydrostatic head with the cell stationary or under a centrifugal field with the cell assembly rotating about the axis, E. The permeability of each cake was measured for water flo>ying through the material under each of the two force fields, giving values for the filtration permeability and hydroextraction permeability of the cake. The filtration permeability was measured using a falling head technique by connecting the long head tube shown in Figure 8B.
The hydroextraction permeability was assessed as K , in the force equation
The equation depends on all the assumptions regarding flowmechanism discussed in the previous section, on the supposition that the liquid fills space d in the cell (Figure 8), and on the fact that in all hydroextraction tests the liquid is fed a t a rate. q, to maintain the level in the feed tube at G \Then the cell rotates at n revolutions per second around axis E. The pressure on the liquid is taken as atmospheric at the surfaces at G and at r = T o . The frictional and expansion losses in the 1-em. diameter feed tube and cell compartment A are assumed negligible compared to the energy losses to maintain flow through the packed material. Under the experimental conditions for hydroextraction, h was equivalent to 0.2% of the centrifugally induced force and thus could be neglected. The flom- equation thence becomes
Taking the resistance of the system as equivalent to a mean permeability, Kp, as in the hydroextraction analysis, the flow rate in filtration under hydrostatic head H i s given bv
and when the head falls from H Ato Hz during the period from time t, to t~ in a vertical feed tube of cross-sectional area u (Figure 8B)
Experimental Technique
The cell mxs fitted with layers of duck cloth up to a compact thickness of 0.6 cm. (Table V). Water was fed to tfie cloth with the cell spinning to compact the cloth layer, and then the cake was formed by introducing a thin slurry of chalk in water. A cake produced without protection was never uniform in thickness,
INDUSTRIAL AND ENGINEERING CHEMISTRY
November 1952
Table
V.
Dimensions of Cakes Tested in the Small Spinning Cell
(Cell dimensions: diameter
=
3.8 cm., depth TO
Cake Mass 5 6
=
= 9.4 om.)
5.08 om., rw = 10.0 om., and
Cake Thickness‘‘ C ha1k
(W), G.
(TO
-
0.Q2
1.10 1.29
7 8 Q
Cm. Starch 0.67
TO),
0.83 0.97
1.10 1.25 a The maximum deviation ever found for cakes of a given maas waa 10.1 cm., b u t the usual variation was less than dzO.02 om.
1.47 1.66
B
A
I
PERFORATIONS IN BASE
C
V
Figure 8.
2757
ridge across the surface in the position where the division between the two eddies was expected, e.g., sample 10. The secondary circulation is powerful, particularly so on the leading side of the sample. At high speeds a cavity is also opened a t the trailing end of the ridge. The use of a glass wool layer on the cake during permeability tests was successful in maintaining samples in the condition of No. 11 after considerable spinning times. I n all the small cell tests reported the chalk used had a density of 2.69grams per cc.and specificsurfaceof 17,200squarecm.per gram. I n the tests in series I, a slurry containing 1 gram of chalk in 30 ml. of water was fed slowly to the cell that was spinning a t 900 r.p.m. The liquid level in the vertical tube was kept a t G in Figure 8A, the slurry being followed by a controlled distilled water rate after the cake of selected W had formed. The cell speed was increased slowly to 1900 r.p.m. and kept there for about 5 minutes. Thereafter the cake was in a “reproducible” state (4) in that tests of p, n data were independent of the test chronology. Flow rates, p, were found to maintain the water level at G in the feed tube over the experimental range of speeds, n. The centrifuging tests having extended over about 30 minutes were concluded by checking that the p and n tests did not show progressive consolidation. The static cake was then tested under a hydrostatic head falling from HI = 140 cm. to HZ= 100 cm. I n the preparation of the samples for series I1 the cell was held with its perforated base horizontal and connected to a rubber sleeve from a vacuum receiver. Cakes of known quantities of chalk were formed in the cell by normal filtration on to the duck cloth under a vacuum of about 1000 cm. of water. This represents a frictional head similar to those developed in the centrifugal field. Without allowing the cake to dry, the cell containing
Cell in Position for Spinning (A) and for Hydrostatic Test (B) A. Freespace
E. Cake C. Cloth
D. Rubber bung
e.g., cake No. 10 in Figure 8D. After testing various protective devices, the most uniform cakes were obtained by fitting a “star” of wire gauze (Figure 8C) with its axis lying along the center line of the cell. The star was held to the rubber bung by wires so that its outer face was close to the final inner face of the cake to be formed. The cake No. 11 (Figure 8D) exemplifies the uniformity attained a t speeds u p to 900 r.p.m. To maintain such uniform thickness during spinning at the highest speeds during permeability tests it was necessary to protect further the face of the cake, since the gauze star failed to do so a t high speeds, e.g., cake sample No. 12, Figure 8D. This was done by removing the star and partly filling compartment A with loosely packed glass wool. The wool did not contribute appreciable resistance to motion or compressive stress to the chalk cake when present in sufficient quantity to protect the cake from eddies. Thus cakes were formed with the gauze star in position a t lower speedi, and then the glass wool was inserted instead of the star before proceeding to washing tests. Cakes formed and washed without any protection from the eddies formed in compartment A of the cell showed a strong surface attack which appeared to confirm the presence of a rudimentary double helical motion perhaps caused by the tangential acceleration of the fluid moving outward through the cell (6). Samples such as those in Figure 8D were obtained without significant deformation by blowing them back from the cloth end in the cell. The flow direction, i.e., the radial direction away from the axis of revolution, was downward and normal to the plane shown in Figure 8D. The direction of rotation was as shown b y %hearrow marked o. I n all cases unprotected samples showed a
Figure 8C.
Wire Gauze Star
i t was then transferred to the centrifuge clamp, tested under falling head, and then tested in centrifuging by the same procedure as before. The cake was finally tested again under hydrostatic head to detect any permanent deformation produced b y the spinning. The cakes tested in series I11 were of multilayer type. After testing the 5-gram cake in series I, 1 gram of chalk was fed as a thin slurry to form a cake of W = 6 grams. This was tested for
INDUSTRIAL AND ENGINEERING CHEMISTRY
2158
oa --
Vol. 44, No. 1 1
0.8k
-
0.6
-
0.6
0.4 -
i
i \
3
Y
-
U
< CT
w‘ B cc
I I :
50.2
3 LL
0.4
\
-
50.2
9
LL
0.I
0.I
SPEED,
nx l ~ G p . m . ,
Figure 9. Flow Rates for Series I Chalk Cakes in Hydroextraction
Figure 10. Flow Rates for Series II Chalk Cakes in Hydroextraction
A. Decreasing speed E. Tests A lor new cake
A. E. C. D.
C. Increasing speed
E.
Decreasing speed Tests A lor new cake Increasing speed With one layer of backing gauze With two layers of backing gauze
the usual q, n, and H , t functions after spinning a t the highest speed. The cake was then augmented by a further 1 gram of chalk to give a 7-gram cake. This layer-built cake was tested up t o W = 9-gram cakes. Experimental Results on Chalk Cakes
The hydroextraction results are shown in Figures 9, 10, and 11, the graphs including data which show the reproducibility attained for various cakes of the same nominal mass. The gradients of the q, n plots for all cakes from series I, 11, and I11 lie between 1.96 and 2.18 and mainly betxeen 2.00 and 2.10. Except for one cake the q, n gradients were greater than 2.00, which suggests that the permeability K Oincreases slightly with increasing n, perhaps because of the effect of increasing flow rate or microcracks in the cake, Whatever the cause of the phenomenon it was “elastic” in
Table VI.
a b
A. Decreasing speed E. Tests A lor new cake C. Increasing speed
that it appeared and disappeared with variations in n, the p, n data for each cake in Figures 9, 10, and 11 being independent of time. There 1%-asthus no evidence of compressive effects on centrifugal stress on these cakes as far as the speed function was concerned in that K Owould have been reduced by the increasing centrifugal stress as n increased, giving a q, n gradient less than 2.00. The permeahilities, K , from Equation 11 are shown in Figure 15 for all the cakes of each series. The cake dimensions are quoted in Table V.
I
Permeability Relationships from Tests in the Small Spinning Cell
Series
W ,G.
I11
5 6 7 8
Starch
Figure 11. Flow Rates for Series 111 Chalk Cakes in Hydroextraction
K~
x
1075,
G./Sq. See.
9
4.35 4.60 4.40 3.88 4.30
5 7 9
3.86 4.44 3.88
K F x io? G./Sq. Sec.
KFIKc
5.30
1.28
5.01
1.09
4.85 4.95
1.10 1.27 1.18 1.13 1.05 1.02
5.05
Mean 4.05 4.51 4.71
1.21
Re values at n‘ = 1000 r.p.m.
K F values for filtration flow,after spinning, under a head of 120 om. of mater.
Figure 12.
Filtration Tests for Series I Chalk Cakes
November 1952
Figure 13.
J
INDUSTRIAL AND ENGINEERING CHEMISTRY
Filtration Tests for Series I1 Chalk Cakes A. Before spinning B. After spinning
The tests under hydrostatic heads are shown in the semilogarithmic plots of falling head H against time, t, in Figures 12, 13, and 14. The falling-head tests show little effect of flow rate or time on permeability, and KF was obtained from the gradient of each H , t line. The permeabilities, KP, are included with representative K , values for two centrifuging speeds with the various cake weights, W , in Figure 16. The data in Figures 11 and 16 for the preformed cakes (series 11) showed that the cake packing was altered only slightly by the centrifuging, the difference in curves 1A and 1B in Figure 16 (11) being less than that between the K , and KF curves. The average difference between KF and K, found in the present cell is only about 10 to 20% (Table VI). This residual difference is of the order to be expected because of the difference in compressive stresses applied to the cake in the two force fields (5). The fact that the compressive stress effects are not detected in the q, n plots suggests that there may be another explanation. The possibility of a flow regime analogous to double helical streamline flow should be investigated. The strength of the eddies in compartment A discussed earlier j u s t i f y a further 0 5 10 examination of this TIME. t x l @ sec. possible flow mechFigure 14. Filtration Tests for Series 111 anism. Such a Chalk Cakes
study is now proceeding. The permeability relationship between cakes of the same W is shown in Figures 17 and 18. It will be observed that the cakes are always in the same order of permeability in the hydrostatic tests (Figure 18) but change their order systematically in hydroextraction a t the higher W values. The striking feature about the hydroextraction data on Figure 17 is that the different formation methods have only a small effect on the cake permeability, being about 7 % a t the maximum and 4% as the average. Though there is a progressive change with increasing cake weight in the position of the q, n lines for the different formation methods, the permeability variation is a minor matter. It seems improbable that the original differences of 400 to 500% between K , and Kp from the hydroextractor
2759
,
Figure 15. Variations in Hydroextraction Permeabilities with Spinning Speed
cakes (9) were due to formation mechanism differences between filtration and hydroextractor cake samples.
Time Effects
Figure 16. Variation in Permeabilities with Cake Mass 7A. Filtration before centrifuging 18. Filtration after centrifuging 2. Centrifuging at n' = 1000 r.p m. 3. Centrifuging at n' = POOO r&n.
The decrease in filtration permeability of a preformed cake after centrifuging suggested that the vibration and stresses in spinning the cake had produced a small but significant consolidation. Tests were made to find out whether this consolidation could become a major matter with the centrifuged cakes. The q, n data for any specific cake had shown very small decreases in permeability during the period of test (up to 1 hour) as with the data A , B, and C in Figures 9, 10, and 11. T h i s was confirmed b y tests over longer periods, which showed that a t various speeds the permeability of cakes fell by
INDUSTRIAL AND ENGINEERING CHEMISTRY
2760
Vol. 44, No. 11
about 3 to 4% after 1 hour and b y about 7% after 5 hours of spinning. The difference between 1A and 1B in Figure 16 (11) was due to an effect of centrifuging stress on the filtration cake packing, considerably greater than the consolidation of a centrifuge-formed cake by continuous spinning during the test period. The reproducibility of p, n characteristics irrespective of the chronology of tests means that if, for instance, stress effects produce a cake permeability as a function of speed, then the deformation of the cake is elastic. The ability of these cake systems to recover after being stressed is definite. rl cake was formed by centrifuging a t n' = 900 r.p.m. and then spun a t n' = 1900 r.p.m. for 10 minutes, water being fed continuously to the cake. The flow rate through the cake was then tested under a constant hydrostatic head of 149 cm. of water and shon-ed about 30% increase in permeability after 3 hours of flow. The cake was centrifuged again for 10 minutes at 1900 r.p.m. reducing the permeability b y about 15%, followed by a 10% recovery after flow under constant head for an hour. The frictional drag in the filtration tests was considerably less than the compressive forces operating at n' = 1900 r.p.m. when spinning, and the cakes could recover elastically from the compressed condition. Effect
Figure 17.
Hydroextraction Relationships A . Series I
E. Series 111 C. Series II
of Wire Gauze Backing
The presence of one or two layers of 60-mesh plain Keave copper gauze behind the cloth in the present cell had no detectable effect. The p, n data in Figure 10 for a single layer (D)or double layer (E) of gauze agree with those from cakes without gauze backing ( A ,B, C). The times of fall of the level H in the data included in Figure 13 agreed within 1% with all the times already shown thereon for the cakes without backing gauze. The effect of gauze does not assist drainage in the small cell. Experimental Results
on Starch Cakes
To check these results on chalk, cakes were made of maize starch. The q, n relationships for cakes of series I1 are shown
0.I
Figure 18.
Filtration Relationships
A. Series I E. Series 111 C. Series II aRer spinning D. Series II before spinning
a 1 o
15 20 SPEED. n ' x d r.p.m.
Figure 19. Flow Rates for Series Starch Cakes in Hydroextraction
II
November 1952
INDUSTRIAL AND ENGINEERING CHEMISTRY
in Figure 19. The H , t data for filtration are given in Figure 20, and the permeabilities to filtration and hydroextraction are presented in Figure 21. The data on maize starch confirm those on chalk, the values of KF and Kc being near together (Table VI).
700-Gram Starch Cake in the Hydroextractor Basket np
t
R.p.h.
Seb.
KO X 10' K F X 107 P G./Sq. Seo. G./Sq. Sec. Cm. df Hg
-
CENTRIFUGB TEST (TO = 10.75 am., r ~ , 7.92 am.,
Samples from Hydroextractor Cakes
To confirm the a g r e e m e n t between filtration and hydroextraction permeabilities for the cakes formed in the 9inch diameter hydroextractor i t was necessary to remove samples for filtration tests. The cakes were formed, and Kc was obtained by the measurement
Table VII.
2761
TO
= 9.38 om., and
= 8.72 cm.) ---l 2180 42 2.1 .. ., TL*
1520 955
2.08 2.1
86
217
.. ..
..
..
FILTRATION TEST^ (V = 15.8 ml., L = 1.37 om., and A = 11.4 aquare cm.) Sample I Sample I1 Sample I11
*. ....
.. .. ..
77.2 77.5 76.0
2.78 2.78 2.82
75.0 74.6 74.8
a Samples I, 11, and I11 were cut from the top, middle, and bottom of the cake, respectively.
i
$20I
d
-
U
I
W
r
110-
I, ~,~
IO0
Table VIII.
600-Gram Chalk Cake in the Hydroextractor Basket Itp t K O X 107 KF X lo7 P R.p.h.
Sic.
G./Sq. Se;.
CENTRIFUGB TEST(ro = 10.75 cm. 2 0 4 0 , 60 1650 91 1030 233
T L ~=
G./Sq. Se;.
Cm.
