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IN
EDIBLEOIL REFIREWY, Pnocmn & GAMIILR ~XAYUFACI'UIIINO COMPANY, I'onr IVORY, STATEN ISLAND, lv. Y.
Studies in Filtration 11.
h n d a m e n tal Axiom of Constant - Pr e m i r e Filtration
B. P. RUTH WITH G . H. MONTILLO~ ANI H. E. .\IONTONN~&, Cnivrrsity of Minnesota, :Minneapolis, Minn.
T
HE general lack of agreement between experimental 8.886 sq. din. (134.7 square ,inches), which is comiderably data and the various filtration equations n~hichhave larger than that used by such workers in tlie past as did not been proposed has been discussed in Part I of this employ plant-scale apparatus. Tlie choice of a press of this paper (IO). Reasons were advanced for believing that a size was prompted by the following coilsiderations: valid theoretical basis for treatment of the filtration probAvoidnnce of expense and difficulty in handling the large quanlem has not been estahlislied. Tlie conclusion was reached tities of suspended solids necessary in the performance of tests that the proper method of attack must lie in first determining upon pltint-siae equipment. Increasing ciiffioultiespresented in t.he acciirate measurement of by means of precise experimental observatioris the true g e volumes of filtrate. nature of the mathematical relation betmreen filtrate volume l u Nocossity of making operation during tests largely automatic. and the time of filtration. DeSirabiiity of performing the work upon a scale large enough, The purpose of this paper is to demonstrate that a single and rr.ith apparatus similar to commercial equipment, so that there would be no doubt as to the e q u a t i o n - is able to -describe applicability of the results to comaccurately the b e h a v i o r , not It is shown that the irregularities obserued in mercial practice. only of s l i g h t l y compressible the V z us. 8 plols at t h beginnirig of filtration are m a t e r i a l s , hut of the entire due to the resistame of the filter medium. PurFiltrations were carried out range of materials commonly at constant pressures up to 60 ther, if this resistance is expressed as units of filtered. pounds per square inch (4.2 kg. cake resistance u r d considered as a n integral part per sq. em.) by means of cornak'PARATUS A S U ?dETHOD OP of the filtratiori cycle, the relation of volume and pressed air frmn an autoniatiPROCEDDi%E time i s shozun fn be parnbolic lhrougiloal the cally governed air compressor. The air was a d m i t t e d t o t h e whole coune of the filtration. The simple equaDuriiig this research the apmonte-jus under reduced presparatus e m p l o y e d has undertion ( V C)z = K(0 I%) is shown to hold sures by means of a Mason regugone many changes and improvethroughout the whole course of the Jiltration cycle lator, capable of maintaining the ments, arid for this reason a defor a number of different types of sludges varying pressure c o n s t a n t within 0.2 tailed description af its present in character from highly rigid to hiQhly compound per square inch (0.014 kg. form will be reserved for a later pressible particles. Filtration data from many per sq. em.). Filtrations were paper, in wliieh the a.pplieation of its various details to the prabbegun by opening quickly a cock sources in the lilerature are correlated by the use lems under d i s c u s s i o n will be in the sludge line, after tlie deof this simple equation. This leads to the fundusired pressure had been estabmore apparent. It will be SUEmental axiom of constant-pressure filtration: eient now to m e n t i o n that a lished in the monte-jus. The time-volume curve of a properly performed single circular frame, having an The sludge in the monte-jus constant-pressure filtration forms a portion of a was kept in s u s p e n s i o n by a area of 4.343 sq. dm. (67.3 square inches), and a width of 3 em. large p r o p e l l e r , r u n n i n g a t perfect purabola in which the missing portion about 50 r. p. m. This action (1.18 inches) was supported in a represents the theoretical course of a similar f;lw a s a i d e d t o some extent by vertical position upon a bracket tration which would generate a resistance equal a t the edge of a c y l i n d r i c a l a d m i t t i n g the compressed air to that already ezi.?ting when the ezperimentally monte-jus of 22 liters capacity. used during the test through measuredfiltrate volume is zero. a c i r c u l a r perforated ring a t This provided a filtering area of
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INDUSTRIAL AND E S G I N E E R l N G CHEMISTRY
154
the bottom of the monte-jus. A long helix of copper tubing fitting snugly against the interior wall made possible the maintenance of constant temperature, when desired, by the passage through it of mixtures of hot and cold water from the laboratory supply. A special mixing device provided with thermometers enabled the adjustment of the temperature. The filtrate was conducted from the press heads into a cylindrical galvanized-iron can of about 14 liters capacity, set as closely to the press head as possible This receiver waq built of such a diameter that one-inch (2.5-cm.) rise of liquid
VOl. 25. No. 2
accurate to 0.002 second, and the distance of the filtrate volume curve above the base line could be measured to the equivalent of several cubic centimeters in 7 liters, the accuracy actually obtainable by this method does not warrant the trouble involved. In the first place, it is quite difficult to insure an absolutely vertical rise of the filtrate pen relative to the time marks. Although this rarely amounted to more than several millimeters, it was sometimes equivalent to an error of as much as one second in the time. The second objection is that in the subsequent measurement upon the drafting board, the construction of the time lines involves errors. A much simpler and very accurate arrangement was subsequently devised and used throughout the greater portion of this work. This will be described in a later paper. The sheet taken from the kymograph in the early method of measurement presented the appearance of a family of smooth parabolic'curves. This record was placed upon a drafting board, and parallel lines were drawn through the time marks perpendicular to the base lines which had been established prior to the beginning of each test. By measurement with a finely graduated engineers scale, the curves were reduced to values of V and 0. The problems selected for initial attack were: (1) development of experimental technic, (2) reproducibility of experimental behavior, and (3) determination of the degree to which a material most nearly approaching a noncompressible or rigid filtration behavior would obey the theoretical law, 1'2 = KO.
I
0
4
8
I2
I6
20
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19
28
32
36
level in it was nearly equivalent to one liter in volume. The advantage of this relation is that it is unnecessary to convert inches of filtrate level rise into liters by multiplication with a constant factor, since this factor is entirely similar to the correction for density, and may be used in a similar fashion after the data have been analyzed. In the early experiments, data records were made in the manner devised by Sperry (II), although with several refinements. In the method of Sperry the rising level of filtrate was made to lift a pen attached to a rod borne by a cork float. The pen traced a volume-time curve upon a sheet of paper fastened tightly to a cardboard cylinder rotated once an hour by the action of an alarm clock. In the present work, a kymograph was substituted for the clockwork-driven cylinder. This consisted of a 10-inch (25.4-cm.) aluminum drum. 7 inches (17.8 em.) in diameter, driven by an inclosed spring motor. Constant speed of rotation was insured by a magnetic governing device. The drum speed was easily adjusted from several millimeters to several meters per minute. I n spite of the constant-speed characteristic of such a device, it was desirable to correlate time with filtrate volume directly, rather than trust to calculated speeds of revolution. For this purpose a Jaquet graphic chronometer was fitted with a fine pen, and supported upon an adjustable standard, so that an independent time record could be traced simultaneously with the filtrate volume curve. The time record thus provided consisted of delicate vertical marks a t intervals of 3 or 6 seconds a t the top of the drum. By lowering the chronometer several millimeters a t each revolution, a number of tests could be recorded upon one sheet of glazed paper. Although the chronometer was
The material selected for this purpose was an ordinary grade of diatomaceous filter aid known as Filter-Cel. To determine the reproducibility of filter behavior, it was customary to perform tests in series of four or five filtrations, carried out under conditions as nearly identical as possible. When such data were plotted in the customary manner as 1'* vs. 0, curved plots similar to Figure 1 resulted. It was invariably found that the later tests of a series showed better agreement with each other than did the early tests, and that the slope of the T'2 vs. 0 plots were always less. This inability to obtain identical vs. 0 plots, while disconcerting, shed interesting light upon the anomalous solutions for n sometimes obtained by students in the past. It is clear that if, instead of making all four tests in Figure 1 a t identical constant pressures, a number of different pressures had been employed, the solution n = log e2 - log el log PI - log Ps
could have yielded values of n either greater or less than unity, depending upon the order of change in test pressures. Reflection showed that the only factor which could not be controlled or measured in such a series of identical tests was the resistance of the cloth used as a filter septum. Moreover, the probability that the cloth resistance did change was great, especially in those test series where a clean and sometimes dry filter cloth was used a t the start. This possibility was further supported by the observation that, in those tests where the cloth had been initially dry or clean, the change in the value of K was most rapid. Examination of a family of curves as recorded upon the kymograph usually revealed a corresponding curvature as far as the eye could detect. However, the tangents to such curves, compared a t the base line, sometimes decreased noticeably in slope from the first test to the last. Since the tangent to a time-volume curve is a measure of the instantaneous rate of filtrate flow, it was obvious that the initial rates of filtrate flow were less in the later tests. This, again, was to have been expected, if the cloth possessed a greater resistance t o flow in the later tests. The appearance of the
c u r v ~ ssuggested tliat, ii the I:it,cr uw in the series were extrapdated dowiiwards to sutrie negativc value of 17, new base lines could be establislsetl a t nliicli the tangents ~uould ail possess the same dope. Xoreovix, this was a rensonnhle proecdure siiice, if the c l o t h l i d not inrreased in resistance, a greater initial rate of flow in the later tests woiild have caused a larger total volume OS filtrate to liavc been recorded a t any given moment. In Fiblm: 2 is illustrated the effect of extrapolating such n timevolume curve below tlie recorded base line. The volume below the base line lias been designated as C . As will be obanrvsd, successively larger values of C l i a r e been
0 1 solids wliich woulil Ire separated from C liters of filtrat,e iss an irnngirinry filtration beginniiig with zero resistance to filtrate flow. It is well reoagnized that in any actual filtration proecss resistnnce to filtrate How can never bo zero a t t,lle start. Tliis is bucnusc of t l i e necessary presence of some supporting septum wliich was, in this ease, a filter cloth. Tlic cquiitiuii (1‘ f C)* = IC (0 t Ha>) satisfies this conditim nicely, for, &en it is diffcrentintcd,
arbitrarily a s s ~ ~ n ~aeidd , thc siiiii has I i w r l plot!ari 8s (1. ~t~ C)%vs. 0. AB the extrapohtbn is carried to g:n?tlt,eriicgatisr values of V , tlie corresponding plot of (I’ C’jX YS. H lo its upward curv:itiire at the origin, arid a t tlie same tinit: creases in slope; n t a definite value of C = 0.9 (found licre by trial and error) it beconies quite straight. Tiiercsfter, as C i s made still Is~ger,nil incrcasing curvature in the opposite direction appears. It becomes evidcnt that, for tlie single case wliere C = 0.9, the entire course of t,lie filtration may be aecurately described by the equat,ion:
Ilei,cc, wlieii u l ~ ~ r v 1iltr:itc rd YUILU~W is zero, rate i d flow i i it defiriit.: mpliilid In Iiigure 2, C is to be regarded as a iiicasiire of the resistance that existed previously to the instant. filtrate beE:i:;tn to appear at the mcasurisig device. Whatever may be tlin actual nature of titis resistance, it is c1c:ir that it is eqizi\.:ili~iit to, arid hence may be considered i s , tbc rciist>nnce nE ii layer
still
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l’,
wirere l’, = total resswe of filtration iii ti!
