For a given helix, rotating in a specified direction, good mixing (dispersion coil) operation is achieved only if there is a bulk interface in the entry tube of the minor phase; if the minor phase enters in dropmise fashion, it passes through the coil in slug flow and poor ext,raction is achieved. Correspondingly, if two sequential coils are in dispersion flow, there will be a bulk interface in the tube connecting them. The phase which within a dispersion coil repeatedly breaks up into droplets is determined b y the extraction system. The best extraction for a given helix is achieved when the phase which disperses within the coil is also made the major phase. It is possible to operate such that each coil in a series assembly of identical coils is a dispersion coil, a selected phase being major or minor depending on the placing of the controlled interface either above or below the assembly. An extraction may be int'errupted without affecting the volume distribution of bhe two phases along t>helengt,h of the column. Nult,iple, bulk phase separations, and redispersions are possible without mechanical internals. Samples of eit'her phase may conveniently be taken along the length of the column. Nomenclature
A-F, a-h = representations in Figure 1 KTU = number of transfer units U,, U , = linear flow rate, superficial; aqueous or organic, cm/sec
y = interfacial tension, dyn/cm p = pa, p o , A p = w =
viscosity, CP density aqueous phase, organic phase, difference in density, g/cc rotational speed, revolutions/min
literature Cited
Chantry, W. A., Von Berg, R. L., Wiegandt, H. F., Ind. Eng. Chem., 47, 1153 (1955). Cohen, R . M., Beyer, G. H., Chem. Eng. Progr., 59,279 (1953). Dykstra, J., Thompson, B. H., Clouse, R. J., Znd. Eng. Chem., 50.161 ilR.581. \_.._,
LetahlRuth, Kehat, E., AIChE J., 13,443 (1968). Letan, Ruth, Kehat, E., ibid., 15, 4 (1970). Logsdail, D. H., Thornton, J. D., Trans. Znst. Chem. Eng., 35, 331 11957).
hliyauchi, T., Vermeulen, T., Ind. Eng. Chem. Fundam., 2, 113 (1963).
Morello, V. S., Poffenberger, N., Ind. Eng. Chem., 42,1021 (1950). Oldshue, J. Y., Rushton, J. H., Chem. Eng. Progr., 48,298 (1952). Reman, G. H., Olney, R. B., ibid., 51, 141 (1955). Scheibel, E. G., AIChEJ., 2, 75 (1956). Shulman, H. L., Youngquist, G. R., Allen, J. L., Ruths, D. W., Press, S., Ind. Eng. Chem. Process Des. Develop., 5, 359 (1966a). Shulman, H. L., Youngquist, G. R., Covert, J. R., ibid., p 257 (1966b).
Thornton, J. S., Pratt, R. C., Trans. Inst. Chem. Eng., 31, 289 (1953).
Treybal, R. E., "Liquid Extraction," 2nd ed., RlcGraw-Hill, New York. N. Y.. 1963. DD 485.489. ~ - Vogt, H . J., Geankoplis, C. J., Ind. Eng. Chem., 46, 1763 (1954) VonBerg, R. L., Wiegandt, H. F., Chem. Eng., 59 (6), 189 (1952) I
~
--,=A
- - I
RECEIVED for review January 11, 1971 ACCEPTEDApril 30, 1971
COMMUNICATIONS
Cylinder Apparatus for Continuous Withdrawal Studies An apparatus for the continuous withdrawal of wires from baths of wetting liquids has been designed, constructed, and tested experimentally. The new entrainment data verify the applicability of extrapolated removal data to continuous withdrawal. Data were obtained with a 2-mm wire in a 2.46-P fluid; the Goucher number was 0.4, and the capillary number was varied from 0.2 to 6.
T h e problem of entrainment in wit,hdraival geometries is one of continuing widespread research interest. Important theoretical aspects are connected with the problem, in addition to iiunierous applications in commercial operations such as coating, washing, and lubrication (Tallmadge and Gutfinger, 1967). I n particular, the concern here is with films entrained on cylinders which are withdrawn from a bath of a completely wett'ing Xewtonian liquid. The first purpose of this note is to describe our apparatus for obtaining precise data under continuous withdrawal conditions. The second purpose is to compare new experimental data wit'h existing theory. The apparatus aiid dat,a reported here represent the first published description of a precise apparatus for cont'inuous cylinder withdrawal. As noted by Tallmadge and Gutfinger (1967, Tables VI1 and VIII), two such devices have been described earlier by Goucher and K a r d (1922) and by Tall592
Ind. Eng. Chem. Process Des. Develop., Vol. 10, No. 4, 1971
madge'et al. (1965). The freezing method used in the 1922 work raises questions of imprecision due to thermal gradients and variable viscosity. The results reported jn the 1965 photographic method paper had large uncertainties. The previous devices were not nearly so precise as the device reported here. Heretofore, precise data for cylinder entrainment have been obtained from removal experiments (White and Tallmadge, 1966; Tallmadge aiid Gutfinger, 1967). With proper corrections for end effects, removal data can be transformed for comparison to the continuous withdrawal situation. However, the removal technique becomes increasingly difficult to employ with accuracy as withdrawal speed increases. Because the trend in continuous commercial operations is toward increasing speeds, there is a need for a precise, highspeed cylinder apparatus. Continuous devices for flat plates have been utilized for
some time (Van Rossum, 1958; Gutfinger and Tallmadge, 1965). However, the withdrawal of cylinders possesses mechanical problems not present in the flat plate geometry. The present equipment was designed and demonstrated to meet these experimental needs. The apparatus described here is similar in concept to that employed in unpublished work by Gutfinger and Roy (1966). (An experimental paper on wire withdrawal was scheduled for presentation a t the International Symposium on Two-Phase Systems, Haifa, Israel, September 1971. The authors are Gutfinger and Chiu of Technion, Israel.) Description of Apparatus
T h e cylinder apparatus (Soroka, 1969b) is shown schematically in Figure 1. The endless cylinder consisted of a 323-em long, 0.204-em (0.080-in.) diameter piece of medium hardness No. 304 stainless steel wire but,t welded toget,her with t,he joint ground to 0.080 i 0.005 in. The wire was wrapped around two 25-em i.d. "V" pulleys of which t8heupper v a s driven. X large-diameter pulley was used to minimize flexing of the relat'ively large-diameter wire. The position of the lower pulley was adjustable to permit the wire to be placed under tension. The center-to-center pulley distance was 121 cm after tightening. The entire apparatus was assembled in a shockmounted frame constructed of 0.3-cni thick angle iron. T o eliminate vibrations, the drive system was mounted separately f roin the withdraw a1 apgarat,us. The witlidrawal speed was carefully cont,rolled and the allparatus was located in a constant temperature roorii. Ent'rainment was measured by determining the mass flow rate withdrawi by the wire, as follows. Wipers -4 and B comprised two pieces of neoprene rubber cut to fit tightly the contour of the "V" pulley and were pressed against the pulley (Figure 1). Wiper 4 rollected most of the liquid ent,raiiied by the wire, and wiper B collected the residual liquid before t,he wiped portion of the pulley again met t'he netted wire. Wiper C was a neoprene rubber gasket employed to ensure a complet,ely clean wire before it returned to the lower pulley. JViper C was housed in a Plexiglas collector, 13 cm long, 8 cm wide, and 8 em deep. Two 1.9-cm holes in the bottom of the collector allowed the wiped liquid t o drain into a funnel for return t o the bath. Timed samples for flow rate measurements were taken a t the discharge of t.he collector and weighed. Each data point represented the average of a t least two or three separat,e samples. Tithdrawal
DRIVEN PULLEY WIPER A-
B
Table 1. Tabular Data Measured valuesa Speed, Mass UW, entrained cmlsec W, g/sec
Run no.
Nondimensional form Mass entrained
Speed, Ca
r
-
h/R
F1M
2.15 0.0436 0.173 0.399 0.309 F6h1 0.326 4.01 0.125 0.409 0.433 4.84 0.172 F2M 0.428 0.500 0.392 0.576 7.12 0.324 0.430 0.608 F5M 0.446 0.662 F3M 0.635 7.84 0.395 0.722 9.54 0.493 0.431 0.681 SllOM 0.970 12.0 0.783 F481 0.446 0.819 1,55 SlllhI 19.1 1.59 0.422 0.979 3.04 S112M 37.5 4.76 0.410 1.33 4.62 57.1 9.41 S113M 0.400 1.60 6.22 76.9 15.2 S11411 0.390 1.81 a The variation of three individual measurements of mass entrained from the average values reported here were all less than +1.27,, except one run (4.84 cm/sec) had a variation of +2.0%. The speed variations, measured for the six F runs, were less than &3y0for all these runs.
speed was det.ermined by measuring t'he number of revolutions of the upper (driven) pulley over a given time with a hand t,achometer. An important feature of the cylinder apparatus is the bath locat,ion. Instead of immersing the lower pulley directly in the bath (Gutfinger and Tallmadge, 1965), the bath was placed bet.ween the pulleys as in Van Rossum (1958). The cent,ral bath location eliminated the effect of the lower pulley, which dist,urbed the surface a t high speeds. The liquid bath coiisisted of a 1.3-cni wall thickness Plexiglas container (36 em long, 36 cm wide, and 31 em deep) and was located 18 cm above the center line of the lower pulley. The wire passes through the center of t,he bath with a similar sealing device as described for wiper C. S o seepage of liquid was det'ected, even a t high wit'hdrawal speeds. One difficulty concerns the maximum diameter wire which possesses sufficient flexibility to be wrapped around the pulleys. For the apparat'us described here, it, was not feasible t'o increase the wire diameter above 0.2 em. There is a related problem in providing a continuous loop. Sumerous variations for joining the ends of t,he wire were tried before the b u t t weld approach was selected. However, the butt weld method may introduce a weak point in the loop if it is more subject to breakage as a result of the flexing t h a t occurs. Breakage of one wire occurred after the apparatus mas in use for 20 hr. Data
T o demonstrate operability, experiments were performed a t 22.1 0.4OC wit'h a Sewtonian fluid, S o . 30 Quaker State nondetergent~motor oil (fluid 11).The physical properties of this oil a t 22OC were 2.46-P viscosity, 0.875 g/ml density, aiid 31.1 dyn/cm surface tension (Soroka, 196913). Mass flow rate data were obtained a t 2-80 cm/sec, as shown in Table I. The runs a t 9 cmjsec and above 15 cmjsec mere taken b y Soroka (1969a) aiid the remaiiider by Fitzjohn. In all of the experiment's, stable films which completely wetted the wire were observed. Neither surface ripples nor droplet formation was detected a t any height.
*
MEASUREMEN O F FLOWRATE
Comparison with Theory Figure 1
.
Apparatus for continuous cylinder withdrawal
Figure 2 shows the good agreement of the gravity theory (White aiid Tallmadge, 1967) for data a t speeds up to about Ind. Eng. Chem. Process Des. Develop., Vol. 10, No. 4, 1971
593
1
I R = 0,102
1
.
1.0
1
1
CM
C = 0.38
o',
I
3
0.8
-
I
OIL #J 2.46 POISE
2 .-
';fl
1
I
-
n
GRAVITY THEORY
0.6
. E$ 0.4 : -/
GRAVITY
9 0.2 -
3Y v) v)
C
w
.
$
0 0.1
DATA G R 0 0 . 3 8 0.102CM
I 1 WITHDRAWAL SPEED,
10 Ca, Uw(u /e)
Figure 3. Comparison between d a t a and theory
OIL A 2.46 POISE
-Gravity
(7 form)
theory, Equotion 1
Conclusions 1
10
100
WIRE WITHDRAWAL SPEED, U,,CM/SEC
Figure 2. Mass flow rate d a t a ---Gravity
theory, Equation 1
15 cm/sec. The gravity t.heory D = +(Ca,G) is given in Ca explicit form (Tallmadge and White, 1968) by
+ 2 YG2
CU = 1.09 (DCM)3'2
(1)
where
Y
=
Y ( h / R ) = S2In S - 0.5 (S2 - 1)
and
(14
C M = C,(h/R,G) The experimental combination of mire size (E = 0.102 cm) and fluid chosen (a = 0.271 cm) is especially well suited for demonstration purposes, since they yield a nondimensional radius of G = 0.38. This G value is intermediate (Tallmadge and White, 1968) between the large cylinder range (G 2 3) and the small wire range (G 5 0.03). The comparison between t,heory and experiment is more accurately assessed in nondimensional vs. Ca form. Figure 3 shows that the theory predicts data precisely up to a Ca of approximately 0.7. The point of departure between theory and experiment is consistent wit,h Ca limits established by White and Tallrnadge (1967), based 011 removal daba. The correspondence between the data shown in Figure 3 and removal data may be considered as evidence for consistency between withdrawal and removal or as direct corroboration of the applicability of the finite-cylinder removal technique to the continuous withdrawal case. The lack of agreement of t.he theory with experiment (at Ca above 1 for G of 0.38) is believed to be due to neglecting radial curvature in the flow equation of the theory. Radial curvature was considered in the gravity theory as part of a static equation boundary condition involving C,. The term, C M ,has been determined to be (Tallmadge, 1969) 3.36 GS 1 c -- 1 + +-2 GS 3.36 GS
(2)
The second term in Equation 2 is due to the radial curvature. For t.he conditions plotted in Figure 3, there is less then 2% difference between from Equation 2 and the larger value from an earlier expression given by Equation 3 2.4 GS
'M'
=
GGGS
+- 1
(3)
2 GS
This is the first numerical comparison of Equations 2 and 3. 594 Ind. Eng. Chem.
Process Des. Develop., Vol. 10,
No. 4, 1971
A continuous cylinder withdrawal apparatus has been designed, const'ructed, and experimeiitally demonstrat'ed. New experimental dat'a verify the applicability of cylinder removal data to continuous withdrawal. It is believed that the apparat'us can also be used to study film thickness, film st,ability, obstructed flow, and other withdrawal problems. Nomenclature
a
h
= = = = = = =
h
=
R
= = = = = =
Ca C,tf CU' D G
s
T C,
UI
Y
Capillary length = (2 u / p g ) ' i Z capillary number = U u ( p / u ) defined by Equation 2 defined by Equation 3 dimeiisionless film thickness = h ( p g , ' u ) ' i 2 Goucher number = R(pg,/2 u ) l j 2 film thickness, cni mean film thickness = [w/aU:,p R 2 ] " 2- R wire radius, cm 1 (h/R) ii(pg/pUw)'j2 wire speed, cm/'sec mass flow rate, g,/sec defined by Equation 1X
+
+
literature Cited
Goucher, F. S., Ward, H., Phil. Mag., 6th Ser., 44, 1002 (1922). Gutfinger, Chaim, Roy, S. C., personal communication (1966). Gutfinger, Chaim, Tallmadge, J. A , , A I C h E J . , 11, 403 (1965). Soroka, A. J., personal communication, 1969a. Soroka, A. J., PhD dissert,atiori, Ilrexel T'niv., Philadelphia, Pa., .-...T n n ~1RRRh. ~... Tallmadge, J. A,, AIChEJ,, 15, 941 (1969). Tallmadge, J. A,, Gutfinger, Chaim, Ind. Eng. Cheni., 59 ( l l ) , 18 (1967); errata 60 ( 2 ) , 74 (1968). Tallmadge, J. 4.,Labine, R. A., Wood, €3. IT., Ind. Eng. Chenl. Fundam., 4 (4), 400 j1963). Tallmadw. J. A , . White. 1).A.. Ind. Eno. Cheni. Process Des. Van IEossum, J. J., A p p l . Sci. Res., A7, 121 (193%). White, D. A., Tallmadge, J. A., d I C h E J . , 12, 333 (1966) zbzd., 13, 743 (1967). White, D. A,, Tallmadge, J. -4., AKTHONY J. SOROKA' J O H S L. FITZJOHX' JOHN A . T.4LLXADGE2 Department of Chemical Engineering, Drexel University, Philadelphia, Pa. 19104 Present address, Du Pont Experimental Station, Wilmington, Del. 2 To whom correspondence should be addressed. RT,CI:IVED for review August 11, 1970 A C C E P T E D LIarch 26, 1971 This work was supported primarily by Yational Science Foundation Grant GK-1206. One of the authors (JLF) was supported in part by E. I. du Pont de Nemours & CO.
