Continuous Nonfoaming Adsorptive Bubble Fractionation Solke Bruin,*l Joyce
E. Hudson, and Arthur 1. Morgan, Jr.
Western Regional Research and Development Division, Agricultural Research Service, Albany, Calif. 94710
A continuous flow system for nonfoaming adsorptive bubble fractionation was developed and tested. Separation of organic components from aqueous liquid mixtures was studied experimentally. The experimental results were compared with predictions from a differentially continuous flow model with axial dispersion.
B u b b l e fractionation as a separation method uses the tendency of certain classes of organic molecules to adsorb strongly at a gas-liquid interface (Dorman and Lemlich, 1965; Harper and Lemlich, 1965; Karger, et al., 1967; Peters, 1952; Schutz, 1946). This method is related t o foam fractionation and t o flotation type processes, the main difference being that no stable foam is formed in bubble fractionation. Lemlich (1968) reviewed the literature on bubble fractionation. Bikerman (1953) lists treatment of bile acids, sugar juice, and beet root juice as possible applications of bubble adsorption separation techniques. Most of the literature on the subject indicates qualitatively what separations can be achieved, and frequently considers only batch experiments (Charm, et al., 1966; Dorman and Lemlich, 1965; Sebba, 1959, 1960). An exception is recent work of Lemlich (1966), who analyzed the steady-state concentration profiles that will build up in a bubble column, without feed or take-off liquid a t bottom or top. Shah and Lemlich (1970) measured such steady-state concentration profiles of crystal violet dye in a batch bubble column. Their results supported the equations Lemlich (1966) derived for a situation where equilibrium exists between surface excess (r) and concentration of the bulk liquid. Shah and Lemlich studied the effects of variation in gas flow rate and column dimensions. Most of the work on bubble adsorption has been done on nonvolatile compounds, such as dyes. Bruin (1969) reported phase separation t o occur when nitrogen gas was bubbled through an aqueous solution of 1-decanol, a phenomenon that can be explained from adsorption effects. I n view of the above discussion there seem t o be potential applications of bubble fractionation, perhaps in some cases combined with foam fractionation, in the agricultural and food industry where separation of organic molecules from dilute aqueous liquid mixtures is a frequently encountered separation problem (waste water treatment, separation of proteins, aroma recovery processes). The low energy input needed to create a “surface phase” as compared t o the energy input needed t o create, e.g., a vapor phase in evaporationdistillation processes is attractive. I n the present study a continuous flow bubble adsorption separation system was developed and tested. Separation of volatile (n-alcohols, octanoic acid) and nonvolatile components (dyes, proteins) could be achieved. An axial dispersion Present address, Koninklijke/Shell Laboratorium, Shell Research N.V., Amsterdam, The Netherlands.
model for continuous flow adsorptive bubble separation was formulated and as far as possible compared with experimental results obtained with the apparatus. First the model will be discussed, followed by a description of the apparatus and of the experiments performed. The experimental results are then compared with predicted separations from the model. Analysis
Figure 1 is a schematic picture of the bubble column. overall mass balance over the column gives
F = W + D
An (18)
The flows W’ and D‘ inside the column in top and stripping sections are defined by the relations
W‘=W+6-
Gdi db
where d, is the thickness of a surface phase layer surrounding a bubble of diameter db. G is the gas flow rate. An overall mass balance of the component t o be separated is
FCF = WC,
+ DCD
(2)
The flow over the top (cnD) consists of two parts: a bulk liquid flow ( D ’ c ’ ~ )and a flow of component adsorbed a t t h e bubble surfaces (6Grldb)
(3)
In eq 3 r is the “surface excess” in kg/m2. Axial mixing effects can be suitably described with a dispersion coefficient or eddy diffusivity in a differentially continuous model (Danckwerts, 1953; Miyauchi and Vermeulen, 1963). The equation of continuity a t steady state for the surface active component in the liquid phase, excluding the “surface phase,” can be written as follows (see Figure 1)
where cli is liquid phase concentration immediately adjacent t o the surface phase; v ~ is, the ~ superficial liquid velocity. El is an effective axial dispersion coefficient in the liquid phase describing mixing effects caused by nonuniformity of the flow pattern and the carry-up of liquid in the wake of the Ind. Eng. Chem. Fundam., Vol. 1 1 , No. 2, 1972
175
*=l----
As a consequence the surface excess is in equilibrium with the bulk liquid concentration, throughout the column. I n model I1 it is assumed that for the transfer from bulk liquid t o surface phase one has the relation
r"i
I n eq 7 kl is the liquid phase mass transfer coefficient and k , is a first order adsorption reaction rate constant. Introducing an overall transfer coefficient kl' to eliminate cli from (7) in the usual manner defined by
the relation for +r becomes
Figure 1. Schematic picture of an adsorptive bubble separation column
gas bubbles (Rietema and Rijpkema, 1966; Wijffels, 1970). For the ''surface phases" a balance over a differential height Az gives (Figure 1) 6v, d r_ 6v,wAl dzr __ --db dz db dzz
-"=
(5)
hssumptions are that the bubbles rise with superficial velocity u,; d b is a surface averaged bubble diameter; w is t'he "frequency" with which bubbles rising with velocity u, make backward jumps of A1 ( i e . , axial dispersivity E d = wu,AL). Axial dispersivity for the dispersed phase is difficult to est'imat'e. Let'an and Kehat (1969) conclude, for kerosene dispersed in water, that' if no coalescence takes place, plug flow ( E d = 0) is a reasonable assumption. Diboun and Schugerl (1967) give measurements of Ed for an air-water system from which it must be concluded that axial dispersivity of the bubbles is appreciable and even larger than of the continuous phase. We only xi11 derive solutions for plug flow of the bubbles, but along the same lines, relations for situations where Ed # 0 can be derived easily. The equilibrium surface excess (req)is assumed to be related to the concentration a t the liquid surface, eli. According to the Gibbs adsorption equation (Guggenheim, 1957) for a binary misture a t low concentrations of the surface active component the equilibrium value of r reads
I n eq 6, xi is the liquid phase mole fraction of the solute adjacent to the interface between surface phase and liquid phase. I n dilute solutions, as we used in our experiments, the activity coefficient y mill be constant ( b In y/bx = 0) and the surface tension u will be linearly dependent on x; t,herefore in the dilute solution region K can be assumed bo be independent of eli as a good approsimat,ion. Two types of solutions of the differential eq 4 and 5 will be given. I n model I it is assumed that no mass transfer or adsorption rate limitations exist. This means that solute is transferred a t an infinit,e rate from bulk liquid to surface phase and t'hat the adsorption process itself is infinitely fast. 176
Ind. Eng. Chem. Fundom., Vol. 11,
No. 2, 1972
Estimation of k , is a difficult task. I n the first place it was assumed that the adsorption kinetics is first order and not much esperimental evidence is available about this. Tsonopoulos, et al. (1971), indicated a method to determine a first-order k.. They found for adsorption of 1-hesanol-water systems k , = 0.0173 sec-l, indicating that equilibrium on a stepwise change of bulk concentration is reached in about 0.1-1 sec. England and Berg (1971) also report that adsorption barriers can play an important role in the transfer of surface active components from the bulk of an aqueous solution to the surface phase. Values for k l may be estimated from the modification of the R a m and Marshall correlation (1952) proposed by Hughmark (1967)
For decreasing db this correlation, as does the Ranz-hlarshall correlation, predicts increasing of k l . Model I is therefore expected to be an approximation for small bubbles if adsorption is fast. Model I, kl' Very Large. Because cI = cli in this case, the surface excess is in equilibrium with the bulk of the solution
r
=
KC^
(9)
Boundary conditions for the system of eq 4 and 5 are for the bottom section (CH)
at z
and for the top section
=
0
c11
(10)
= cw
(~12)
Equation 13 is a mass balance over the top section of the column. The concentration profile for the bottom section of the column (the stripping section) is given by 5 1
cw
- 1-
K~
exp[-P6,(1 1 - KW
-
K ~ ) < ]
(14)
For the top and stripped products the concentrations are
where
IO
IO
2t1p;,
The K, and KD as defined by (16) are analogous to the familiar extraction factors or absorption factors for gas-liquid and liquid-liquid transfer processes. I t is of interest to note that eq 14 reduces t o one of the equations given by Lemlich (1966) in the limit K , + m . If, as in Lemlich's model, F = D = W = 0, the values for K, and K D approach infinity. From eq 14 in this case one finds c'1
cw
-
-
KW
- 1)ij - 1 -1
exp{P6,(KW Kw
100
2% AE I
Figure 2. Nomograph giving degree of separation for varying PBclet numbers and K,,. factors. Negligible mass transfer resistance and infinite adsorption rate constant assumed (model I)
The solut,ion for the concentration profile in the bottom section is (17)
This relation is equivalent t o eq 14 in the study by Lemlich (1966). The recovery fraction (= CDD/(CFF)) increases linearly with R in this model. Another convenient measure for the separating power of the column is the follon-ing ratio CDD - CFD -- I - CFF- CFD
cw
~~
CF
where
X1 = (-al
al = P6, a2 =
(18)
This ratio represents the difference between the actual flow of the surface active component over the top (DeD) and the flow over the top if no separating action were accomplished (cFD), divided by the maximum difference obtained if all surface active material navere coming over the top (cFF e&). Using eq 15 and 16 one obtains the following relation for this ratio
+ d a l Z - 4a,)/2 + d u l Z - 4u2)/2
X1 = (-al
+N
~ / K ~
I
PBw(l - K ~ ) N ~ / K ~
and
pi
=
1- {1-
KW
+ ht[Kw(l - At/pdw)/Ni + 1/P6w1) exp(XirF) Ni
=
(24)
kl'LA/W
N I is the number of liquid phase transfer units. The roots In Figure 2 this relation is plotted as a function of the Pdclet number, with K , as a parameter. At large P6clet numbers and for K , 5 1 the separation reaches an asymptotic value Complete removal of the surface active comequal t o K,. ponent is only possible if K,, 2 1.0 and can be reached for lower xw values when the P6clet number becomes larger. If and K,, can be estimated a priori this figure can be used to determine the length of the stripping section needed to obtain a specified degree of separation. Separating action in the top section in this model is negligible because of the concurrent flow situation and the fact that almost all surface active material arriving a t z = L is removed, except for some back-dispersion. Model 11, Finite M a s s Transfer or Adsorption Rate Resistance. I n this situation, the following boundary conditions are used to solve the coupled differential eq 4 and 5
h l and hz are a l m y s real. Relations for the concentration of top and stripped product are equivalent t o eq 15 if p is replaced by p' defined as
fi'
=
(5 a=1
Ai[KD
- hi{l/P6D
+KD(1
+ ha/Pb)/A'I}
1x
For the degree of separation as defined in ey 18 one obtains
If K , = 1 the solution 21 has to be replaced b y a degenerated solution. It can be shown that if XI +. a ,the solutions 17 and 21 become similar. For large kl' (large phase contact Ind. Eng. Chem. Fundam., Vol. 1 1 , No. 2, 1972
177
10
0.8 I.
-
,023M)
I.D. ,025MI
Y
U 0.6
-
Y \
1
L
N( R
.. y- 0 . 4
= Pe‘w =
Y
NI R Piw
U
0 2
-1-1-1-1-
= =
=
= = Phw =
44.5 O.SO 3.77 2.96 0.50 3.77
Nl
2.96
R
0.50
‘O-RING
4 Figure 5. Detailed view of overflow tube used to separate bubbles from liquid phase
23.4
n 0
0.2
0.4
[
CF
0.6
0.8
1.0
z/L
Figure 3. Concentration profiles and surface excess profiles in stripping section and top section. Finite mass transfer resistance in liquid phase and/or adsorption rate limitation (model II)
1
FLEECE FLOW METER TOP
8U00LI
PRODUCl
COLUM
PERISTALTIC
I n Figure 3 concentration profiles in a column with the feed location a t half the total column length calculated from eq 21 and the equivalent equation for the top section are given. The model separation is calculated for 1-octanol in water m), assuming bubbles of 0.03-m diameter ( K N 0.9 X rising with a velocity of 0.22 m/sec. A total gas flow rate (G) of ma/sec is assumed. The total length of the bubble column is 1.0 m , with i.d. = 0.0249 m. Three situations are calculated, with widely varying A.1 and PC,. (Pbclet numbers were estimated from data of Bischoff and Phillips (1966), eq 27.) Both the liquid phase concentration (CI/CF) and the surface excess a t the bubble-liquid interfaces [r/(KcF)] are plotted as a function of zlL. As would be expected, most of the separation takes place in the stripping section as no reflux is applied to the top section. If the PCclet number increases (less axial mixing) the concentration of the surface active component in the stripped stream decreases. If the number of liquid phase transfer units (LVl)increases the same phenomenon appears, at the same time the difference (cli cI)/cF decreases strongly. In the next section we attempt to compare both models I and I1 with experimental data obtained in a laboratory scale apparatus for separation of various organic components from aqueous liquid mixtures. Experimental Section
ZENITH PUMP
SPARGER 1 DEVICE
VALVE
8
DRAIN
Figure 4. Experimental setup
area and low transfer and adsorption resistance in liquid phase) and low liquid phase flow rates the condition N1 -+ m will be approximated. Equation 21 undoubtedly is similar to comparable equations given by Miyauchi and Vermeulen (1963) for extraction if the appropriate analogies are introduced between estractionabsorption and bubble fractionation. X relation similar to eq 21 was developed for the top section of the column where a concurl,ent flow situation prevails and for the situation Kw
=
1.
178 Ind. Eng. Chem. Fundarn., Vol. 1 1 , No. 2, 1972
Figure 4 shows the experimental setup. ,4 glass bubble column ( i d . 0.025 m ; length 1.42 m) was used. Gas bubbles were generated at a fine metal screen (twilled “Dutch double’’ weave; wire diameter 0.011 X 0.009 in., type 304 stainless steel, 50 X 250 mesh) at the bottom of the column. The gas stream was circulated by a peristaltic pump (Masterflex, variable speed: cap. 2-16 x 10-6 m3,/sec). The rate of gas flow was measured with a soap-bubble gas flow meter. The gas flow could be saturated with vapors of some organic liquid in a saturator (liquid height 0.3 m) before returning to the sparger device. The whole flow system c d d be flushed with nitrogen gas. The liquid mixture vias brought into the column a t the midpoint by a Zenith gear-type rotary pump (cap. 0.1-0.7 X 10-6 m3/sec) driven by a variable-speed motor (Zero-Max control). The flow of the bottom product was regulated with a pyecisZn needle-valve (Whitey, Model 316) and a Fischer and Porter rotameter (02F-1/8-12-5/36). The gas bubbles were separated from the liquid using an overflow tube (Figure 5 gives details) to minimize back mixing a t the outlet.
1.0
-
0
A n-OCTANOL
=
ICp
.35xIO-'kg/kgl
A n-OCTANOL (Cp
=
I
.7X10"
kg/ks)
v
0 o-HEPTANOL
"3 1:
,
TUBE D I A
n - O C T A N O I C ACID IPH 4.51 fTHYL -2METHYL BUTYRATE
0 25
CRYSTAL VIOLET 2 2
-
n-HEXANAL
=
0 2 4 9 lml X
0
OCTANOIC ACID I 3 x
V
DISTILLED WATER
ikg/kel
W 4l k g / k g l
0.5
c
010
I1
-
I
0 0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
16.0
0
G x lo6 [ m J / r e c ]
Figure 6. Degree of separation of various organic components from aqueous solutions for variable gas flow rate. ) j model I (--); model Curves are for Pi,, = a (-
11 (-.
-. -. -.-1
O S
Ob
10
12
14
5
G x 106 (rn3/sccj
Figure
----
13ubble sizes were measured photographically and varied from 0.002 to 0.005 111, dependelit on the surface tension of the solution. The column was operated a t ambient temperature (25 i 1°C). l q u e o u s solutions were made up from tripledistilled water or iii the case of crystal violet, demineralized water. The concentration of cryst'al violet was measured in a spectrophotometer (Bauscli and Lomb, Spectronic 20) a t a wavelength of 585 f i , Concent'rat'ions of the other organic componeiits were determined with a Beckman Infrared tota1,'organic carbon analyzer (Model 915). I n conducting the esperiments the column was first flushed with nitrogen gas. Liquid was pumped int'o the column, and gas circulation was started. Samples from feed, top, and bottom products were taken a t regular intervals until steady state was attained (1.5-2 hr). Figure 6 gives results for separation of volatile organic components from water for a number of gas flow rates. Each experimental point represents the average of duplicate measurements. I n all measurements F = 0.35 X 10-6 m3/sec and JV N I f ' = 0.175 X 10-6 m3/sec. The degree of separation of the volatile components increases in the sequence: 1-hexanal, ethyl 2-methylbutyrate, 1-heptanol, 1-octanol, 1-octanol, n-octanoic acid. The separation of n-octanoic acid will be dependent on pH; the solution used in the experiments was a t pH 4.5, giving a ratio between ionized and nonionized acid molecules of 0.57. Separation of the longer chain alcohols and carboxylic acids is easily achieved. The extent of separation (I - c n i c ~ )initially increases with increasing gas flow rate (G) and approaches a n asymptotic value for large flow rates. T o be able t o compare estimates from the models with the esperimental results, axial dispersion coefficients, liquid phase mass transfer coefficients, adsorpt'ion rate coefficients, and specific surface area have to be estimated. Liquid phase mass transfer coefficients were estimated from Hughmark's correlat'ioiifor swarms of bubbles! eq 8. Many other possible correlatioiis call be fouiid in the literat'ure, e.g., Sideman (1966). Axial dispersion Coefficients were estimat'ed from data given by Bischoff and Phillips (1966). Bischoff and Phillips reduced data 011 asial dispersion coefficients in airwater columns from various sources (Argo and Cova, 1965; Sienies and Uorchers, 1960; Siemes and Reiss, 1957) and supplemented t,hese with their on-n measurements in a graph from which the followiiig approximate correlation can be derived
0 4
0 2
7. Gas hold-up as a function of gas flow rate
-J \
5 0
I
4.0
c
*E
2
30 YI
2.0 1.0
0
2.0
4.0
6
o
0
e.0 X
10.0
12 o
14
o
0 16o
lob (m3/sec)
Figure 8.Comparison of simulated separation curves for 1 octanol from water for model I and model (I. Axial dispersivity is estimated from eq 2 7
EIA -dtG
=
76.9
(E)
2.57
(G/(A%)< 0.30)
(27)
The specific surface area, a, was estimated from measurements of gas-phase hold-up (Figure 7) and the measured bubble diameter
a = 6H/db
(28)
Bubble sizes varied markedly among the various liquid mixtures and agreed qualitatively with the observations reported in the literature (Zieminsky, et al., 1967; Zieminski and Lessard, 1969). The carboxy>.ic acids and aliphatic alcohols in dilute aqueous solutions decrease bubble size and reduce coalescence strongly. This yesults in increased gas hold-ups and specific surface area. I n Figure 6 experimental data are also compared with predictions from the theory outlined above. Calculated curves from both model I (ICl' --t m , eq 19) and from model I1 (ICl' finite, eq 26) are given. Figure 8 gives calculated curves for the separation of 1-octanol from water separately. The value for K is 9 X 10-6 m (Davies and Rideal, 1963). The straight line (P6, = m ) pertains t o the situation where both gas and liquid phase move in plug flow: model I with E1 = 0. If the asial dispersion in the liquid phitse is taken into account according to eq 27, the dashed curve is obtained from model I. The other curves in Figure 8 were obtained from model I1 with three values for ICl' as indicated in the figure. The curves from Figure 8 are compared with the esperimental results for 1-octanol in Figure 6. At low gas flow rates the degree of separation is limited by the adsorption factor (K,) and it will increase with gas flow rate (G); a t flow rates of about 6.0 x 6-6 m3/sec the axial mising effects and/or adsorption rate and mass transfer rate limitations become Ind. Eng. Chern. Fundorn., Vol. 1 1, No. 2, 1972
179
1.0
%d' COQ
I
0.5
c
CRYSTAL VIOLET SOLUTIONS:
0
0 CF =
3x10-b
Q CF
3 x 1 0 - 6 , t HEPTANE I N GAS
A 0
2.0
4,O
6.0
CF
=
kg/kg
t OCTANOIC ACID pH 6 . 2
8.0
10.0
12.0
14.0
16.0
G x 106 [ m3/sec]
Figure 9. Degree of separation of crystal violet from an aqueous soluton as a function of gas flow rate (dashed curve is fitted to experimental data, not a prediction from theory)
limiting factors. The quantitative agreement between theory and experimental data is good in the linear part of the curves. The leveling off of the extent of adsorption with increasing gas flow rates is predicted a t about the right gas flow rate. Figure 6 also contains two curves from model I for 1-heptanol Bakker, et a/., 1966), showing the same (here K = 3 X quantitative agreement. Unfortunately, it is not possible to draw quantitative conclusions regarding the results of model 11. From the work of Tsonopoulos, et al. (1971), the order of magnitude of k , (and if k l is sufficiently large also h')for 1-hexanol is 2 X sec-l. In Figure 6 the resulting curve for ICl' = 3.78 X is close t o the experimental data for 1-octanol. Figure 9 gives measurements for nonvolatile components, Le., crystal violet in water. Data are given for three situations. The lowest degree of separation occurs for crystal violet dissolved in demineralized water. Fitting to model I with K as the fitting parameter and assuming PBw = a gives K = 5 X 10-6 m (lowest curve in Figure 9). Shah and Lemlich (1970) report 1.0 X 10-6m, but also noted that impurities in the water may increase the value for K strongly. A much better extent of adsorption is obtained by saturating the circulating gas mixture with vapor of n-heptane. This result confirms the findings of Maas (1969). The mechanism for this increase is not certain; it may be caused by formation of water-alkane layers a t the gas-liquid interface stabilized by the surface-active crystal violet. h still better separation was obtained by using a kind of ion-flotation technique (Sebba, 1962). The crystal violet was mixed with triple distilled water and some n-octanoic acid was added as a collector molecule to the solution (1.3 X kg/kg). The resulting mixture had a pH of 5.5 and this was adjusted to 6.2 by adding NaOH. At this p H about 95y0 of the octanoic acid is hydrolyzed and consequently can form complexes with the crystal violet molecules. The degree of separation is almost 100% down to very low gas flow rates. The effective value for K is 4.5 X 10-5 which is about a tenfold increase compared with the K value for crystal violet dissolved in water only (or a 50-fold increase compared with the value reported by Shah and Lemlich). Conclusions
An axial dispersion model for a continuous flow adsorptive bubble fractionation column was developed and tested. Experimental separations of surface active organic compounds from dilute aqueous solutions compared well with predicted 180 Ind. Eng. Chem. Fundam., Vol. 1 1, No. 2, 1972
separations in the region where no mass transfer rate or adsorption rate limitation exists (model I). In the operat,ion region where no mass transfer rate, adsorption kinetics, and/or axial mixing effects limit the separation only qualit,ative agreement between experiment and theory \vas found. I n this region, however, our predictions are strongly dependent on estimated values for parameters such as the axial dispersivity, adsorption rate coefficients, and mass-transfer coefficients. There are indications in the literat'ure (England and Berg, 1971; Tsonopoulos, et al., 1971) that adsorption rate limitations can occur in situations of practical interest. For the situation of negligible mass transfer rate resistance and no adsorpt'ion rate resistance (an infinite number of liquid phase transfer units, 3)a simple nomograph is given (Figure 2) from which the length of an adsorption section needed for a specific separation can be estimated. For crystal violet solutions, addition of n-heptane to the gas stream used t'o bubble through the liquid resulted in a marked increase of the extent of adsorptive separation. An even stronger increase in separation efficiency can be obtained by using n-octanoic acid as a collector molecule for the crystal violet. Nomenclature
A A,
=
area of cross section of tube, ni2
= constants defined in eq 23
= specific gas-liquid interfacial area, m2/m3 a2 = defined in eq 22 B , = constants defined in eq 27 c = concentration, kg/m3 = molar concentration of liquid phase, kmol/m3 c, d = diameter, m D = flow rate leaving top section, m3/sec D = diffusion coefficient, m2/sec E = dispersion coefficient, eddy diffusivity, ni2/sec F = flow rate of feed stream, m3/sec = acceleration of gravity, m2/sec g = gas circulation flow rate, m3/sec G H = hold-up of gas phase = mass transfer coefficient, m/sec kl = adsorption reaction rate constant, l/sec IC, = constant defined in eq 6, ni K L = length of column, m N = number of transfer units, eq 24 P , = constants defined in eq 23 R = gas constant, Sm/kmol deg I( = D / F = ratio of top stream to feed stream R T = temperature, O K = superficial gas velocity, m/sec v, W' = flow rate leaving stripping section, m3/sec = liquid phase mole fraction, kniol/kmol z z = coordinate in axial direction along column, m
a
al,
GREEKLETTERS = parameter defined in eq 16, 25 p = liquid phase activity coefficient of surface active y component r = surface excess, kg/m2 = dimensionless coordinate in axial direction { K = quantity analogous to strip factor, defined in eq 16 = characteristic values of differential eq 4, defined in A, eq 22 Y = kinematic viscosity, m2/sec = surface tension a t gas-liquid interface, K 'm r = rate of transfer between surface phase and bulk 4 liquid phase, kg/m3 sec DIMEMIOXLESS GROCPS R e = Reynolds number, u b d b / v i Sc = Schmidt number, VI/DI Shl = Sherwood number, kIdb/'D)l PB, = PBclet number for stripping section, TI"L J E I PBD = Pkclet number for top section, D'L/dEl
SUBSCRIPTS a = adsorption = of bubble, bottom section b g = gas phase 1 = liquid phase 2 = in z direction = tube, top section t 1, 2 = pertaining to stripping-resp.
top section
Hughmark, G. A,, Ind. Eng. Chem., Process Des.Develop. 6,218 11967). Karger,’G. L., Grieves, R. B., Lemlich, R., Rubin, A. J., Sebba, F.,Separ. Sci. 2,401 (1967). Lemlich. R.. AZChE J . 12. 802 (1966). Lemlich: R.: Znd. Ena. Chkm. 60. 16 il96Sl. Letan, R.,kehat, E.yAIChE J . i5,4 (1969). Maas, K.,Separ. Sci. 4, 457 (1969). Miyauchi, T., Vermeulen, Th., IND. ENG.CHEM.,FUNDAM. 2, 113 ilOG. O., Lemlich, li., Ind. Enp. Chem.. Process Des. Declop. 4, 13 (1965). I
_
Peters, D., Kolloid Z . Z . Polym. 125, 157 (1952). Ranz, W.E., hlarshall, W. R., Chem. Eng. Progr. 48, 141, 173 (1952). Rietema, K., Rijpkema, J. J. M., Zngenieur, 78, 15 (1966). Schutz, R., Trans. Faraday Soc. 42, 437 (1946). Sebba, F.,Sature 184, 1062 11959). Sebba, F., A-ature 188, 736 (1960). Sebba, F., “Ion Flotation,” Chapter XI, Elsevier, Amsterdam, 1962. Shah, G. X., Lemlich, R., IKD.ENG. CHEM.,FENDAM. 9, 350 (1970). Sideman, P., Advan. Chem. Eng. 6, 207 (1966). Siemes, W., Borchers, E., Chem. Eng. Sci. 12, 77 (1960). Siemes, W.,Weiss, W., Chem. Zng. Technik. 29, 727 (1957). Tsonopoulos, C.,Newman, J., Prausnitz, J. M., Chem. Eng. Sci. ZG,817 (1971). Wijffels, J-B., doctoral thesis, Eindhoven University of Technology, Eindhoven, The Netherlands, Chapter 111, 1970. Zieminski, S. A., Caron, M. &I.,Blackmore, R. B., IND.ENG. CHEY.. FCNDAM. 6. 233 11967). Zieminsk, S. A,, Leskard, R. R.; Ind. Eng. Chem., Process Des. Develop. 8,69 (1969). RECEIVED for review December 9, 1970 ACCEPTED November 27, 1971 Reference to a company or product name does not imply approval or recommendation of the product by the U. S. Department of Agriculture to the exclusion of others that may be suitable.
Continuous Surface Chromatography Martin V. Sussman, Kenneth N. Astill, Rudolph Rombach, Arthur Cerullo, and S. S. Chen Department of Chemical Engineering, Tufts Cniversity, Medford, Mass. 02155
Continuous surface chromatography (CSC), a technique for separating gas mixtures through the use of rotating chromatographic channels formed from closely spaced, solvent-coated surfaces of revolution, i s described, with emphasis on methods for computer simulation of CSC behavior.
G a s chromatograpiiy is perhaps the most broadly applicable chemical analysis technique used today. -4lthough it is basically a separation technique, i.e., analysis is performed by separating components in a characteristic sequence, gas chromatography has not found appreciable application as a method for separating quantities of solutions into constituent coniyonents because of the low capacity and the batchn-ise operation of the conventional gas chromatograph. 111 ail attempt to overcome the capacity limitation of gas chromatographs, a group at the Tufts University Chemical Eiigiiieeriiig Department has devised a system for carrying out gas chromatography continuously (Huang, 1967; Merchant, 1968; Sussman, 1970; Sussman and Huang, 1967). The basic feature of the continuous system is the replacement of the conventional tubular chromatographic column b y a
rotating chromatographic channel formed b y two very closely spaced, solvent-coated surfaces of revolution. The continuous chromatograph is shown schematically in Figure 1. The chromatographic channel is formed between two flat glass disks held apart by small plastic spacers. The thickness of the spacers determines the thickness of the gas passageway between the plates. Carrier gas and the gas mixture to be separated are fed continuously into the gas passage from a supply orifice in the center of the glass disks. The gases then flow radially outward between the parallel disks. The feed mixture is introduced through a stationary nozzle located on the periphery of the supply orifice. The carrier gas enters the channel a t all points on the periphery of the supply orifice except the section occupied b y the feed gas nozzle. Ind. Eng. Chem. Fundam., Vol. 1 1, No. 2, 1972
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