I
WILLIAM J. TlMSONl and CECIL G. DUNN Massachusetts Institute of Technology, Cambridge, Mass.
Mechanism of Gas Absorption from Bubbles Under Shear Gases are absorbed in agitated liquids in accordance with the penetration theory. A new correlation is presented with which gas absorption coefficients for bubbles under shear can be calculated T
I n general, past investigations on gas absorption in agitated liquids have been of an empirical nature. Such studies have given useful information on the gas absorption performance of agitated tanks of specific design; but unfortunately, they have not shed much light on the mechanism whereby gases are absorbed in agitated liquids. This study shows that the surface area is normally the controlling factor in gas absorption in agitated liquids. Equipment a n d Methods
T o obtain controlled shearing conditio% an apparatus resembling a coaxial viscometer was built as shown below. The outer cylinder was made of a Lucite tube 30 cm. in inside diameter and 90 cm. long. The rotating drum was made of a Ryertex phenol-formaldehyde resin tube 28 cm. in outside diameter sealed on both ends with steel plates. The diameter of the drum was further increased by covering it with a smooth rubber sheet. The gap widths between the stationary cylinder and the rotating drum were 1.O and 0.42 cm. Pure oxygen and air were used for this study. Most of the experiments were Va.
Present address, Merck & Go., Elkton,
Cylindrical drum rotating within the outer cylinder provides controlled shearing conditions for absorption experiments
made with distilled water containing 0.01M potassium chloride and 3 X IOp4M phosphate buffer to ensure a pH of 7 . The liquid was rendered viscous with neutralized Carbopol. The rheological properties (Figure 1) of the viscous liquids were determined with a Precision Interchemical Rotational viscometer and spot checks of viscosities were made with a Brookfield viscometer. The pH of the solutions was checked with a Beckman p H meter. For absorption experiments with surfactant, 15 p.p.m. of pentapropylbenzene sulfonate (PPBS) were added to the liquid. The surface tensions of the liquids were determined with a Du Nouy tensiometer (Table 1).
Table
Surface Tension Measurements Surface
Tension, Liquid Distilled water Distilled water containing 0.5% Carbopol, 0.01M KC1, and 3 X IO-*M phosphate buffer Distilled water containing o.s% Carbopol, 0.01M KCl, 3 X 10-4M phosphate buffer, and 15 p.p.rn. pentapropylbenzenesulfonate
Dynes/ Cm.
The liquids were deaerated under vacuum prior to gas absorption experiments. The absorption process was followed by measuring the volumetric decrease of the gas in the system, as well as by the increased dissolved oxygen concentration, as determined polarographically with a dropping mercury electrode ( 7 ) . The flow rate of the recirculating gas was measured with a calibrated rotameter. The frequency of bubble formation at the orifice was measured with a strobotack. Highspeed photography was used to record the size and shape of the bubbles under shear as shown below. The residence times of the bubbles in the liquid were measured with a stop watch. The experimental conditions were such that it was possible to measure and control accurately : interfacial gasliquid contact area; rate of shear of the liquid; viscosity of the liquid; composition of the liquid; composition of the gas.
72
Theory 72
48
A theoretical equation for the coefficient of oxygen absorption from bubbles under shear was derived by combining the Higbie penetration theory with the surface drag theory proposed herein.
S,OMA PUMP
ROTOMETER
A S BUBBLES
a SPEED MOTOR
GAS
Figure 1. Rheograms of Carbopol solutions determined with a Precision Interchemical Rotational viscometer. The viscosities of the solutions at various shear rates were calculated from similar rheograms. Spot checks were made with a Brookfield viscometer VOL. 52,
NO. 9
SEPTEMBER 1960
799
Higbie ( 6 ) postulated that a gas bubble moving through a liquid splits the liquid at its advancing tip. The liquid which is split is originally at rest, but must be accelerated if the surface of the bubble is to travel at a certain velocity. The forces that are capable of accelerating the liquid, at the interface, in the direction of bubble movement are : a The vertical component of the buoyant force of the bubble surface a A surface force due to a surface pressure gradient The vertical component of the buoyant force hardly imparts a vertical velocity to the liquid at the interface, because absorption from clean bubbles follows Higbie's mass transfer law. Several investigators have observed that surface circulation of bubbles and droplets in liquids is reduced by surface active materials (3-5). To simplify the derivation of the equations describing the effect of shear on gas absorption from bubbles: a flat surface is considered. Consider the flat surface of a flowing stream of water containing a certain concentration of surface active material. If the surface is allowed to age, surfactant molecules will appear on the surface and form a monolayer of surFactant molecules. Suppose that a thin, stationary, vertical barrier is placed in the surface extending only a short distance below the surface of the water. Although the barrier cuts off sharply the presence of monolayer on the flowing liquid, it is supposed not to disturb in any way the flow of the liquid as shown below. As the liquid flows past the barrier, the surface immediately behind the barrier is freshly formed and therefore contains hardly any surfactant molecules. The pressure of this surface will be low. Immediately after formation of the surface, surfactant molecules start to appear on the surface. The surface pressure increases as surfactant concentration on the surface increases. But, in the meantime, the aged surface has moved a certain distance downstream, while some new surface has been created
immediately behind the barrier. A surface pressure gradient exists between the clean surface immediately behind the barrier and the aged surface a distance downstream. The surface pressure gradient pushes the aged surface upstream. In this process of surface movement, the liquid below the monofilm is carried along by viscous drag. The liquid below the monofilm is decelerated from the bulk velocity, v b r to a new characteristic velocity, u . The decelerating force is transmitted to the liquid film by viscous drag. The age of the surface film behind the barrier is controlled by the ability of the surface pressure gradient to decelerate the fluid film underneath the monolayer. According to Sewton's theory of viscosity, dv - F (1) a.2 - J d2u -
dZ2
w h e n y = 0 , u = 74, therefore
GI
= 0
For the case where a surface pressure gradient prevails on a liquid surface:
Ao
= -
(17)
X
Combining
dF pAdZ
According to Newton's law of mechanics, dF
F = ma adm f mda
(3)
=
The fluid flow pattern is in a steady state, if the stream velocity is kept constant. The deceleration of liquid at any fixed point in space can be assumed to be constant, consequently (da), = 0. Taking as a basis the mass, m, of liquid decelerated during a period of 1 second, per unit width dm =
p(u6
At the interface u = u,, and
(4)
- v)dZ
(5)
The rate at which the monomolecular film travels with respect to the bulk of the solution is u b - u , = u,.
In the case of perfectly circulating bubbles, (An = 0), the velocity of the surface with respect to the bulk of the solution is zero. The time of contact of the surface with the gas may be assumed to be equal to the diameter of the bubble divided by the terminal velocity of the bubble (6).
Combining With surfactants present, the time of contact is 2r
t=Ut
1.5 -
STATIONARY BARRIER
Figure 2.
The area
-
(23)
UP
.
a: 1.4
of spherical bubbles E increases because of 2
-
~-
I I .3
~
_-
their deformation into ellipsoids
Surface pressure gradient on the surface of a surfactant solution flowing past a stationary barrier
800
INDUSTRIAL AND ENGINEERING CHEMISTRY
I
2
3
4
RATIO OF ( M A J O R A X I S ) / ( M I N O R A X I S )
5
6
GAS ABSORPTION According to the Higbie penetration theory, the value of gas absorption coefficients should be K =2
2
-
I
(y
0
--____-
V L - -
I n the absence of surfactants the absorption coefficient for bubbles is
e -
4
I -/
D
-
-v-v------
--
-
/’
0-
I
C
]
I
I n the presence of surfactants, the absorption coefficient for bubbles should be
g2.
s
“g
I
v
__-j --1 --
- 7 7 -
I’Ff.\--
- --
--
- -- v-
I
--
____
X
Y
F z $ 0
(27) Calculation of t h e Experimental Absorption Coefficients. According to accepted mass transfer theories :
dN
- = KA(S dt dC - d N 5 - Ldt
- C1)
(28 1
HI
-x
I
-I--
a
-
+
‘ ! 7
LL
Y 8 82 i= p ::-e
I
1
ST
’
_ _ _ _ ~ _ _ _ _ _ _
2
(3 W
Rearranging
Calculation of Bubble Contact Area. T h e volume of a spherical bubble is: (34) The area of the bubbles in the annulus is : A = n(4rr2)tc 3Gt, I7
(35)
r =
(:n3”3 (36)
= ( 36GZnr)1,3t, (37) This area was corrected for nonsphericity of the bubbles (Figure 2). The final expression for the experimental absorption coefficient is : L i - Cr ( 3 8 ) K = In c -(36G2nr)’13ttof Ca - c o
A good correlation of the experimental oxygen absorption coefficients was obtained with:
(39) The constant nature of the factor 4 / 3 indicates that it might be attributed to uncertainties in the fluid flow pattern around the bubble or to some other constant discrepancy. Higbie (6) and Peaceman ( 7 7) required similar correction factors for the correlation of their experimental absorption coefficients
with the theoretical culated in accordance tion theory. Figures 3 A to D imentally determined tion coefficients and ficients as a function of the liquid in which suspended.
coefficients calwith the penetrashow the experoxygen absorptheoretical coefof the shear rate the bubbles were
Discussion This study indicates that a gas bubble under shear continually creates new interfacial area, just as a gas bubble moving through a liquid continually
creates new interfacial area a t its advancing tip (6). If a surface active material is present in the liquid, the concentration of surface active material a t the advancing tip of the bubble will be lower than a t the trailing end. This sets u p a surface pressure gradient, which reduces surface circulation. The increased back pressure of gas in the slower circulating surface film causes the observed increase in resistance to gas absorption. The surface active material itself is not believed to offer a significant resistance to gas absorption. Addition of 15 p.p.m. of pentaVOL. 52, NO. 9
SEPTEMBER 1960
801
Table II.
Oxygen Absorption Coefficients a t Quiet Water Surfaces at Room Temperature Absorptioii 0% Absorption Number Liquid Period, Coefficient X 104, L esse1 of Expts. Height, Cm. Hours Cm./Sec. Distilled Water 2 9.3 21 1.84 Bottle 4 55 21 2.09 Buret 1.99 4 55 72 Buret Distilled Water Containing Pentapropylbenzenesulfonate, 15 P.P.M. Bottle 2 9.0 21 1.82 Buret 4 55 21 2.09 Buret 4 55 72 1.84
Table 111.
=
= area
G = K = L = m = n = r t
= =
t, =
Over-all Gas Absorption Coefficients, K l a as Determined by Various lnvestig ators ICla,
Iiivebtigatora Holroyd and Parker ( 7 ) Wise ( 1 B ) Olson and Johnson (9) Maxon and Johnson (8) Cooper, Fernstrom, and Miller (2) Overton ( I O ) propylbenzenesulfonate to water decreased substantially the absorption of oxygen from bubbles by as much as 67% in viscous solutions under low shear (Figures 3 C and D). In still Tvater experiments, the absorption corfficients were not affected by pentapropylbenzenesulfonate (Table 11). For the case where the surface film has a collapse pressure greater than the surface drag on the bubble, a completely stagnant surface is possible. In that case, the absorption coefficent is not affected by the shear rate. This occurred when oxygen bubbles were suspended in water containing 15 p.p.m. of PPBS (Figure 3B). In viscous solutions the surface drag was sufficient to cause circulation to occur (Figure 3D). Agitation increases the over-all gas absorption cocfficients of liquids significantly. Table I11 shows the over-all gas absorption coefficients as determined by several investigators. Cooper, Fernstrom, and Miller (2) reported a 40-fold increase in the overall gas absorption coefficient with agitation. This study shows that fluid shear does not increase the actual gas absorption coefficient much. Hence, the large increase in the over-all gas absorption coefficient must have been caused by a reduction in tbe.-size of the bubbles. When the bubble size is reduced, the surface area of the bubbles is increased, first because the surface area per unit volume of gas is greater, and secondly because the smaller bubbles remain in the liquid for a longer time. The terminal velocities of small bubbles are approximately inversely proportional to their size (5). Agitation further reduces the terminal velocity by eliminating the chimney effect which causes the bubbles to rise faster in the wake of other bubbles. I n this study, the
802
F
f
Agitating Systeiii Bubble aeration Shake flask Shake flask Turbine 500 r.p.m. Turbine 750 r.p.m. Turbine 1,680 r.p.m. Vaned disks Turbine 2 , 7 0 0 r.p.m.
1/Hour
5 24 200 350 1,000 2,650 30-450 2,500
v
=
v, = u, =
41.6
Acknowledgment Gratitude is accorded to the late B.E. Proctor, Food Technology Department, M.I.T., for financial assistance in purchasing parts of the apparatus. Thanks are rendered to C. P. Penucci and J. J. Lennon, New England Tank and Tower Co.; to J. M. Gaines, Linde C o . ; and to F. L. Chase and A . W. Bourque, Dewey and ,41my Chemical Co. Nomenclature A = Area A , = effective surface area for shear based on one second’s operation. A , = (u,) (unitwidth) a = acceleration c = concentration of oxygen C, = concentration of oxygen a t the interface. assumed to be equal to the equilibrium concentration C1 = concentration of oxygen in the bulk of the liquid a t the end of the absorption experiment Co = concentration of oxygen in the bulk of the liquid at the start of the absorption experiment D = diffusion coefficient
INDUSTRIAL AND ENGINEERING CHEMISTRY
=
tib =
terminal velocity of the bubbles decreased with increasing shear rates, and was about half of normal at shear rates above 50 sec. If these factors are taken into consideration, it can be shown that a fourfold reduction in bubble size will increase the over-all gas absorption coefficient in agitated tanks about 40-fold. A breakdown of the factors folloivs : Increased absorption coefficient 1.3 Increased retention time due to elimination of chimney effect 2 Increased retention time due to reduction in bubble size 4 Increased surface area per unit volume of gas 4 Total increase in the over-all gas absorption coefficient is 1.3 X 2 X 2 x 4
t,
x
=
X
= = =
p
p g T
= =
force correction factor for norisphericity of the bubbles gas flow rate absorption coefficicnt liquid volume involved in the absorption experiment mass number of bubbles produced per second radius of bubble time of contact of liquid surface with gas time of acceleration of liquid in the film under the monolayer. I t is based on the time that it takes for the bulk stream to pass by the region of surface pressure gradient, tb = x / ( v b - v,) residence time of bubbles in the liquid velocity of liquid at a fixed point in space velocity of bulk of liquid velocity of monolayer velocity of surface with respect to the bulk of the liquid, u, = Ob - v,,, distance over which surface pressure gradient is effective depth below interface viscosity density surface tension 3.14
Literature Cited (1) Bush, A . W.,“Application of the Dropping Mercury Electrode to B.O.D. Determinations:” M.S. thesis, Massachusetts Institute of Technology, Cambridge, Mass., 1952. (2) Cooper, C. M., Fernstrom, G. A., Miller, S. A , , IND.ENC. CHEY.36, 504 (1944). (3) Garner, F. H., Skelland, A. H. P., Zbzd., 48, 51 (19563. (4) Haberman, W. L., Morton, R. K., “An ExDerimental Investigation of the Drag of’Air Bubbles Moving in Viscous Liquids,” Naby Taylor Basin, Rept. 802, 1953. (5) Hammerton, D., Garner, F. H., T r a n s . Inst. Chem. Engrs. (London) 32, 518 (1954). (6) Higbie, R., Trans. Am. Chem. En,g.rs. 31, 365 (1935). (7) Holroyd, A , , Parker, H. B., J . PIOG. Irist. Sewage PurzJications 3 , 292 ( I 949). (8) Maxon, W. D., Johnson, M. J., IND.ENG.CHEM.45, 2554 (1953). (9) Olson, B. H., Johnson, M. J., J . Bacteriol. 57, 235 (1942). (IO) Overton. W. 0.. A Studv of Rate Factors for Mechanical Agitated GasLiquid Contactors” Ph.D. thesis, Ohio State University, Columbus, Ohio, 1955. 1) Peaceman, D. W., “Liquid-Side Resistance in Gas Absorption With and Without Chemical Reaction,” Sc.D. thesis, Massachusetts Institute of Technology, Cambridge, Mass., 1951. 2) Miise, W. S., J . Gen. Microbiology 5 , 167 (1951). RECEIVED for review November 20, 1956 RESUBMITTED August 3, 1959 ACCEPTEDMay 17, 1960 Contribution No. 305, Department of Food Technology, M.I.T., based on the Sc.D. thesis of W. Tereshkevitch, Massachusetts Institute of Technology, Cambridge, Mass., 1956. Division of Agricultural and Food Chemistry, 130th Meeting, ACS, Atlantic City, N. J., September 1956.
