Mass transfer between two turbulent liquid phases

Chemical fingineering Science, 1976, Vol. 31, pp. 137-M.

PCIL!MIOII Press.

Printed in Great

Britain

MASS TRANSFER BETWEEN TWO TURBULENT LIQUID PHASES J. BULItKA

and J. PROCHtiKA

Institute of Chemical Process Fundamentals, Czechoslovak Academy of Sciences, 165 02 Prague bSuchdo1, Czechoslovakia (Received 13March 1975;accepted 4 September 1975) Abstract-The effect of forced turbulence on interfacial mass transfer between two liquid phases is investigated. A fheoretical model is derived on the assumption that the mass transfer. is controlled by unsteady diffusion into the vortices of the viscous subrange of the range of universal equilibrium. Mutual interaction of the turbulent fields in both phases is also accounted for. Experimental mass transfer rates for binary and ternary systems are presented; these were measured in a mixing cell of a new design. The model presented is shown to describe the process we& provided that fhe chosen liquid system is interfacially stable. The deviations due to interfacial instabilities are demonstrated for the case of the water-acetone-carbon tetrachloride system.

INTRODUCTION The mechanism of mass transfer across so-called free interfaces, i.e. boundaries between two fluid phases, is not fully understood. The problem becomes particularly complex if one or both of the phases are in turbulent

motion. An important property of the free interface is that it permits exchange of momentum between the fluids. The interface itself may also become a source of regular or chaotic motion in its close vicinity if mass and/or heat transfer gives rise to the Marangoni effect. The present work deals with mass transfer between two turbulent liquid phases under conditions where the phases may be regarded as semi-infinite. The original concepts of Higbie [ 11,Danckwerts [2] and Kishinevskii [3], describing mass transfer under these conditions, were later developed and generalized by a number of workers [4-131. Our approach is directly concerned with the theories relating the parameters of the above models [ l-31 to the structure of the turbulent flow near the interface. Commonly it is started from the assumption of Danckwerts, later experimentally confirmed[l4,15], that the turbulent disturbances penetrating from the bulk phase toward the interface cause its periodic renewal. Some of these models (e.g. Kolti[6]), assume in accordance with Higbie that the controlling step is unsteady molecular diffusion into the liquid elements forming the interface. In contrast, Levich[9] assumes steady molecular diffusion into a boundary layer, the thickness of which depends on the thickness, h, of the zone of deformed turbulence corresponding to the characteristic size of the vortices causing surface renewal. The basic prerequisite of Levi&s theory, as well as that of Davies[l3], is the decay of Gi within the zone of thickness A,while the fi: component is assumed to remain constant. The thickness of the zone is assessed from a balance of the inertial and surface tension forces, and also for a horizontal interface the gravity force. This relation has been tested experimentally by Davies and Driscoll[l3] by measuring the approach velocity of individual disturbances in a quiescent liquid toward the interface. Unfortunately, this technique does not reflect the effect of

instability of the turbulent medium surrounding the individual disturbance which may result in excessive damping due to the viscous forces. Further, photographs taken by the same authors[13], indicate that the vertical component of the disturbance is partly transformed, after deformation of the interface, into a horizontal one, indicating a possible increase of the latter above the value prevailing in the turbulent core. Davies’ model also incorporates an interaction of the turbulent fields in both phases, which becomes particularly significant for systems with two liquid phases. In the model due to KolG[6] it is assumed that the diffusional resistance is concentrated within the boundary layer of thickness So,proportional to the scale of turbulent disturbances, &,, from the Kolmogorov’s viscous subrange. Surface renewal within this boundary layer occurs at a frequency equal to &/lo, giving rise to an unsteady diffusion through a semi-infinite or finite layer depending on the magnitude of the Schmidt number. A general model encompassing the above theories as special cases has been formulated by King [ 111. The mass transfer rate between two turbulent liquid phases is usually measured in various modifications of the Lewis cell [ 15-231.To use this cell as a model for the study of turbulent mass transfer across a plane free liquid-liquid interface, one has to ensure that the core turbulence in both phases is sufficiently intensive for the turbulent disturbances to reach the interface. In view of the limited extent of the interface confined by the walls of the cell this is not achieved unless the core is highly turbulent as shown by Austin and Sawistowski[ 151.Increased turbulence of the core, however, is accompanied by a tendency to wave formation on the interface and an uncontrolled increase of its area. Theories of interfacial mass transfer under forced turbulence mostly assume that the physical properties of its phases near the interface are functions of composition only, and that neither adsorption nor instabilities of any kind exist at the interface. It is also assumed that no chemical reaction takes place, except in studies of diffusion accompanied by chemical reaction. Correct 137

J. BUJ..N%A and

138

appraisal of the data obtained with mixing cells should therefore necessarily include a check as to whether the liquid systems used meet these requirements. Transport of mass is nearly always accompanied by local density gradients, and it has been shown[21,24] that mass transfer between two ~rnob~e phases or iaminar Finns may be signiticantly affected by convection induced by such gradients. However, with forced turbulence reaching as far as the interface one can expect that this effect would be unimportant. Part of the results presented here is contained in the Thesis of one of the authors[22]. .

J.

PROCHAZKA

According to the assu~tion coefficients are related by k - Q(o/e)

(4), the mass transfer

= tl(o[~hf’~).

(2)

Using ~sumption (5) one can write (3) (4) And, finally, from assumption (3) one has

TEEORY

The mode1 starts from the concept of surface renewal by turbulent disturbances, and unsteady mass transfer into the elementary vortices by mofecular diffusion. The basic assumptions are as follows: (1) The surface is renewed by the whole spectrum of vortices present in the t~b~ent core of the phase, but the over-ah resistance to mass transfer is controlled by the vortices of characteristic dimension A0 and velocity g6, for which 6;. ho- Y. The thickness of the effusion boundarylayer is praportionai to Ao. (2) The vortices ofi the above dimensions obey KoImog~ov’s assump~n of local isotropic turbulence [25,26]. (3) The turbulence in the core of the phases is approximately homogeneous. (4) The rate of renewal of the boundary layer is propo~ion~ to the cheesy frequency S/ho. The mass transfer within the boundary layer takes place by unsteady diffusion into a semi-inGnite layer, with an initial c~~n~t~on equal to that wit~n the core of the given phase. (5) The boundary layers affect each other in such a way that the total energy d~ssip~on in both bang layers equals the sum of the dissipations which would occur in each layer separately if there were no mutual interference; the frequency of the renewal in both layers is the same. The first assumption is common with the models of Levich, Davies and Kolti. The assumption of local isotropy originates from an ideahsed concept of the free interface being an elastic membrane with no frictional resistance of its own to tangential velocity components. Owing to the presence of the other viscous phase the mobili~ of the interface is in fact hampered. The assumption (4) of equal renewal frequency in both boundary layers originates from the intuitive feeling that the dist~b~~es, the characteristic ~rnen~on of which equals the thickness of the corresponding layer, must affect both layers simultaneously in view of the perfect mobility of the interface. A similar assumption has been made also by Austin and Sawistowski[23] and Braginskii and Pavlushe~o[iO]. In this point the presented theory differs from the earlier Version[l2]. From assumptions (1) and (2) it follows for ho, gb and the time scale f?

On combining eqns (l), (3) and (4) one obtains

(6) and substituting into (2)

&, = .~. I

The quantity & represents the rate of surface renewaI as a function of energy dissipation in both phases and the physical properties of the phases. With the aid of eqn (5) the energy assertions may be subsume by the characteristics of the macroflow. Equation (7) may be rendered dimensionless as follows

The factor #, expresses the effect of the turbulence in the jth phase on the mass transfer in the ith phase and will be termed the interaction factor. In a particular case of a cell with the phases mixed inde~ndently by impellers and the top and the bottom compartments geometrically similar, i.e. where li = 1, = d, L - L, UI- ni, one has

Here x9 is the proportionality constant characterizing the ceil geometry. From 0, ,m accordance with (4), follows

Masstransferbetweentwo hubulentliquidphases

According to the proposed theory the ratio of the mass transfer coefficients is thus independent of the intensity of turbulence provided that the assumptions of the model are met. The latter concerns mainly the sufficient intensity of turbulence preventing formation of a lam&r layer at the interface. The value of this ratio is independent of the geometry of the system so that eqn (11) should hold over a wider range of conditions than e.g. relations (7) and (8). Equation (8) shows that for a given system and geometry, the interaction factor is a function of the ratio of macrovelocities only. If the latter is held constant the dependence of Shi on velocity is given by the appropriate power of Re. The same applies also to the dimensions of the system providing that the geometrical similarity is preserved. In an earlier version of this model[l2] the boundary condition used instead bf eqn (4) for momentum transfer across the interface stipulated equality of instantaneous local tangential stresses, i.e.

139

electromotors with electronic control of rpm, both pumping the liquid toward the interface. The impellers were surrounded by a stator equipped with 12 vertical batIles mounted on a horizontal plate, so that the tangential velocity components were canceled and the axial flow leaving the impeller was transformed to a radial one at the interface. The stator included a cylindrical grid with circular 3 mm openings to facilitate formation of a uniform turbulent flow structure; its perforations were omitted over the height of the impellers and over two 4 mm wide strips on each side of the interface. The interface had the form of an 18 mm wide annulus confined by the walls of the stator and the cell. Both the upper and lower parts of the cell were completely tilled with liquid and had almost identical geometry. The cell was submerged in water bath made of perspex glass.

Systems used The majority of experiments was carried out with the partially miscible binary liquid systems waterTi = rj (12) ethylacetate, water-n-butanol and water-isobutanol. Some measurements were performed with the ternary and waterTi - ElplAoilfibi. (13) systems water-succinic acid-n-butanol acetone-carbon tetrachloride. Physical properties of the It was shown that this assumption leads to the following chemicals used are shown in Table 1. All liquids were distilled twice before use and the apparatus flushed by expressions ether and the appropriate solvent. Water in solvent in the binary experimental runs was determined by the Karl-Fisher titration while the content of the organic solvents in the water phase was analyzed by refractometry. Acetone in both water and organic phases was analyzed by refractometry, since the mutual solubility of the solvents over the experimental concentSki - Sci’nRe,!“X,j; XI~ = ration range was too small to affect the analysis. Succinic acid was titrated in both phases by sodium hydroxide using phenolphtalein. In all systems used the behaviour of the interface during mass transfer under static conditions was observed -AL by the schlieren technique. For binary systems the The experiments in this work were carried out in a interface between a pendant drop and the continuous mixed cell with impellers in both phases. Thecell (Fig. 1) phase was observed and in no case was any sign of differs from the original Lewis cell and its later instability detected. In the ternary systems the response modifications, providing for a better stability of the of the interface to mass transfer was observed on one interface and hence permitting higher intensity of hand between the drop and the continuous phase, and on turbulence of the phases. The impellers, each with four the other hand between two quiescent liquids separated 4.5”inclined blades, were driven independently by two by a plane interface. The results of these observations, together with the condition of instability according to Stemling and Scriven[27], are shown in Table 2. 1

2_

Pi. 1. Final fom of the mixingceil. 1, Cylindricalglass wall; 2, inner stator rlag; 3, vertical batfles; 4, impeller; 5, 6, upper and lowerflange;7, cylindricalgrid;8, interface.

Experimental method The measurements were started by filling the cell tirst with the heavier phase and then with the lighter one after bringing the phases and the equipment to the same temperature. The initial interface level was chosen so as to remain within the non-perforated strip of the stator throughout the experiment. After turning on the impellers, both phases were regularly sampled by a syringe. The amount of samples drawn never exceeded 2% by mass of the appropriate phase. For the binary experiments, both phases were initially unsaturated while in the ternary experiments mutually saturated solvents were used.

140

J. BUI.I~ and J. ~PsocrrAzt~

Table 1. Physicalmopertiesof systemsused System

Tempe-

PiXiElO p x 103

px

10-3

D x 10'

rsturr OC Water-ethyl acetate

w+

6-x=103

bSS

(kg m-%-l)

(kg III-~)

(02.-l)

:;;:t-

(N/m)

"

1.00

1.00'

0

0.46

0.90

1.00 3.20

76.6 0.0309

6-S

*

0.80

0

0.40

1.00 0.69

1.29 3.81

72.70'" 0.0350

4*8

20

W 0

1.00 3.95

1.00 0.50

0.83 0.35

30

= 0

0.80 2.68

1.00 0.79

1.08 0.50

Water-n-butanol

a0

" 0

1.00 2.95

1.00 0.81

0.76 0.26

Suooinio aoid-water-n-butanol

eo

'I 0

1.50 3.?1

0.99 0.65

0.54 0.22

Acetone-water-Ccl*

a0

*

1.10

i.00

1.16

0

0.97

1.59

1.86

20

30

Water-isobutanol

,

for 2s"c

*=

conosntrationa in slgethyl aostats Per 1 ml of solution

Table2. Interfaciaistability of the ternary systems

I

System

:

Direction of ma88 transfer

i : ;

i a Axaoinic acidn-butanol-water

organic to rater

Behaviour of interface under mass transfer conditions Quiescent ’ Turbulent phase Phase ; Plane : Plane Drop ' InteffaOe ,I i. InterfaOe

Very weak IT", damped rapidly

Stable

Water to organia

Organic to water Acetone-C'Jl*-water

i :i :

Theory of ref.27

I i

convection cell Stable or oscillation

Stable

Water to organic

IT"

IT" Stable

IT"

Stable or oscillation

IT*

Convection cell

' IT - interfacial turbulence

The mass transfer coefficient for experiments with the binary systems was calculated using the least-square method from the relation ~glwi’-wiI=-kipiAtfGi+B

(17)

where B is an integration constant. Equilibrium concentrations of the saturated solvents, wf, for the binary systems used are summarized in Table 1. For the ternary systems the experimental concentration range was chosen so as to permit linear approximation of the equ~brium curve, given by w,=mw.+q.

(18)

The over-ah mass transfer coefficient based on the water phase is given by Ig(Ww-p~=-aKwt+B’ a= (Go + mG,)A~lG,G~~ p = ~,(mG,w,~fG,, + mwz + q)/(G, + mG,l:

(19)

Similarly, for the over-all coethcient based on the organic phase Ig\iv,-Al=-a’K.t+B” 1~’= (mG, + G~~Ap~lmG~G~ A = (G,w:+ G,w,O- Gwq)/(mGwf Go).

(20)

In the derivation of the relations (171,(19) and (20) the mass of each phase was assumed constant.

The experiments withbinary systems were designed to test individual terms of eqn’(9) as well as other published correlations. Binary systems of limited mutual solub~ity are particularly well suited for such investigations as they allow simultaneous evaluation of both mass transfer coefficients under otherwise identical conditions. Figure 2 is a plot of the k*lk, ratio as a function of n, for three values of the ratio of the impeller speeds for the water-isobutanol, water-ethylacetate and water-n-

141

Masstransferbetweentwohubulentliquid phases Ok0 lol

5_

20'C

water-n-Mono1

l

.

*o

3-

**.

0.0.~.

oooooQJooo

80

.k

60

W

0 30%

2-

n,/n,-1

0

water-isc-butanol 20%

10

..*..~*a*

0 l

oooooo*oooo

0 0

l.

20%

0

I 0

mute ettylocetote 20% 0

5

%@I

n,I~,l

i

I

I

5

10

Fig.3(b).

Fig. 2. Plot of k,/k, vs n,.

l k/

I

butanol systems. The data for the former two systems were taken at two different temperatures. The dependence of the mass transfer coefficient on the Reynolds number in the appropriate phase was also studied. In order to suppress the effect of the interaction factor the ratio of the impeller speeds was kept constant, as suggested by eqn (9). Figure 3 shows a plot of ki/n/” vs n, for each phase of the water-ethylacetate, water-nbutanol and water-isobutanol systems. Finally, the coefficients of proportionality Kgin eqn (9) were evaluated from the measured mass transfer coefficients and the physical properties of the systems used, as given in Table 3. Some of the values of K~ presented there are averages for three ratios of frequency of revolution of the impellers; for these values the maximum deviations from the mean are given. As is apparent from the schlieren results in Table 2, the ternary systems were chosen with the aim of having one

10

n&T

Yz20 *;10 3 6

.

/

![

0

l..*0..**

0 ko 20% n&b-l

Oooooo0oo

ti:-wtmd

,

5

lo n$l

Fig. 3(c).

Fig. 3. Plot of t/n:” vs n, for: (a) water-ethylacetate;(b) water-isobutanol;and(c) water-n-butanol systems. system interfacially stable in the whole investigated concentration range and the other displaying Marangoni instability. The water-succinic acid-n-butanol system should demonstrate the applicability of the binary data to the ternary systems as long as these are interfacially stable. The water-acetone-carbon tetrachloride system should exemplify the deviations induced by the Marangoni effect. According to eqns (19) and (20) the quantity ig 1w, - /31, or /g/w0 - AI should be a linear function of t provided the mass transfer coefficient remains constant. With the linear distribution the latter is given by K, = (Ilk,+m/ko)-'

20% n&.-l/Z 000

000

0

0

and as such is independent of concentration and concentration driving force as long as the system does not exhibit interfacial instability. Figure 4 shows the driving force vs time relations given in eqns (19) and (20) for the two ternary systems used. From eqns (9) and (21) it follows that for a ternary system with stable interface ZL/n:” = const.;

0

5

Fig. 3(a).

nJ8l

10

(n,/n, = const.).

(22)

The appropriate values of both ternary systems and both directions of mass transfer are given in Table 4 and plotted vs nl. in Fig. 5. For this purpose the values of K,

Table3. Pro~~io~~ TMP- ?tue nture

ab

caly~acetate

P

30

20

yaz.

$

yu.

dw.

3

zi

u&x. 2j

dsr.

bx.

der.

dev.

x l0'

x lC1

I

6.33 +%a6

5.90 -0.40

6.43 -0.53 6.10 a.30

5.40 +C.M 5.07 w.43

6.37 -0.47

0

a20 -0.60

4.17 -0.07 3.90 +C.l

2.33 W.07 2.83 -0.13 2.23 + 0.07 2.73 -0.13

.

6.0 3.93'.

6.0 5.8

5.2 5.1

5.90 7.7

3.60 3.60

2.30 2.x

2.1 2.1 6.5C -a33 6.03 -0.23

x lo1

5.97 -0.37

2.63 -0.23

3.37 -0.07

6.0

0

5.6C -0.30

3.13 a26

2.93 +O.n

3.73 -0.23

1.97 -0.07 1.80 0

1.40 0 1.30 C

0

5.7 5.1

2.9 3.1

3.4 2.8

5.8 3.4

2.0 1.8

1.40 l.jC

6.2 5.9

2.7 2.4

3.6 2.9

5.0 2.6

2.0

1.3 1.5

.

0

-0.4

1.9

0 water- succinicacid- n-tutanol l

uss.

dsr.

IlC'

30"

-aI-huiuml .>

aa

dar. x lCC

20.

9&C

:yu.

xl02

0 Ieeril0tUtYlOl

ai

dw.

% 9d‘sr-

k.

coefficientsof the rateequations

wa&r-acetone-c0rk1n

,

.

w&r-

7.3 6.3 6.2 6.0

Oirw&n 0

t*trachter~da

L 101

;f_CmOmfer o--w

sacink acid- Autanol

I

Fig.4(a)

0

imtrr-acetone-qdcn bbehloride

e water-sxcinic add-fduhnoi

Fig. 5. Plot of K,/n,‘” vs n, for water-succinicacid-n-butanol and water-acetone-toluenesystems.

Fig.4(b). Fig. 4. Transient development of mass transfer’ in ternary systems. Direction of mass transfer: (a) water to organic; @) organicto water. for the water-acetone-carbon tetrachloride system were calculated from the slopes of the linear sections of the curves in Fig. 4, i.e. in the regions where the M~go~ effect is no longer manifest. An average value of ~9 of 0@60 was used to evaluate the mass transfer coefficients in Table 4 from eqn (9). This.value was found from the results for the binary systems. DISCUSSION

”

Table 5 reviews some published relationships for mass transfer coefficients in liquid-liquid systems under forced turbulence. Apart from relation (B), all equations agree with the expeEimental linding of Fig. 12,that the ratio of the mass transfer coeW&s is independent of the speed of the impellers as well as of their ratio. Equations (11) and

(16) also possess this property. From the tabulated relations it is possible to evaluate the ratio of, the mass transfer ~fficients for the systems examined. The results, summarized in Table 6, indicate that the experimental values agree best with eqn (10, which follows also from (D), (E) and (F). Since relation (B) includes also the ratio of impeller speeds, the corresponding column in Table 6 indicates the range of k,/k,,. Another test of the a~eement of the proposed relations with the present data is the constancy of the group ki In/“, following from Fig. 3. From Table 5 it is seen that for a constant impeller speed ratio the value of the exponent on hi (or Re,) is 1.65,0*9, 1.0, 1.34, 1.0 and 1.5 for eqns (A), (B), (C), (D), (E) and (F) respectively. In this respect only the relations (9) and (15) of this work are in good agreement with the experiments. Relations (A), (B) and (D) were mostly obtained as correlations of Lewis’ data[l6]. The fact that the correlation of the same set of data yielded such widely different expressions, which exhibited approximately equal accuracy for the given set and distinctly different agreement when applied to another set of data, may possibly be explained by intensive turbulof the in Lewis’

143

Mass transfer between two turbulent liquid phases Table 4. Experimental results for water-succinic acid-n-butanol and water-acetone-ccl, .llun

NO.

Speed or *wo1ution (*-1)

%(exp.)

= lo5

$,(theor.) ' lo5

(m s-l)

systems

(%(,,&~,',k'~'~ lo6

(m *-l)

(. n-l/')

Succinic acid transferred from water to organic phase 1 a 3 4 5 6 7 6

3.23 3.84 4.41 4.65 5.39 5.95 6.03 6.46

9 10 11 12 13 14 15

'3.26 3.11 4.31 4.65 5.40 5.93 6.52

0.914 0.997 1.131 1.266 1.311 1.353 1.371 1.406

0.746 0.651 0.946 1.014 1.097 1.183 1.195 1.256

3.79 3.63 3.71 3.93 3.71 3.55 3.56 3.47

Succinic acid transferred from organic to water phase

Note:

0.665 1.030 1.104 1.136 1.326 1.365 1.469

0.756 0.664 0.934 1.021 1.105 1.187 1.216

3.65 3.61 3.69 3.46 3.74 3.64 3.60

In the concentration range used the equilibrium is expressed by L = 0.6126 x wn - 0.0077

Acetone transterrsd from water to organic phase 1 2 3 4 5 6 7 8 9 10 Note:

-3.50 4.60 6.11 6.76 7'. 76 9.40 10.80 11.01 11.30 11.55

2.36 3.63 5.15 6.65 6.03 6.96

1.05 1.29 1.61 1.73 1.92 2.21

0.93

6.22 9.45 11.40 11.58

2.46 2.49 2.54 2.56

1.38 1.56 1.66 1.85

1.28 1.32 1.35 1.29 1.30

In the concentration range used the equilibrium is expressed ww = 3.225x1, + 0.0056

by

Acetone transPer from organic to rater phase 1 a 3 4. 5 6 7 8 9 Note:

4.06 4.60 5.22 5.62 6.52 7.61 6.46 9.16 10.13

4.09 4.91 5.52 5.63 5.75 7.12 6.00 7.10 9.17

Vd.31.No.LD

1.39 1.56 1.60 1.55 1.41 1.54 1.61 1.46 1.61

In the concentration range used the equilibrium is expressed by "_ = 3.61J(no+ 0.0025

Equation (9) as well as eqns (A)-(F) listed in Table 5 contain an empirical proportionality constant K independent of the impeller speed and the liquid systems used. As seen from Table 3, these requirements are met appreciably better by eqn (9) than by the other relationships. The main purpose of the design of the mixed cell was to achieve intensive renewal of the interface and to preserve simultaneously its constant surface area. The intensity of turbulence achievedmay be assessed from the range of CES

1.09 1.19 1.31 1.43 1.55 1.75 1.66 2.00 2.15

the Reynolds numbers and the corresponding mass transfer coefficients shown in Table 7. The observations of Austin and Sawistowski[lS] regarding formation of a laminar sublayer at low intensity of turbulence are indirectly conhrmed by some of the results in Figs. 2 and 3. At sutkiently low stirrer speed in the more viscous organic phase, the water-n-butanol and water-isobutanol systems exhibit rapidly decreasing %. This is accomganied by a decrease of k, due to interaction, even though

Table 5. Relations for mass-transfer coefficients

Table 6. Values of k,Jk, for the systems used

system

Oc

Water-ethyl

acetate

Water-lsobutanal

Water-n-butanol

k_,'k,computed froa aqn

TeiBperature Exp.value

(II),(D),(E).(F)

(16)

(A)

(0)

(C)

20

0.60

0.56

0.38

0.54

0.52-0.59

0.76

30

0.59

0.58

0.41

0.51

0.57

0.76

20

1.64

1.54

3.06

1.95

1.33-1.52

1.01

30

1.54

I.47

2.79

1.82

1.35

0.98

20

1.62

1.73

2.97

1.64

1.46

1.03

Table 7. Ranges of Re, k and K used SysteEE

Temperature

Phase

Re x x0-3

20

w 0

2.2 - 16.6 4.4 - 30.6

1.37 - 6.92 2.20 - 11.10

30

iv 0

2.7 - 18.4 12.5 - 32.6

1.69 - 7.08 2.76 - 11.40

20

1 D

7.4 - 17.9 1.5 - 3.7

2.15 1.36 -

4.76 2.69

30

w 0

6.5 - 20.4 1.9 - 4.5

2.47 1.68 -

5.22 3.46

Water-n-butanol

20

II ll

6.6 - 10.3 1.6 - 4.5

1.77 1.03 -

5.12 2.60

Water-succinic acid-n-butanol

20

w 0

4.3 1.5 -

(m-l-1

*C

water-ethylacetate

Water-isobutanol

Wstst-acetane-cC14

20

k x to5

w 0

6.7 3.0

6.4 - 20.1 11.6 - 37.1

K, x IO5 (Ins-')

0.9 -

I.4

3.0 - 11.5

145

Mass transfer between two turbulent liquid phases

the value of Re, is approximately four times higher. The latter decrease, of course, is lower making the ratio kW/k, increase. Some experiments at high intensity of mixing display enhanced increase of mass transfer coefficients. This seeming increase can be ascribed to the increase of the interfacial area due to rippling. The results presented in Fig. 6 are in accord with the above reasoning. These were obtained in the two earlier forms of our cell[12] (see Figs. 7 and 8) where the tangential component of the macroflow had not been fully suppressed, causing excessive wave formation on the interface at higher intensities of mixing. As is apparent, the interface renewal region free of rippling has widened in the second modification of the cell for the waterethylacetate system. In case of the water-isobutanol system, however, this region was not reached even in the second modification of the cell. Only in the third modification, where we succeeded in increasing the range of stirrer speed by half of an order of magnitude, were we able to detect this region even for the latter system. It may be noted that the first modification of the cell is similar to that used by Austin and SawistowskWl. As may be seen from Fig. 5, the data for the ternary systems confirm the use of eqn (22) in accord with the results of the binary measurements. In case of the system water-succinic acid-n-butanol, good agreement was obtained between the calculated and measured values of K, (see Table 4). In contrast, the water-acetone-carbon tetrachloride exhibits considerable differences in these values. No satisfactory explanation has been found so far for this discrepancy, but this matter is being studied further.

Fig. 7. Arrangement of tist form of the cell. 1, Cylindrical glass wail; 2, outer stator ring; 3, inner stator ring; 4, impeller; 5, 6, upper and lower flange; 7, vertical battles.

CONCLUSIONS

(1) A mixing cell has been devised to investigate

experimentally mass transfer between two turbulent liquids at high turbulence intensities, to ensure intensive interfacial renewal. (2) The kinetics of mass transfer between two turbulent liquids has been described by a surface renewal model

oko 3 2 10 i

I

5 rii$_

+-1 3 1 2

water-ethylacetak II.

l-

..os0.3-

0%

Fig. 8. Armngement of second form of the cell. 1, Cylindrical glass wall; 3, inner stator ring; 4, impellers; $6, upper and lower flange; 8, cylindrical grids of wire mesh.

based on the assumption that the process is controlled by the vortices in the viscous subrange of the region of universal equilibrium. Phase interaction has been accounted for using a balance of the energy dissipated in the diffusional boundary layers and the condition of equality of the frequency of renewal of these layers. (3) The model proposed is in good agreement with the kinetic data obtained for partially miscible binary systems and a ternary system displaying no interfacial instability. In the case of an unstable system, we were able to detect a significant change of the rate constant with variation in driving force. (4) Turbulent transport within the diffusional boundary layer turns out to be strongly damped if the adjacent phase is insufficiently turbulent. If this is the case the dependence k,(Ref”) does not apply.

QQi@

0

water-isobutanolII.

Fig. 6. Plot of /&I,“~ vs n, in two earlier forms of the cell.

NOTATION

A B,B’ d D G

area of interface (L’) integration constants in eqns (17) and (19) diameter of impeller (L) diffusion coefficient (L*T-‘) mass of phase (M)

J. BULICKA and J. PROCHAZKA

146 k mass transfer coethcient {LT-‘)

K t m, q n

overall-mass transfer coefficient (IX’-‘) ch~a~te~stic ~mension of systems (L) constants of equilibrium relation (18) speed of revoiution of impeller (‘I-‘)

i, f time(T) II velocity of macroflow (LT-‘)

8’ mean square tluctuation velocity (LT-‘) w mass ratio composition W+ equ~bri~~m value of mass ratio Re = nd’lv Reynolds number SC = v/D Schmidt number Sh = kdlD Sherwood number a defined by eqn (19) (L-l) /? defined by eqn (19) SO thickness of boundary layer (L) d defined by eqn (20) c rate of energy dissipation per unit mass of liquid (15’Te3) 6 time scale of turbulence (T) K COnStaId in eqns (9), (A)-(F) A thickness of zone of deformed turbulence (L) AC scale of ~buience in the viscous subrange (L) p dynamic viscosity (ML-IT-‘) u kinematic viscosity (LT’) p density (MLm3) S interfacial tension (MT2) r tangential stress (ML-‘T-‘) cptx defined by eqns (14) and (IS) 4 rate of surface renewal (T-‘) JI inter~tion factor Subscripts b i j o 0

bulk phase phase i phase j organic phase ch~acte~stics of turbulence of viscous subrange

w water phase x direction parallel to interface y duration ~~~c~~ to interface Supersc~pf~ 0 initial value’

~~ [I] HigbieR., Trans. Am Inst. Chem. Engrs. 193531 65.

[2] Danckwerts P. V., hd. Engng C/mm. 195143 1460. 131~~n~s~ M. Kh. and Pamfilcv A. V., Zk. B&-L Kkim., Moscow 194922 1173. [4] Toor L. H. and Marchello J. M., A.1.Ck.E. J. 19584 97. [S] Kolsl: V., Co& Czech Ckem. Commun, 195924 3811. 161Kolsf V., Coil. Czech. Ckem. Commun. 1%1 26 335. 171Perltbutter D. D., Ckem. Engnn Sci. 196116 287. (4 Hariiot P., &tern. Engng Sci i%2 17 149. 191Levich V. G.‘.Phvsicockemical Hvdrodvnamics.DU.689-697. Prentice-Hall, New York 1%2. * * ’ a_ [lo] Braginskii L. N. and Pavlushenko I. S., ZhdPrifd. Khim., Moscow 1%5 38 1290. [ll] Kii C. J., Ind. Engng Ckem. Fundl. 1%5 5 1. [12] Pro&&b J. and BuliEkaJ., International SOlventExtractioh Conference, The Hague, Paper 27, 1971. 1131Davies J. T., Turbulence Pke~me~, pp. 175-187 and 225-229.Academic Press, New York and London, 1972. [14] Davies J. T. and Kohn W., Chem. Engng Sci. 1%5 20 713. 1151Austin L. J. and Sawistowski H., I. Cftem. E. Symp. Ser. No. 26, 1%7. f16] Lewis J. B., Chem. Engng Sci. 19543 248. 1171McManamey W. J., Chem. Engng Sci. 196115 241: [ 181Davies J. T. and Mayers G. R. A., Ckem. &ngngSci. 1%1 16 55. [19] Mayers G. R. A., #tern. Engng Sci. 1961 16 69. 1201Olander D. R. and Reddv L. B.. Ckem. EnnnnSci. 19641967. i21j Sawistowski H. and A&tin L: J., Ckem-Iig. Tech. 1%7 39 224. [22] BuliEkaJ., Ph.D. Thesis, Inst. of Chemical Process Fundamentals, Prague 1972. [23] McManamey W. J., Davies J. T., Woolen J. M. and Coe J. R., Chem. Elrgng Sci. 197328, 1061. 1241 _ Maroudas N. G. and Sa~stows~ H.. Ckem. Engng II Sci. 1964 Lo919. [25] Kolmogdrov A. N., DAN SSSR 194130 301. 1261Kolmogerov A. N.,‘DAN SSSR 194132 16. [27] Stemling C. V. and Striven L. E., A.LCk.E. J. 19595 514.