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THE CONTINUOUS PHASE HEAT AND MASS TRANSFER PROPERTIES OF DISPERSIONS P. H. C A L D E R B A N K a n d M. B. M O O - Y O U N G Department of Chemical Technology, University of Edinburgh, Scotland

(Received 2 September 1960; in revised form 22 December 1960) Abstract--Techniques have been developed for measuring the interfacial area in gas-liquid dispersions. It has thus been possible to measure the liquid-phase mass transfer coefficients in gas-liquid dispersions such as are produced in aerated mixing vessels, and sieve and sintered plate columns. The results have been combined with other published data for heat and mass transfer in liquid-liquid and solid-gas dispersions in which the dispersed phases are free to move under the action of gravity, and also with data on transfer by free convection from spheres. These data can all be correlated by ~ 9 y/ / 3 " kL(Nsc)2/3 = ~ hc (Npr)2/3 = 0.31 \( ~ 2Pc

(1)

For large gas bubbles which do not behave like rigid spheres as the smaller ones do

kL(Nsc)l/2 = 0.42 (AP~2~°')x/3" \

Pc /

(2)

If the particles of the dispersed phase are not free to move under gravity and transfer is due to turbulence in the surrounding fluid,

kL(Nsc)2/3 = ~ hc (Npr)2/3 = 0 . 1 3k[ ~ ]Pc -[~/'t

(3)

where P/v is the power dissipation per unit volume. This correlation applies to heat and mass transfer in mixing vessels where the solid phase is in the form of a single fixed submerged body and also predicts the small increase in mass transfer coefficients as the power dissipation level is increased beyond that needed for just completely suspending dispersed solid particles in mixing vessels. The correlation also applies to heat and mass transfer in turbulent fluids flowing through fixed beds of particles and through pipes. R~sume--Des m6thodes ont 6t6 d6velopp6es pour mesurer la surface d'6change dans les dispersions gaz-liquide. C'est ainsi qu'il a 6t6 possible de mesurer les coefficients de transfert de masse en phase liquide dans des dispersions gaz-liquide telles que celles qu6 ron rencontre dans des m61angeurs/l air et dans des colonnes ~ grilles, et~ plateaux fritt6s. Les r6sultats ont 6t6 compar6s avec d'autres donn6es publi6es pour les transferts de masse et de chaleur dans les dispersions liquide-liquide et solide-gaz o/l les phases dispers6es sont iibres de se d6placer sous l'action de la pesanteur et 6galement avec les donn6es sur le transfert par convection libre de sph6res. Ces donn6es peuvent routes 6tre mises sous la forme:

hc kL(Nsc)2/3=~p~c(Spr)2/3=O'31(~N}l/3"\Pc f

(1)

Pour de grosses bulles gazeuses qui ne se comportent pas comme des sph6res rigides contrairement aux petites bulles, on a:

kL(Nsc)1/2 =

0,42 (AP~2~gy/3" \ Pc /

(2)

Si les particules de se la phase dispers6e ne sont pas libres de se d6placer sous I'action de la pesanteur et si le transfert est dfi fi la turbulence dans le fluide environnant, on a:

kL(Nsc)2/3 = ~ hc

(Np')2/3 =

0' 13[(P/v) q L--~FJ

(3)

on Ply est la puissance dissip6e par unit6 de volume. Cette relation s'applique au transfert de chaleur et de masse dans les m61angeurs oh la phase solide se pr6sente sous forme d'un corps unique fixe et submerg6, et pr6voit aussi le petit accroissement des coefficients de transfert de masse quand la quantit6 d'6nergie dissip6e est augment6e au-del~ de ce qui est n6cessaire pour disperser compl6tement les particules solides dans ies m61angeurs. La relation s'applique aussi aux transferts de chaleur et de masse dans les fluides turbulents s'6coulant ~ travers les lits fixes et ~ travers les tubes.

Reprinted from Chem. Engng Sci. 16, 39-54, 1961. 3921

P. H. CALDERBANKand M. B. Moo-YOUNG

3922

Zusammenfassung--Eswurden Verfahren entwickelt zur Messung yon Phasengrenzfl~ichenin Gas-Fliissigkeits-Dispersionen. Hierdurch war es mfglieh, die Stofftransportkoeffizienten fiir die fliissige Phase bei Gas-Fliissigkeits-Dispersionenzu messen, wie sic in begasten Riihrkesseln sowie in Kolonnen mit Siebund Sinterplatten vorkommen. Die Ergebnisse wurden kombiniert mit anderen verfffentlichten Daten fiber den W~irme-undStoffaustausch in Fliissig-Fl(issig-und Gas-Feststoff-Dispersionen,bei denen die verteilten Phasen sich frei unter dem Einfluss der Schwerkraft bewegen, und solchen Daten, bei denen der Transport durch freie Konvektion von Kugeln erfolgt. Alle Daten k6nnen wie folgt korreliert werden: hc

A

"

"

t/3

Fiir grosse Blasen, die sich nicht wie kleine starre Kugeln verhalten:

kL(Ns~)U2= 0 '42(\ AP'02#~" 9"~ ,] .

(2)

Wenn die Partikel der verteilten Phase sich nicht frei unter dem Einfluss der Schwerkraft bewegen und der Stofftransport yon der Turbulenz des umgebenden Fluidums abh/ingt, gilt:

hc ,~.r ~2/3__

kL(Nsc)2/3 = re'pc

t"Vr,

-

0

,

13F(P/v)'#cl

L

p~

/

TM

(3)

wobei Ply der Kraftverbrauch pro Volumeneinheit ist. Diese Korrelation kann angewandt werden auf den W~irme-und Stofftransport in Riihrkesseln, in denen die feste Phase in Form eines einzelnen festen K6rpers vorliegt, und fiir die Voraussage des leichten Ansteigens der Stofftransportkoeffizienten beim Ansteigen des Kraftverbrauchs bis unterhalb des Wertes, der ben~tigt wird, um die Feststoffteilchen in v611igerSuspension zu halten. Die Korrelation kann auch beim W~irme- und Stofftransport turbulenter Medien in Schiittschichten und Rohren.

INTRODUCTION

TO PREVIOUS

WORK

The present work was undertaken in order to evaluate separately the mass transfer coefficients and interfacial areas in gas-liquid dispersions such as obtained in fermentation vessels and distillation plate columns. Hitherto it has not been possible to arrive at these values because of a lack of means of measuring interfacial areas. The present authors have described a light transmission method for measuring interracial areas in not too optically dense dispersions [1] and also a lightreflection technique for dense dispersions of optically transparent phases [2]. In addition, a y-ray transmission method was described for measuring the gas hold-up in these systems 1"2"1,from which the Sauter mean bubble size could be deduced. The latter value was checked in many cases by a statistical analysis of high-speed flash photographs. Details of the photographic techniques and statistical analysis will be described in a subsequent publication. Experiments were performed in which sparingly soluble volatile or gaseous solutes were desorbed from or dissolved in liquid solvents, the gaseous phase being dispersed in the liquid as a bubble cloud. The rate of material transfer and the interfacial area were simultaneously observed, the experimental equipment being such as to ensure that the liquid phase was perfectly mixed. In this way values of the liquid-phase mass transfer coefficients were determined in aerated mixing vessels and sintered and sieve plate columns, as has been previously described [2, 3]. This work covered a wide range of bubble sizes and liquid-phase diffusion coefficients, extreme variations in the latter being achieved by the use of aqueous glycol and glycerol solutions, and smaller variations by the use of various solutes. Diffusion coefficients of

carbon dioxide in aqueous glycol and glycerol were measured by the liquid jet technique [3"1, and these results have now been confirmed using the Stokes diffusion cell. The above work showed that the value of the liquid-phase diffusion coefficient was the major factor which influenced the value of the mass transfer coefficient. The independent effect of liquid-phase viscosity was not, however, revealed. It was clear that agitation intensity, bubble size and bubble free rising velocity had no effect on the mass transfer coefficient, but that large bubbles ( > 2.5 mm diameter) gave greater mass transfer coefficients than small bubbles ( < 2.5mm diameter) whose mass transfer coefficients correlated well with those observed for solid-liquid dispersions. It was concluded that small "rigid-sphere" bubbles experienced friction drag causing hindered flow in the boundary layer sense, and that under these circumstances the mass transfer coefficient was proportional to the z3power of the diffusion coefficient, as found by Froessling [4] and others. For large bubbles ( > 2.5 mm diameter) form drag predominated and the conditions of unhindered flow envisaged by Higbie 15] obtained, and as postulated by Higbie the mass transfer coefficient was proportional to the 22power of the diffusion coefficient. It is important to appreciate that the Froessling and Higbie equations have never hitherto been tested with systems of gas bubbles for extreme variations of diffusion coefficients and liquid viscosities. Although the authors' results supported these equations as regards the effect of the diffusion coefficient on the mass transfer coefficient, they also showed that the effects of bubble size and slip velocity were such as to be mutually compensating, so that these variables were replaceable by physical property parameters.

The continuous phase heat and mass transfer properties of dispersions PRESENT WORK In the present work the previous mass transfer data for bubble swarms have been extended, firstly by the use of an aqueous thickening agent (Polyacrylamide) which enabled the viscosity to be independently and largely increased without affecting the diffusion coefficient. Solutions having viscosities up to 87 cP were used and found to be Newtonian in rheological behaviour, and to have the same diffusion coefficient for carbon dioxide as pure water (determined with the Stokes diffusion cell). The data have also been extended to include the high diffusion coefficients obtained using hydrogen as solute. This has been achieved by measuring the rates of catalytic hydrogenation reactions in various solvents containing an excess of catalyst and through which hydrogen bubble swarms were passed. The excess of catalyst ensured that the chemical reaction rate was fast and not rate determining, and the progress of the reaction was determined by the rate of solution of hydrogen, and followed by the infra-red absorption characteristics of the product of reaction. Finally, published data on continuous-phase heat and mass transfer to dispersions of solids and to single bubbles and drops have been combined with the present work to achieve a more comprehensive and convincing correlation. RESULTS

Figure 1 shows two correlations for liquid-phase mass transfer coefficients for bubble swarms passing

3923

through liquids in sieve and sintered plate columns and in aerated mixing vessels. The upper correlation line refers to bubble swarms of average bubble diameter greater than about 2.5 mm such as are produced when pure liquids are aerated in mixing vessels and sieve plate columns, and leads to the result:

Nsh = 0.42 N1/2N1/3 s~ o,

(2)

kL(Ns=)'/== 0 .42(AP~eg~ \---~ j 1/3 .

(2)

or

The lower correlation line refers to bubble swarms of average bubble diameter less than about 2.5 mm such as are produced when aqueous solutions of hydrophilic solutes are aerated in mixing vessels, or when liquids generally are aerated with sintered plates or plates containing very small perforations. This leads to the result that

hc ( Ap#~g'~I/3 (1) kL(Nsc)Z/3 = Cep~(Ne')2/3 = 0.31 \ p~ ,) . It will be seen that both correlations show that the liquid-phase mass transfer coefficients are independent of bubble size and slip velocity and depend only on the physical properties of the system. In mixing vessels the mass transfer co¢fficients are independent of the power dissipated by the agitator, and in sieveplate columns they are independent of the fluid flow rates.

i.o

,$f

_~

IO-'

Unh;ndered ;nrerfoCiQI

~'~

flow and oscillofion ~

~ /

ee/

,o-, W

IO"

IO'S

........

I

I0"4

........

I

I0") -!

........

I

I0"z

. . . . . . . .

I

I0-I

. . . . . .

.1

I'O

,

-!

NS¢ or Np, Fig. I. Corre]ation of heat and mass transfer coefficientsfor dispersions of small bubbles and rigid spheres (lower line) and large bubbles (upper line). See "Source of data" and "Range of variables'.

3924

P.H. CALDERBANKand M. B. Moo-YOUNG

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