Znd. Eng. Chem. Res. 1992,31, 1739-1744
1739
Terminal Velocity Studies of Whole Broth Single Drops in a Liquid-Liquid System Laurence R. Weatherley* and Caroline Turmel Department of Chemical and Process Engineering, Heriot Watt University, Riccarton, Edinburgh EH14 4AS, United Kingdom
Terminal velocity data for discrete drops of mycelial culture broth, filtered mycelial culture broth (based upon Penicillium chrysogenum), and water descending through a continuum of tri-n-butyl phosphate as a 30% (v/v) solution in heavy distillate are reported as a function of drop size. The application of high-speed video techniques to the study of drop motion in liquid-liquid systems is described. The terminal velocity data are compared with existing correlations which were developed using pure liquids and using liquids contaminated with trace impurities. The experimental data are also compared with terminal velocity predictions for rigid spheres. Each set of comparisons indicate that the presence of surface-active impurities and the structured nature of drops of untreated fermentation broths are major influences in determining the terminal velocity behavior.
Introduction The present work is concerned with studying the terminal velocity behavior of drops of untreated fermentation broths in contact with an immiscible solvent phase. In addition to providing a valuable insight into the likely effeda of the presence of mycelia and other fermentation debris and surface-active contaminants upon the hydrodynamic behavior in continuous contactors, the possible role of these materials in interfacial mass transfer in whole broth systems was considered. There is significant qualitative evidence that liquidliquid extraction behavior can be significantly modified in the presence of fermentation solutions containing solid material such as lysed cells and mycelia. For example, substantial reductions in the rate of mass transfer have been reported in yeast-based systems and in systems involving mycelial culture broths (see Crabbe (1983) and Laughland et al. (1987)). The mechanistic reasons for the observed reductions in mass transf2r are not well understood; indeed several possible stages in the interfacial mass-transfer process could be rate-controlling. The two possible major factors involved are the presence of solid material and the presence of soluble surface-active agents. The accumulation of insoluble solids at the liquid-liquid interface could effectively reduce the area of contact, as postulated by Crabbe (1983). A further possibility is the stabilization of drop hydrodynamics at the interface thus reducing the beneficial effects of Marangoni instabilities (see Skelland and Caenpeel (1972)). The effect of the presence of solids upon internal drop circulation is also relevant particularly when the presence of mycelia increases the effective viscosity of the drop phase. The presence of solids within drops is also likely to influence the distortion characteristics of the drop and thus the oscillation rate with obvious implications for terminal velocity. The influence of soluble surfactants upon interfacial mass transfer and drop hydrodynamics in liquid-liquid systems is well known (see Kindland and Terjesen (1956) and Skelland et al. (1987)). Thorsen et al. (1968) also proposed that the presence of surfactants in liquid-liquid systems reduces interfacial instabilities and momentum transfer across the interface, consequently reducing internal circulation and terminal velocity. The reduction of wave formation at the interface in the presence of surface-active agents is a further possibility put forward by
Skelland and Caenpeel(1972)and would influence mass transfer on both sides of the interface. The scope of the present work was to examine the relationship between drop size, system physical properties, and terminal velocity for single drops of a mycelial fermentation broth falling by gravity through a large continuum of organic phase. The behavior of drops of untreated liquor was compared with that of drops of liquor from which the mycelia were removed by filtration and with that of drops of pure water.
Theory and Review Garner and Skelland (1955) proposed that the unhindered motion of fluid drops dispersing from a nozzle in the nonjetting region into a second immiscible fluid differed from the free-fall motion of solid spheres in three respects: (i) Frictional drag of the surrounding fluid may induce circulation of the interface and the interior of the drop. (ii) Gravitational forces acting on the drop may cause its shape to depart from exact sphericity and assume a degree of oblateness. (iii) Prolate-oblate type oscillations may occur during the motion of the drop. It is generally accepted that modeling of single drop motion in a second immiscible liquid medium can conveniently use the motion of rigid spheres as a reference point for determining the deviation of terminal velocity behavior of nonrigid drops due to the above effects. Hu and Kintner (1955) found no difference between the behavior of a liquid drop and a rigid sphere at drop Reynolds numbers less than 300, where the drop Reynolds number is defined thus:
Re = PcuTD/k (1) Their experimental studies confirmed a linear relationship between drag coefficient and Reynolds number in this regime. Further studies of the relationship between terminal velocity and drop diameter showed the classical maximum value of terminal velocity above which drop oscillation increasingly hinders the motion of the drop. The peak terminal velocity in terms of the system physical properties was expressed thus: (uT)p
= 1.23[~/~c]~'238
where
* To whom correspondence should be addressed. 0888-5885/92/2631-1739$03.00/00 1992 American Chemical Society
(2)
1740 Ind. Eng. Chem. Res., Vol. 31, No. 7, 1992
The criterion for the onset of drop oscillation which results in the sharp increases in drag coefficient reported was expressed in terms of the Weber number, We, where We = DpcuT2/u (4) Drop oscillation becomes significant when We > 3.58. Hu and Kintner also presented a general correlation for prediction of terminal velocity in terms of system physical properties and drop diameter alone. The correlation is in two parts; thus (9 Y = 1.333X1.275 for 2 < Y < 70 (5) (ii) where
Y = 0.045x.37
for Y > 70
Y = Cd(We)po.15;X = ( R e / P . 1 5 )+ 0.75
(6) (7)
and
The error limits for Hu and Kintner’s correlations are stated at 10%. The correlation was later examined by Thorsen et al. (1968), who demonstrated the major effect of small concentrations of impurities upon the terminal velocity behavior. They concluded that the Hu and Kintner correlation was not generally accurate for high-purity systems. Significantly, it was shown to be much more accurate for the prediction of terminal velocity in systems deliberately dosed with surface-active agent. Later work by Skelland, Woo, and Ramsay (1987) confirmed the importance of surface-active agents shown in Thorsen’s work. It was also shown that the type of surfactant has a relatively unimportant effect upon terminal velocity behavior. Bond and Newton (1928) modeled terminal velocity in viscous fluids by considering rectilinear motion of rigid spheres through a viscous continuous phase; thus
where
k=
0.6667 + &/pc
(10) 1 + pd/C(c Thus if pd >> pc the drop will behave a8 a rigid sphere. Garner and Skelland (1951,1955) considered the effects of internal drop circulation and showed that the Reynolds number above which the transition from noncirculatory to circulatory flow within the drop occurs is highly dependent upon the drop-phase viscosity. They also identified the effect of interfacial tension of the system upon this transition and showed that reduction in interfacial tension is accompanied by reduction in the drop Reynolds number at which circulation becomes significant. Klee and Treybal(l956) also divided the velocity-size relationship into two regions and proposed the following: (i) For region I where velocity increases with drop diameter Re = 22a2C d-6.18We+.169 (11) (ii) For region I1 where velocity remains substantially constant with respect to diameter Re = 0 . ~ 4 1 8 c d 2 ~ 9 1 (12) In dimensionless form the terminal velocity values were expressed for each regime respectively:
= 38.3pc-0.45L\pO~58pc~~1100.7 17.6pc-0.55Ap0.28p O.0lqO.18 uT(II) C +(I)
(13)
(14) The average deviation for terminal velocity prediction is quoted at 4.5%. Skelland et al. (1987) studied the validity of the Klee and Treybal correlation for drop terminal velocity prediction in the presence of surface-active agents and concluded that it was roughly accurate providing the appropriate values of interfacial tension, determined in the presence of surfactant, were used. It is also signifcant that the correlation was based upon experimental measurements using drops of technical grade reagents, Le., in the presence of impurities. Thorsen et al. (1968) studied drop motion in high-purity liquid-liquid systems at high interfacial tension and successfully correlated velocity-size data for spherical circulating drops using the correlation of Winnikow and Chao (1966) thus:
The derivation of this expression is based on the assumption of complete internal circulation in the drop. For oscillating drops Thorsen correlated terminal velocity thus:
This correlation was accurate for ultrapure liquid-liquid systems. Grace et al. (1976) conducted a wide-ranging study of both gas bubble and liquid drop motion in liquids and cross correlated terminal velocity data for many systems, involving a wide range of physical property values, to produce a general graphical correlation of drop Reynolds number and Eotvos number, where Eotvos number is defined as
Eo = gp?Ap/u (17) Grace et al. also considered the modified terminal velocity behavior exhibited by very pure liquid-liquid systems and proposed a semiempirical correlation to describe the modified terminal velocity Up,, in terms of the value U obtained from their correlation for nonpure systems, an experimentally determined parameter r, and the viscosity ratio K .
Experimental Section System. The overall aim of the experiments was to develop an accurate determination of the terminal velocities of single drops across a defined size range and to establish a comparison between experimental values of terminal velocity with those anticipated according to established correlations. In order to effectively use the correlations described above, a program of accurate physical property determinations with respect to phase densities, viscosities, and interfacial tensions was conducted. The methods used for physical property determinations are described in detail by Caprani and Weatherley (1989). The viscosity values were determined using a paddle viscometer (Rheomat 1500 Contraves) calibrated at a range of rotational speeds. Rheometric data for Penicillium
Ind. Eng. Chem. Res., Vol. 31, No. 7,1992 1741 "0.
Table I. Physical Properties of the Liquids at 20 OC interfacial density density, tension, diff, N m-l kg m-s solution kg m-3 viscosity, N s m-2 distilled 996 0.00098 (kO.ooOo5) 0.0103 157 water filtered 997 0.0012 (*O.ooOOS) 0.0119 158 broth whole broth 1002 0.0062 (*0.0005) 0.0163 163 solvent 839 0.00181 (*O.oOoaS) Table 11. Nozzle Dimensions nozzle external diam, mm 1 3.18 2 2.12 3 2.06 4 1.62 5 1.42 6 1.62 7 1.00 8 1.27
15m _I I I
I I
I
I
I I I
I I I I
internal diam, mm 2.35 1.83 1.60 1.22 1.00 0.81 0.65 0.56
chrysogenum broths by Bongenaar et al. (1973) suggest either Bingham plastic behavior or Casson behavior. Surprisingly, in the case of the broth used in the present study it was possible to obtain a value of viscosity of the untreated broth which was constant within the limits of N s m-2);see Table I. experimental scatter (h0.5 X The liquid-liquid systems studied comprised a continuous phase of a 30% (v/v) solution of tri-n-butyl phosphate in heavy distillate (BDH) made from laboratory grade materials. The drop phase comprised a filamentous mycelial culture broth derived from the fermentation of corn steep liquor in the presence of Penicillium chrysogenum according to the method described earlier by Caprani and Weatherley (1989). The average solids mncentration of the untreated broth was 2.3 w t % on a dry basis. For direct comparison, dropphase solutions comprising filtered broth solutions deriving from the same batch of whole broth liquor were also used in a parallel series of experiments. A further set of experiments was conducted using drops of distilled water. In all cases the phases were preequilibrated prior to the experiments in order to ensure the absence of mass transfer. Equipment. The experiments were conducted with the organic solvent as the continuous phase which was contained in a rectangular PVC tank, (see Figure l), 0.3 m X 0.3 m X 1.0 m. Theae dimensions were chosen on the basis of criteria described by Schiffler (1965) to avoid significant wall effects. During the course of each experiment the continuous organic phase was kept stationary, and the dispersing drop phase was introduced using a 50-mL syringe pump (Perfuser VI), pumping into a single hypodermic stainless steel nozzle located at the upper end of the tank. The nozzle dimensions were also varied in order to study a range of drop sizes. The range of nozzle dimensions used is shown in Table II. This pumping system gave a steady flow of discrete drops into the continuous phase. A system of rear illumination was employed adjacent to the tank which enabled precision filming of drop motion using a high-speed video system (NAC High Speed Video System HSV-400) equipped with a 105-mm lens (MicroNikkor). Real time was recorded by the video system during each experiment, and this enabled time to be read from the on-screen display to within an accuracy of 5 ms. Velocities were calculated from the distance-time rela-
+'Ti II
I
I
I
Drain
I
Figure 1. Apparatus for measuring droplet L-,e and velocity.
tionship monitored for each drop during ita passage between two fiducial marks located accurately on the side of the tank. The rate of fall was determined at different distances from the point of discharge to ensure that the velocity measured was indeed the terminal value. Drop diameters were measured from a sequence of still photographs which were taken simultaneouslyduring each experiment using a single lens reflex camera (Pentax P r o g r a m A) fitted with a macrofocusing teleconvertor (Vivitar 2X) and 50-mm lens. Comparison of the drop dimensions with that of the nozzle which was recorded in each photograph yielded the appropriate dimensions for calculation of the diameter of the drops. The drops were ellipsoidal in shape and were photographed at approximately 5 times their actual size.
Results The maximum horizontal and vertical dimensions of each drop were measured from the photographs and the diameter, D, calculated after the method of Lewis et al. (1951) according to eq 19; thus
D = (D12D2)1/3
(19)
The physical property data for the liquid phases are shown in Table I and include the experimental values of density, viscosity, and interfacial tension. The experimentaldropsize/terminalvelocity data which were measured were compared with the predictions of the correlations of Hu and Kintner, (see eqs 5-8), of Klee and Treybal (see eqs 13 and 14), and of Winnikow and Chao (see eqs 15 and 16). Comparisons with the predictions of Hu and Kintner were conveniently expressed using the correlation parameters defined in eqs 7 and 8. Thus the groups Y and X
1742 Ind. Eng. Chem. Res., Vol. 31, No. 7, 1992 2 0
r----
DRRG COEFFICIENT
7 1 / I
-- I
REYNOLOS NUMBER DRTR
UNTREATED BROTH SYSTEM
T E R n l W VELWITYUNTRERTEO WDTH SVSTEM
-i B C
1.2
i,e
1
,/
HU &
'
Kcntner model
1
5
/'
6
I
I
.7
,E
I
I
1
9
1.0
1
1 1
1
1,3
1.2
I
1
1,4
I
3.5
3.0
5
I
4.0
b.5
0
s u t e r R4.m D r o p S L Z e ( m 1
lOp(RdP"')
Figure 5.
Figure 2.
n
2 0 r DRRG COEFFICIENT
-
REYNOLOS NO
TERMINW VELCCITY
DRTR
-
FILTERED BROTH SYSTEM
FDR FILTERED BROTH SYSTEM
t
I
3.5
03.0
Swtw
nmm 4Drop .0
Slzm(mm)
5.8 8
4.5
Figure 6.
Figure 3.
20
-
O R ~ GCOEFFICIENT
REYNOLOS NO
TERMINM VELOCITY
min
OF MATER DROPLETS
FOR YRTER DROPLETS
i n +
1.0
,5
I
I
I
,6
.?
,B
,9
1 1.0
1
Ll
1
1
1.2
1.3
1.4
2,0
1 5
3.0
2.5
Figure 4.
are plotted in Figures 2,3, and 4 as logarithmic functions using the physical property data and in the range of drop sizes defined in the experiments involving untreated broth, filtered broth, and distilled water, respectively. The data were also compared with the Nee and Treybal correlation by calculation of the terminal velocity using values of drop size in the range which were measured experimentally and using the appropriate physical property data. Comparisons of the predictions of eqs 13 and 14 with the experimental data are shown in Figures 5,6, and 7 for each system, respectively. The model proposed by Winnikow and Chao was based on a direct correlation of the drag coefficientand the drop Reynolds number; see eqs 15 and 16. The experimental values of Reynolds number and drag coefficient were therefore calculated using the definitions expressed in eqs 1and 8, respectively. The appropriate experimentalvalues of terminal velocity and drop size were used. The predicted data were based upon eqs 15 and 16 with the
3.5
5.ut.r
IOp(RdP-)
m
C,5
C,8
5.1
Pop S l u ( r )
Figure 7. DRIlD COEFFICIENTS FOR UNTRERTED
SYSTEH
\
1.5
.
j"
's ! L
1.0 .
,5
.
8,8
I0
I
51
1w
I
I
158
R.ynoldr
,
200 250 n m r
1
300
I
358
Figure 8.
Reynolds number term in eq 15 being based upon the terminal velocity calculated using eq 16. The comparative plots of drag coefficient, C,, vs Reynolds number are shown
Ind. Eng. Chem. Res., Vol. 31, No. 7, 1992 1743 DRRG C O E F F I C I E N T S FOR F I L T E R E D
BROTH SYSTEn
0.0
1
I
0
1
50
100
I
1
,
I
150 200 250 Reynolds number
300
350
$00
Figure 9. ~
\\e
O R M C O E F F I C I E N T S FDR
rph.r.s
YRTER DROPLETS ~
i
1 5
Ch.0 0 0 0
1
50
I
100
I
1
158
I
200 250 R e y n o l d s number
,
300
equet
