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Drop formation from flat tip nozzles in liquid-liquid system
Pergamon
Int. Comm. HeatMass Transfer, Wol. 28, No. 5, pp. 681-692, 2001 Copyright © 2001 Elsevier Science Ltd Printed in the USA. All rights reserved 0735-1933/01/S-see front matter
P l h S0735-1933(01 )00272-X
DROP FORMATION FROM FLAT TIP NOZZIJES IN LIQUID-LIQUID SYSTEM
Chao-Tai Chen, Jer-Ru Maa*, Yu-Min Yang and Chien-Hsiang Chang Department of Chemical Engineering National Cheng Kung University Tainan, Taiwan 70101 R.O.C.
(Communicated by J.P. Hartnett and W.J. Minkowycz)
ABSTRACT Correct estimation of interracial area for heat or mass transfer is of primary importance in liquid-liquid contacting systems. But the existing correlations for the estimation of the sizes of drops formed by nozzles at low flow rate are based on experimental data using nozzles with tips filed down to sharp or bevel or a very thin thickness, and the inside diameters are used as the characteristic diameters. These correlations would underestimate the size of aqueous drops formed from flat tip metallic nozzles considerably, because as the drops are detached from the nozzle tips, the liquid-liquid-solid contact lines are not just located at the inside edge of the opening. In this work, the formation of drops of aqueous solutions of NaCI and AICl3 from flat tip stainless steel nozzles of various dimensions into a pool of n-dodecane was studied experimentally. It was found that the deviation of the estimated drop sizes by the correlation of Kagan et al. differs only slightly from that of Scheele and Meister. The deviations of the estimated values are not affected by the dissolved salts within the range of concentrations studied. And most importantly, the mean deviation of the correlation of Scheele and Meister can be reduced to a few percents if different characteristic diameters, d~, are used in the computation: d~:O.D, for the cases of relatively large nozzles of about Icm O.D. with wall thickness between 0.098 and 0.170cm; d~= 1.15xO.D. for small thin wall nozzles of O.D. < 0.35cm with wall thickness < 0.036cm.
© 2001 Elsevier Science L t d
In various liquid-liquid contacting operations, one of the liquid phases is usually dispersed into drops in order to provide large interfacial area for heat or mass transfer. The size and uniformity of the
*Author to whom correspondence should be addressed. 681
682
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drops are therefore important factors to be considered. Dispersed drops can be formed by various methods. The simplest method of forming drops of dispersed phase is from nozzles. The rate of formation of the drops and the wetting characteristics of liquids with the nozzle tip are two important factors in the formation of drops at nozzles [6]. But the existing correlations for the estimation of drop volume formed from nozzles at low velocity considered mainly the balance of the interfacial, buoyancy, inertia, and drag forces without taking account of the wetting effect of the drop liquid with the tip of the nozzle. Consequently, most of these correlations are based on experimental measurements using nozzles with the tips filed down to sharp or bevel or a very thin thickness of less than 0.005cm to prevent the drop from wetting the tip of the nozzle [12] as shown in Figure l(a). The inside diameters of the nozzles were used in these correlations.
H
I
I
Sharp-edged nozzle (a)
II
I
Flat trp nozzle (b)
FIG. 1 Sharp-Edged and Flat Tip Nozzles. However, in most practical applications, nozzles of fiat tip type as shown in Figure l(b) would always be used to form drops of the dispersed phase instead of sharp edged nozzles for the saving of manufacturing cost. The wetting of the drop liquid with the fiat tip of the nozzle is unavoidable for metallic nozzles. Investigations of Haynes et al. [8] and Hozawa et al. [11] indicated that the droplet formation from a hole in horizontal flat plate is significantly influenced by the wettability and the position of the liquid-liquid-solid contact line, and the maximum drop size is closely related to the Bond number and the advancing contact angle. Eckstein and Vogeipohl [4, 5] conducted a study of drop formation using a two-phase nozzle. It was found that the needle wall thickness affects the drop sizes and its distribution, this effect can be reduced by increasing the flow rate of the continuous phase. Buchanan [1 ] pointed out that as the velocity of dispersed phase through the orifice is high enough (much higher than the jetting velocity), the liquid momentum becomes sufficient to overcome the adhesion to the plate and the drop formation approaches that occurring in the absence of wetting and the drop size falls. To our knowledge, there is still no quantitative measurement of the wetting effect on drop formation from fiat tip metallic nozzles covering a wide range of sizes have been reported. This work is an experimental examination of the applicability of some widely accepted empirical correlations for drop size prediction at low velocity to
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683
the cases of flat tip stainless steel nozzles. Two types of flat tip nozzles were used, they are needles (small to moderate size with thin wall) and reducers (larger size with moderate thick wall). A simple rule of thumb was developed to modify the commonly used correlations of drop formation at low velocity in order to be applied to the stainless steel fiat tip nozzles.
Relationshi_n~ Relevant to This Study
A number of correlations can be used to estimate the drop volume formed from nozzles at low velocity, such as Hayworth and Treybai [9], Null and Johnson [16], Narasinga Rao et ai. [15], Scheele and Meister [17], de Chazal and Ryan [3] and Kagan et al. [13]. Reviews of related correlations are also available (Kumar and Kuloor [14], Steiner and Hartland [! 8]). The correlation of Scheele and Meister [17] is commonly used to compute the drop volume for systems of low velocity and low viscosity and nozzle inside diameter within the range of 0.0813--0.688 cm. ~rod, 5/tcnd,~U, Vd = F | gAp -~ 2 gdp Ap
~rpdd. U n 3gA,o
~-4.5
ntl,,-'U,/ [~, 4gAp )
(1)
When the viscosity of the continuous phase is less than 0.01Ns/m2, the second term on the right side of this equation, the drag term, can be neglected. Parabolic velocity profile inside of the nozzle was assumed during the derivation of Equation (1). For the case of flat velocity profile, the denominator of the third term on the right side of this equation, the kinetic term, should be changed to 4. The average error of Equation (l) is +6.3%, the computed V0 is larger than the experimental value. The correlation of Kagan et al. [ 13] is based on experimental data for nozzle inside diameter within the range of 0.0405-0.730cm.
Vd - ~ r o d F 1 + 2.39 ,--7-2z-d We 13 _ 0.485We gAp
where
We = (Pc + Pd )d, U, 2 2or
(2)
(3)
The Weber number is based on the average density of the continuous aM dispersed phases. The average deviation of computed Va using Equation (2) is 3.7%. When RWe 3 <0.01, the terms containing We in Equation (2) can all be neglected and the deviation of the computed volumes of drops formed under quasistatic flow conditions can be as low as 2%, where R is the dimensionless nozzle inside radius, R -
I.D./2
F in Equations (1) and (2) is the Harkins and Brown's correction factor [7] which gives
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the relative volume of the detached drop in relation to all liquid of the dispersed phase present at the nozzle tip at the time of drop detachment. Horvath et al. [10] published a simple equation for the estimation of F values:
F = 0 ' 6 + 0 " 4 e x p l - 2 d n (~n'od g A p / ' 3) } [
(4)
Experimental Apparatus and Procedure Figure 2 depicts the experimental apparatus also used by Chen et al. [2] previously. The dropping column is a glass cylinder of 12cm O.D., filled with n-dodecane as the continuous phase. Pure water and aqueous electrolyte solutions of various concentration were used as the dispersed phase, which were introduced into the continuous phase through the top opening of this cylinder. This opening of 3.8cm high and 5.5cm I.D. allows nozzles of various sizes to be inserted to at least 2cm beneath the top level of the liquid content, which may be drained through a stainless steel ball valve joined to the bottom of this cylinder by Teflon thread.
(
/ n'-'~H~
[ 5cc, 10cc, 50cc
\Nozz,e H Lr', '""
t
"~ I Metering valve on/offBall valve
3.s~..~D.
II
1/ l : : _"_
of the opening = 5.5 cm '
O.D.= 12 cm Thickness = 7.5 mm
I" Ball valve (SS 316)
FIG. 2 Experimental Apparatus. Flat tip stainless steel Hamilton replacement needles of various sizes, listed in Table 1 were used as the nozzles for the formation of aqueous drops of small to moderate sizes. The drop liquid came from a 5by 1/20ml microburette with about 18.8cm graduated scale and a Teflon plug. This microburette was connected to the needles via a glass capillary tube and a Teflon tube. A !/16" metering valve and an
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685
on/off ball valve were provided on the section of Teflon tube for flow control. Swageiok reducers made of stainless steel as listed in Table 1 were also used as nozzles for aqueous drops of larger sizes. They were connected to the burettes via tubing of suitable sizes. A 1/8" metering valve was provided for the 10ml burette with 38.3cm graduate scale and an accuracy of 0.05ml; a I/4" metering valve was used for the 50ml burette with 48.1cm graduate scale and an accuracy of 0.1ml. The size of the drops is influenced by the wetting characteristics of the drop liquid with the flat tip of the nozzles, as discussed previously in this work, and the momentum of the emerging drop liquid. The latter effect was minimized by controlling the period of drop formation to about 15 seconds using metering valves. The average drop size reported here was determined by counting the drops formed from a known volume of dispersed phase. The drop forming frequency was also recorded. The counting of more than 50 drops are needed for small drops from nozzles with I.D. < 0.05cm, 25-45 drops are needed for drops of moderate sizes from nozzles of 0.06cm < I.D. < 0.4cm, and 20-25 drops for large drops from nozzles of 0.4cm < I.D. in each run. The experiments were carried out at room temperatures. TABLE 1 Dimensions of the Nozzles Gauge #29 #26 #22 Needles # 19 #17 #15 #12 #10 1/4in O.D. Reducers 3/8in O.D. l/2in O.D.
I.D. (cm) O.D. (era) Thickness(mm) 0.018 0.026 0.041 0.069 0.107 0.137 0.216 0.269 0.434 0.680 0.932
0.034 0.046 0.072 0.107 0.147 0.183 0.277 0.340 0.630 0.952 1.270
0.080 0.100 0.155 0.190 0.200 0.230 0.305 0.355 0.980 1.360 1.690
Nozzle ~eometry I.D./O.D. (O.D.-I.D.)/I.D. 0,53 0.89 0,57 0.77 0,57 0.76 0,64 0.55 0.73 0.37 0.75 0.34 0.78 0.28 0.79 0.26 0.69 0.45 0.71 0.40 0.73 0.36
The physical properties of the experimental liquids are listed in Table 2. In this work, Tedia reagent grade (98.8%) n-dodecane was used as the continuous phase. Pure water and aqueous solutions of NaCI and AICI3 of 102M, 10-1M, IM and 2M were used as the dispersed phases. Double distilled water was used for the preparation of these solutions. Densities of the experimental liquids were determined by the ASTM D-4052 method with a DA-310 KYOTO electronics automatic density meter. Viscosity of the continuous phase was determined by the ASTM D-445 method with a CAV-4 Cannon automatic viscometer. Viscosities of the dispersed phases were measured by No. 70 Ostwald viscometer, using the viscosity of double distilled water at 25°C, 0.g937ep, as reference. However, the viscosities of the dispersed phases were not needed in the correlations for the calculation of drop volumes. The interracial tensions between various aqueous phases and n-dodecane were measured by a BYK dynometer with a platium ring. The results of the above measurements are listed in Table 2.
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TABLE 2 Physical Properties of the Liquids Density(g/cm3) 25°C Pure water (DDW) 10":(M) NaCl 10-1(M)NaC1 I(M) NaCW 2(M) NaCI 10-2(M)AICI3 10-J(M) AICI3 1(M) AICI3 2(M) AICI3 n-Dodecane
0.99693 0.99737 1.00106 1.03638 1.07524 0.99810 1.00845 1.10499 1.20743 0.74516
Viscosity(cp) lnterfacial tension with 25°C n-dodecane(dyne/cm) 0.8937* 0.8995 0.9067 0.9743 1.0781 0.9075 0.9678 1.9870 5.5684 1.3703
43.8(22.0°C) 43.8(22.0°C ) 4Y7(22.0°C) 45.2(22.0°C) 46.1(22.2°C) 4Y7(2Y0°C) 43.6(23.2°C) 46.7(23.5°C) 49.6(23.3°C)
* From literature
Results and Discussion
The mean deviations of the drop volumes calculated by the correlation of Scheele and Meister and the correlation of Kagan et al. from the experimental data of this work are listed in Tables 3 and 4 respectively. The mean deviation of the calculated drop volume is defined as / ~ [(Vd,~ - Vd,e~ )/V~texp], I
-
'
where i is the number of measurements. It is apparent that both of these correlations underestimate the size of drops emerged from fiat tip nozzles, especially when the inside nozzle diameter is less than 0. I cm. Although the addition of salts gives some effect of reducing the drop size, the deviations between the estimated and the experimental values are not affected significantly by the dissolved NaCI and AICI3 within the range of concentrations studied. The averaged values of mean deviations for nozzles of various sizes are also plotted as functions of nozzle I.D. in Figure 3. The correlation of Scheele and Meister gives slightly less deviation from the experimental data than that of Kagan et al., it is thus chosen for further studies in this work. In this work the viscosity of the continuous phase of n-dodecane is 0.00137Ns/m 2, considerably less than 0.01Ns/m 2, the second term on the right hand side of Equation (l) can be dropped. This equation is thus become explicit and much easier to use. Figure 4 shows the comparison between the experimental drop volumes of various aqueous solutions emerged from fiat tip nozzles of different sizes with the calculated values by the correlation of Scheele and Meister. The mean deviations of the calculated drop sizes by using of the correlations of Scheele and Meister (Eq. 1) and Kagan e~ al. (Eq. 2) from their original experimental values are +6.3% and +3.7%, respectively. Both tend to overestimate the drop sizes, quite different from the large negative deviations in Tables 3 and 4 and Figures 3 and 4 of this work. This is because nozzles of flat tip are used in this work,
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DROP FORMATION FROM FLAT TIP NOZZLES
687
the edges of the opening of the nozzles were not filed down to sharp or bevel, the wetting effect of the drop liquid causes the liquid-liquid-solid contact line moves outward and consequently, the drop sizes become larger.
TABLE 3 Deviations between the Estimated Drop Volumes by the Scheele and Meister's Correlation and the Experimental Values :l.=l.D.(cm)
0.018
0.026
0.041
0.069
0.107
-52.49 -52.45 -52.23 -50.95 -51.29 -51.55 -51.99 -52.08 -55.09 -52.24
.50.21 .50.30 -50.52 -49.38 .49.10 .50.27 .50.45 .52.34 -51.46 -50.45
-46.34 -46.91 -47.34 -46.38 -47.17 -46.23 -48.54 -49.24 -48.99 -47.46
-39.83 -40.49 -40.97 -40.30 -34.53 -40.80 -40.01 1-41.55 -42.00 -42.51 -40.94 -34.53 -39.50
0.137
0.216
0.269
0.434
0.680
0.932
-32.62 -33.06 -33.63 -31.88 -33.33 -32.52 -33.74 -33.18 -33.61 -33.06
-26.44 -28.22 -26.99 -24.88 -28.90 -29.01 -29.06 -28.29 -29.42 -27.91
-29.80 -29.08 -29.65 -28.88 -29.64 -29.50 -29.92 -28.34 -30.23 -29.45
-30.36 -29.59 -19.53 -24.04 -29.84 -29.87 -30.44 -28.68 -29.83 -28.02
-27.96 -25.39 -21.34 -28.62 -30.47 -30.46 -30.05 -29.81 -29.43 -28.17 -26.95
-22.83 -27.63 -23.89 -20.91 -27.09 -23.80 -18.88 -29.16 -27.62 -24.65
Devi.(%) \
Pure water
10-2(M)NaCI
I 0-t(M)NaCI I(M)NaCI 2(M)NaCl 10-2(M)A1CI3 10-1(M)A1CI3 1(M)AICI3 2(M)A1CI3 Average
-36.08
TABLE 4 Deviations between the Estimated Drop Volumes by the Kagan's Equation and the Experimental Values d,=l.D.(cm)
0.018
0.026
0.041
0.069
Pure water 10-2(M)NaCI 10"l(M)NaCl I(M)NaCI
-53.62 -53.49 -53.24 -51.90 -52.20 -52.62 -53.10 -53.09 -55.75 -53.22
-51.36 -51.45 -51.60 -50.41 -50.15 -51.36 -51.64 -53.39 -52.34 -51.52
-47.51 -48.01 -48.41 -47.57 -48.32 -47.47 -49.81 -50.31 -49.89 -48.59
-41.23 -41.69 -42.11 -41.42 -35.79 -42.13 -41.38 -42.99 -43.40 -43.45 -42.20 -35.79 -40.67
2(M)NaO I 02(M)AICI3
10-~(M)AICI3 I(M)AICI3 2(M)AICI3 Average
0.107
0.137
0.216
0.269
0.434
-33.95 -27.82 -31.01 -31.46 -34.35 -29.37 -30.02 -30.62 -34.77 -28.14 -30.75 -20.61 -33.23 -26.12 -29.96 -24.82 -34.49 -29.98 -30.58 -30.76 -33.94 -30.36 -30.90 -30.87 -35.28 -30.45 -31.32 -31.53 -34.37 -29.40 -29.38 -29.65 -34.81 -30.49 -31.15 -30.63 -34.35 -29.13 -30.56 -28.99 -37.13
C).680 0.932
-28.70 -26.19 -22.14 -29.29 -31.12 -31.32 -30.96 -30.45 -30.07 -28.92 -27.68
-23.46 -28.14 -24.39 -21.37 -27.54 -24.31 -19.49 -29.50 -27.94 -25.13
688
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Vol. 28, No. 5
0
-10
7
--<3- Scheele and Meister] Kagan et al. /
-20
-40 o
0.01
0.1
I
!. D. of nnzzles (era)
FIG. 3 Predicted Deviations of Drop Sizes by Different Authors as Functions of I.D. of the Nozzles.
0.5
(b) AICI3
(a)NaCI 0.4
,d <
2(M)
/
li!i ! /
•
,X'(M) /
0.3
/
0 Purewater
0 Purewater] + O.Ol(M) | AO.I(M) / |
.".
0.2
0.1 / 0
~ 0.1
'
0 0.2
/ ~ 1
I 0.3
0.4
0
0.1
0.2
t
t
0.3
0.4
0.5
V d EXP (cm 3) FIG. 4 Comparison between the Experimental Drop Volumes and the Calculated Values by the Scheele and Meister's Correlation (d,yl.D.).
Haynes et al. [8] pointed out that if the external phase preferentially wets the material used to construct the nozzle, the inside diameter of the nozzle is used as the characteristic dimension, if not, the outside diameter is taken as characteristic. When the drop liquid wets the fiat tip of the nozzle, an additional adhesion force exists on the base of the drop influencing the attachment area. Since metals could be wetted by either phase, the difference in adhesion tensions between metal and the dispersed and
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689
continuous liquids determines the position of three phase contact line and the attachment area, and consequently, the drop size. The mean deviations of drop volumes calculated by the Scheele and Meister's equation using the outside diameter of the nozzles as the characteristic dimension, d,, are listed in Table 5. This table shows that the Scheele and Meister's equation thus modified gives good estimation of sizes of drops emerged from relatively large nozzles of wall thickness > 0.1cm. But it results a 9-14% underestimation for small nozzles of wall thickness < 0.04em. This is because that for the thin wall small nozzles, the three phase contact lines move beyond the outer circumferences of the nozzle tips and up the outside wall, and consequently, make the hanging drops larger. This phenomenon is not observed in the case of fiat tip nozzles of relatively large diameter and thicker wail. Therefore, larger characteristic diameters should be used for estimating the size of drops emerged from thin wall fiat tip nozzles of relatively small diameter. Table 6 shows that when characteristic diameters of d~--1.15xO.D. are used, the agreement between the experimentally determined sizes of drops emerged from these nozzles and the estimated values by the Scheele and Meister's equation is reasonably good. Significant improvement in the agreement between the estimated and experimental drop sizes is also shown in Figure 5. The estimated values in this figure are based on d,--O.D, for thick wall nozzles as listed in the right portion of Table 5, and d~= 1.15xO.D. for the thin wall nozzles as listed in Table 6. This is perhaps a rule of thumb for the selection of the characteristic diameter, d~, for the estimation of the sizes of drops emerged from flat tip nozzles preferentially wetted by the drop liquid.
TABLE 5 Deviations between the Estimated Drop Volumes by the Scheele and Meister's Correlation Using d~=O.D, and the Experimental Values l.D,(cm) d~=O.D.(cm)
0.018 0.026 0.034 0.046
Pure water
-10.90 -10.96 -10.59 8.41 9.16 9.26 -10.03 •10.47 -16.76 -10.73
.~(M)NaCl I0t(M)NaCI
I(M)NaCl 2(M)NaCI .IO'2(M)AIC1,
,,I,O-:(M)AICI3 I(M)AICI3 2(M)AICI, Average
0.041 0.069 0.072 0.107
9.107 0.137 9.147 0.183
-12.88 7.56 - 8.64 -13.05 8.63 - 9.85 -13.54 9.43 -10.68 -11.74 7.68 -9.75 -12.06 -!1.27 9.16 -10.32 -13.09 7.27 - 8.93 -13.27 -11.14 -11.18 -16.88 -12.86 -12.04 -15.79 -12.89 -13.53 -13.50 9.62 -10.55 -12.06
-11.93 -12.53 -13.39 -11.00 -13.06 -11.74 -13.23 -12.86 -13.46 -12.58
- 11.42
-8.04
~).216 0.269 0.277 0.340
7.63 -10.01 8.50 5.82 -10.93 -10.84 -10.87 -10.15 -11.59 9.59
1.434 0.680 ~).630 0.952
-13.07 1 . 4 8 -12.39 0.56 -12.97 13.50 -12.05 6.78 -13.08 0.88 -12.57 1 . 0 0 -13.08 1 . 5 7 -11.40 0.93 -13.78 0.73 -12.71 1 . 6 7
0.88 2.77 8.26 - 1.71 - 4.08 - 3.94 -3.15 -
- 3.03
-2.13 - 0.88 0.96
0.932 1.270
4.69 2.11 2.90 6.93 1.00 2.99 10.03 - 4.04 - 1.50 2.10
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TABLE 6 Deviations between the Estimated Drop Volumes by the Scheele and Meister's Correlation Using d,=l. 15×O.D. and the Experimental Values for Thin Wall Small Nozzles l.D.(cm) O.D.(cm) n dffO.D.
~).018 0.026 0.041 0.069 D.034 0.046 0.072 0.107 1.15 1.15 1.15 1.15
Pure water 10-2(M)NaCI 10-1(M)NaCI 1(M)NaCI 2(M)NaCI 10-2(M)AICIs I 0-t(M)AICI3 I(M)AICIs 2(M)AICI3 Average
2.36 2.26 2.66 5.10 4.19 4.21 3.35 2.75 - 4.70 2.46
- 0.04 - 0.25 - 0.85 1.16 1.69 - 0.31 -0.48 - 4.71 3.59 0.82
5.83 4.57 3.63 5.68 3.94 6.20 1.81 - 0.33 - 0.53 3.42
4.39 2.91 1.91 2.94 2.39 4.04 1.53 0.47 1.54 2.12
0,107 0.147 1.15
0.14
0.14 1.10
0.137 0.216 0,269 0.183 0.277 0.340 1.15 1.15 1.15
0.25 0.44 1.50 1.30 1.14 0.51 1.12 0.91 1.60 0.52
5.06 2.24 3.95 7.03 1.18 1.41 1.41 2.08 0.44 2.76
1.14 0.54 1.10 0.06 1.29 0.46 1.02 0.68 2.04 0.77
0.5 (a)NaC! 0.4 0.3 <
(b) AICI3
/ ~
0 Purewater + 0.01(M] a 0. t(M) XI(M) I 2(M)
~/~/
o Purewater +0.01(M) ~ 0.1(M) I
,
/ , 0 ~
/"
0.2 0.1
0 0.1
0.2
0.3
0.4
0
0.1
0.2
0.3
0.4
0.5
V d EXP ( c m 3) FIG. 5 Comparison between the Experimental Drop Volumes and the Calculated Values by the Scheele and Meister's Correlation (d,=l. 15xO.D. for Thin Wall Small Nozzles, d,=O.D, for Thick Wall Large Nozzles).
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Conclusions
Correct estimation of drop sizes is important to the design of various liquid-liquid contact equipments. Measurements of the sizes of aqueous drops emerged from stainless steel flat tip nozzles were carried out in this work. It is shown that, since the drop liquid wets the nozzle surface preferentially, the existing correlations reported in the literature, such as the equations of Scheele and Meister, and Kagan et al. usually underestimate the drop size by as much as 55%. This is because that these correlations were based on experimental measurements using nozzles with tips filed down to sharp or bevel or a very thin thickness. The deviation of the estimated sizes by the correlation of Kagan et al. differs very little from that of Scheele and Meister. These deviations are not affected by the dissolved salts within the range of concentrations studied. It is also shown in this work that after some adjustment of the value of the characteristic diameter, d,, the correlation of Scheele and Meister can be used to estimate the sizes of aqueous drops emerged from fiat tip stainless steel nozzles within an error of a few percents. This modified correlation of Scheele and Meister covers a much wider range of nozzle size than the original one. For relatively large nozzles of about l cm O.D. with wall thickness between 0.098 and 0.170era, the d, value is taken to be the outside diameter; for small thin wall nozzles of O.D. less than 0.35cm with wall thickness < 0.036cm, the d, value is taken to be 1.15xO.D..
d. F g I.D. i n O.D. R U, Vd /zc Pc Pd Ap o
Characteristic diameter of the nozzle (cm) Drop diameter (cm) Harkins and Brown's correction factor Gravitational acceleration (cm/sec2), 980.665cm/sec 2 Inside diameter of the nozzle (cm) Number of runs Ratio of characteristic diameter to the O.D. of the nozzle Outside diameter of the nozzle (cm) Dimensionless inside radius of the nozzle Dispersed (drop) phase average velocity through the nozzle (cm/sec) Drop volume (cm3) Viscosity of continuous phase (g/cm see, poise) Density of continuous phase (g/cm3) Density of dispersed phase (g/cm3) Density difference (g/era3) lnterfaeial tension (dyne/cm)
Dimensionless grouns
We
Weber number, (Pc + pd,_,__n 2"~dU 2or
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References 1. Buchanan, R. H., Australian J. Appl. Sci., 3, 233 (1952). 2. Chen, C. T.; Maa, J. R.; Yang, Y. M. and Chang, C. H., To be published, (2001). 3. de Chazal, L. E. M. and Ryan, J. T., AIChE J., 17(5), 1226 (197l). 4. Eckstein, A. and Vogelpohl, A., Part A, Chem. Eng. Technol., 21(12), 952 (1998). 5. Eckstein, A. and Vogelpohl, A., Part B, Chem. Eng. Technol., 22(1), 23 (1999). 6. Godfrey, J. C. and Hanson, C., Liquid-Liquid Systems, in: Hetsroni, G. (Ed.), Handbook of Multiphase Systems, (Hemisphere, Washington, 1982), Chap. 4, p. 4-1-4-46. 7. Harkins, W. D. and Brown, F. E., J. Am. Chem. Soc., 41,499 (1919). 8. Haynes, L.G.; Himmelblau, D. M. and Schechter, R. S., Ind. Eng. Chem., Proc. Des. Dev., 7(4), 508 (1968). 9. Hayworth, C. B. and Treybal, R. E., Ind. Eng. Chem., 42(6), 1174 (1950). 10. Horvath, M.; Steiner, L. and Hartland, S., Can. J. Chem. Eng., 56, 9 (1978). 11. Hozawa, M.; Tsukada, T.; lmaishi, N. and Fujinawa, K., J. Chem. Eng. Japan, 14(5), 358 (1981). 12. lto, R.; Hirata, Y; Inoue, K and Kitagawa, Y., Int. Chem. Eng., 2_Q(4),616 (1980). 13. Kagan, S. E.; Kovalev, Yu. N. and Zakharychev, A. P., Theor. Osn. Ch. Techn. (Moscow), 7(4), 514 (1973). 14. Kumar, R. and Kuloor, N. R., The Formation of Bubbles and Drops, in: Drew, T. B. and Hoopes, J. W., Jr. (Eds.), Advances in Chemical Engineering, Vol. 8, (Academic Press, New York, 1970), p. 255-368. 15. Narasinga Rao, E. V. L.; Kumar, R. and Kuloor, N. R,, Chem. Eng. Sci., 21, 867 (1966). 16. Null, H. R. and Johnson, H. F., AIChE J., _4(3), 273 (1958). 17. Scheele, G. F. and Meister, B. J., AIChE J., 14(1), 9 (1968). 18. Steiner, L. and Hartland, S., Hydrodynamics of Liquid-Liquid Spray Columns, in: Cheremisinoff, N. P. and Gupta, R. (Eds.), Handbook of Fluids in Motion, (Ann Arbor, Michigan, 1983), Chap. 40, p. 1049-1092. Received March 18, 2001
Int. Comm. HeatMass Transfer, Wol. 28, No. 5, pp. 681-692, 2001 Copyright © 2001 Elsevier Science Ltd Printed in the USA. All rights reserved 0735-1933/01/S-see front matter
P l h S0735-1933(01 )00272-X
DROP FORMATION FROM FLAT TIP NOZZIJES IN LIQUID-LIQUID SYSTEM
Chao-Tai Chen, Jer-Ru Maa*, Yu-Min Yang and Chien-Hsiang Chang Department of Chemical Engineering National Cheng Kung University Tainan, Taiwan 70101 R.O.C.
(Communicated by J.P. Hartnett and W.J. Minkowycz)
ABSTRACT Correct estimation of interracial area for heat or mass transfer is of primary importance in liquid-liquid contacting systems. But the existing correlations for the estimation of the sizes of drops formed by nozzles at low flow rate are based on experimental data using nozzles with tips filed down to sharp or bevel or a very thin thickness, and the inside diameters are used as the characteristic diameters. These correlations would underestimate the size of aqueous drops formed from flat tip metallic nozzles considerably, because as the drops are detached from the nozzle tips, the liquid-liquid-solid contact lines are not just located at the inside edge of the opening. In this work, the formation of drops of aqueous solutions of NaCI and AICl3 from flat tip stainless steel nozzles of various dimensions into a pool of n-dodecane was studied experimentally. It was found that the deviation of the estimated drop sizes by the correlation of Kagan et al. differs only slightly from that of Scheele and Meister. The deviations of the estimated values are not affected by the dissolved salts within the range of concentrations studied. And most importantly, the mean deviation of the correlation of Scheele and Meister can be reduced to a few percents if different characteristic diameters, d~, are used in the computation: d~:O.D, for the cases of relatively large nozzles of about Icm O.D. with wall thickness between 0.098 and 0.170cm; d~= 1.15xO.D. for small thin wall nozzles of O.D. < 0.35cm with wall thickness < 0.036cm.
© 2001 Elsevier Science L t d
In various liquid-liquid contacting operations, one of the liquid phases is usually dispersed into drops in order to provide large interfacial area for heat or mass transfer. The size and uniformity of the
*Author to whom correspondence should be addressed. 681
682
C.-T. Chen et al.
Vol. 28, No. 5
drops are therefore important factors to be considered. Dispersed drops can be formed by various methods. The simplest method of forming drops of dispersed phase is from nozzles. The rate of formation of the drops and the wetting characteristics of liquids with the nozzle tip are two important factors in the formation of drops at nozzles [6]. But the existing correlations for the estimation of drop volume formed from nozzles at low velocity considered mainly the balance of the interfacial, buoyancy, inertia, and drag forces without taking account of the wetting effect of the drop liquid with the tip of the nozzle. Consequently, most of these correlations are based on experimental measurements using nozzles with the tips filed down to sharp or bevel or a very thin thickness of less than 0.005cm to prevent the drop from wetting the tip of the nozzle [12] as shown in Figure l(a). The inside diameters of the nozzles were used in these correlations.
H
I
I
Sharp-edged nozzle (a)
II
I
Flat trp nozzle (b)
FIG. 1 Sharp-Edged and Flat Tip Nozzles. However, in most practical applications, nozzles of fiat tip type as shown in Figure l(b) would always be used to form drops of the dispersed phase instead of sharp edged nozzles for the saving of manufacturing cost. The wetting of the drop liquid with the fiat tip of the nozzle is unavoidable for metallic nozzles. Investigations of Haynes et al. [8] and Hozawa et al. [11] indicated that the droplet formation from a hole in horizontal flat plate is significantly influenced by the wettability and the position of the liquid-liquid-solid contact line, and the maximum drop size is closely related to the Bond number and the advancing contact angle. Eckstein and Vogeipohl [4, 5] conducted a study of drop formation using a two-phase nozzle. It was found that the needle wall thickness affects the drop sizes and its distribution, this effect can be reduced by increasing the flow rate of the continuous phase. Buchanan [1 ] pointed out that as the velocity of dispersed phase through the orifice is high enough (much higher than the jetting velocity), the liquid momentum becomes sufficient to overcome the adhesion to the plate and the drop formation approaches that occurring in the absence of wetting and the drop size falls. To our knowledge, there is still no quantitative measurement of the wetting effect on drop formation from fiat tip metallic nozzles covering a wide range of sizes have been reported. This work is an experimental examination of the applicability of some widely accepted empirical correlations for drop size prediction at low velocity to
Vol. 28, No. 5
DROP FORMATION FROM FLAT TIP NOZZLES
683
the cases of flat tip stainless steel nozzles. Two types of flat tip nozzles were used, they are needles (small to moderate size with thin wall) and reducers (larger size with moderate thick wall). A simple rule of thumb was developed to modify the commonly used correlations of drop formation at low velocity in order to be applied to the stainless steel fiat tip nozzles.
Relationshi_n~ Relevant to This Study
A number of correlations can be used to estimate the drop volume formed from nozzles at low velocity, such as Hayworth and Treybai [9], Null and Johnson [16], Narasinga Rao et ai. [15], Scheele and Meister [17], de Chazal and Ryan [3] and Kagan et al. [13]. Reviews of related correlations are also available (Kumar and Kuloor [14], Steiner and Hartland [! 8]). The correlation of Scheele and Meister [17] is commonly used to compute the drop volume for systems of low velocity and low viscosity and nozzle inside diameter within the range of 0.0813--0.688 cm. ~rod, 5/tcnd,~U, Vd = F | gAp -~ 2 gdp Ap
~rpdd. U n 3gA,o
~-4.5
ntl,,-'U,/ [~, 4gAp )
(1)
When the viscosity of the continuous phase is less than 0.01Ns/m2, the second term on the right side of this equation, the drag term, can be neglected. Parabolic velocity profile inside of the nozzle was assumed during the derivation of Equation (1). For the case of flat velocity profile, the denominator of the third term on the right side of this equation, the kinetic term, should be changed to 4. The average error of Equation (l) is +6.3%, the computed V0 is larger than the experimental value. The correlation of Kagan et al. [ 13] is based on experimental data for nozzle inside diameter within the range of 0.0405-0.730cm.
Vd - ~ r o d F 1 + 2.39 ,--7-2z-d We 13 _ 0.485We gAp
where
We = (Pc + Pd )d, U, 2 2or
(2)
(3)
The Weber number is based on the average density of the continuous aM dispersed phases. The average deviation of computed Va using Equation (2) is 3.7%. When RWe 3 <0.01, the terms containing We in Equation (2) can all be neglected and the deviation of the computed volumes of drops formed under quasistatic flow conditions can be as low as 2%, where R is the dimensionless nozzle inside radius, R -
I.D./2
F in Equations (1) and (2) is the Harkins and Brown's correction factor [7] which gives
684
C.-T. Chen et al.
Vol. 28, No. 5
the relative volume of the detached drop in relation to all liquid of the dispersed phase present at the nozzle tip at the time of drop detachment. Horvath et al. [10] published a simple equation for the estimation of F values:
F = 0 ' 6 + 0 " 4 e x p l - 2 d n (~n'od g A p / ' 3) } [
(4)
Experimental Apparatus and Procedure Figure 2 depicts the experimental apparatus also used by Chen et al. [2] previously. The dropping column is a glass cylinder of 12cm O.D., filled with n-dodecane as the continuous phase. Pure water and aqueous electrolyte solutions of various concentration were used as the dispersed phase, which were introduced into the continuous phase through the top opening of this cylinder. This opening of 3.8cm high and 5.5cm I.D. allows nozzles of various sizes to be inserted to at least 2cm beneath the top level of the liquid content, which may be drained through a stainless steel ball valve joined to the bottom of this cylinder by Teflon thread.
(
/ n'-'~H~
[ 5cc, 10cc, 50cc
\Nozz,e H Lr', '""
t
"~ I Metering valve on/offBall valve
3.s~..~D.
II
1/ l : : _"_
of the opening = 5.5 cm '
O.D.= 12 cm Thickness = 7.5 mm
I" Ball valve (SS 316)
FIG. 2 Experimental Apparatus. Flat tip stainless steel Hamilton replacement needles of various sizes, listed in Table 1 were used as the nozzles for the formation of aqueous drops of small to moderate sizes. The drop liquid came from a 5by 1/20ml microburette with about 18.8cm graduated scale and a Teflon plug. This microburette was connected to the needles via a glass capillary tube and a Teflon tube. A !/16" metering valve and an
Vol. 28, No. 5
DROP FORMATION FROM FLAT TIP NOZZLES
685
on/off ball valve were provided on the section of Teflon tube for flow control. Swageiok reducers made of stainless steel as listed in Table 1 were also used as nozzles for aqueous drops of larger sizes. They were connected to the burettes via tubing of suitable sizes. A 1/8" metering valve was provided for the 10ml burette with 38.3cm graduate scale and an accuracy of 0.05ml; a I/4" metering valve was used for the 50ml burette with 48.1cm graduate scale and an accuracy of 0.1ml. The size of the drops is influenced by the wetting characteristics of the drop liquid with the flat tip of the nozzles, as discussed previously in this work, and the momentum of the emerging drop liquid. The latter effect was minimized by controlling the period of drop formation to about 15 seconds using metering valves. The average drop size reported here was determined by counting the drops formed from a known volume of dispersed phase. The drop forming frequency was also recorded. The counting of more than 50 drops are needed for small drops from nozzles with I.D. < 0.05cm, 25-45 drops are needed for drops of moderate sizes from nozzles of 0.06cm < I.D. < 0.4cm, and 20-25 drops for large drops from nozzles of 0.4cm < I.D. in each run. The experiments were carried out at room temperatures. TABLE 1 Dimensions of the Nozzles Gauge #29 #26 #22 Needles # 19 #17 #15 #12 #10 1/4in O.D. Reducers 3/8in O.D. l/2in O.D.
I.D. (cm) O.D. (era) Thickness(mm) 0.018 0.026 0.041 0.069 0.107 0.137 0.216 0.269 0.434 0.680 0.932
0.034 0.046 0.072 0.107 0.147 0.183 0.277 0.340 0.630 0.952 1.270
0.080 0.100 0.155 0.190 0.200 0.230 0.305 0.355 0.980 1.360 1.690
Nozzle ~eometry I.D./O.D. (O.D.-I.D.)/I.D. 0,53 0.89 0,57 0.77 0,57 0.76 0,64 0.55 0.73 0.37 0.75 0.34 0.78 0.28 0.79 0.26 0.69 0.45 0.71 0.40 0.73 0.36
The physical properties of the experimental liquids are listed in Table 2. In this work, Tedia reagent grade (98.8%) n-dodecane was used as the continuous phase. Pure water and aqueous solutions of NaCI and AICI3 of 102M, 10-1M, IM and 2M were used as the dispersed phases. Double distilled water was used for the preparation of these solutions. Densities of the experimental liquids were determined by the ASTM D-4052 method with a DA-310 KYOTO electronics automatic density meter. Viscosity of the continuous phase was determined by the ASTM D-445 method with a CAV-4 Cannon automatic viscometer. Viscosities of the dispersed phases were measured by No. 70 Ostwald viscometer, using the viscosity of double distilled water at 25°C, 0.g937ep, as reference. However, the viscosities of the dispersed phases were not needed in the correlations for the calculation of drop volumes. The interracial tensions between various aqueous phases and n-dodecane were measured by a BYK dynometer with a platium ring. The results of the above measurements are listed in Table 2.
686
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Vol. 28, No. 5
TABLE 2 Physical Properties of the Liquids Density(g/cm3) 25°C Pure water (DDW) 10":(M) NaCl 10-1(M)NaC1 I(M) NaCW 2(M) NaCI 10-2(M)AICI3 10-J(M) AICI3 1(M) AICI3 2(M) AICI3 n-Dodecane
0.99693 0.99737 1.00106 1.03638 1.07524 0.99810 1.00845 1.10499 1.20743 0.74516
Viscosity(cp) lnterfacial tension with 25°C n-dodecane(dyne/cm) 0.8937* 0.8995 0.9067 0.9743 1.0781 0.9075 0.9678 1.9870 5.5684 1.3703
43.8(22.0°C) 43.8(22.0°C ) 4Y7(22.0°C) 45.2(22.0°C) 46.1(22.2°C) 4Y7(2Y0°C) 43.6(23.2°C) 46.7(23.5°C) 49.6(23.3°C)
* From literature
Results and Discussion
The mean deviations of the drop volumes calculated by the correlation of Scheele and Meister and the correlation of Kagan et al. from the experimental data of this work are listed in Tables 3 and 4 respectively. The mean deviation of the calculated drop volume is defined as / ~ [(Vd,~ - Vd,e~ )/V~texp], I
-
'
where i is the number of measurements. It is apparent that both of these correlations underestimate the size of drops emerged from fiat tip nozzles, especially when the inside nozzle diameter is less than 0. I cm. Although the addition of salts gives some effect of reducing the drop size, the deviations between the estimated and the experimental values are not affected significantly by the dissolved NaCI and AICI3 within the range of concentrations studied. The averaged values of mean deviations for nozzles of various sizes are also plotted as functions of nozzle I.D. in Figure 3. The correlation of Scheele and Meister gives slightly less deviation from the experimental data than that of Kagan et al., it is thus chosen for further studies in this work. In this work the viscosity of the continuous phase of n-dodecane is 0.00137Ns/m 2, considerably less than 0.01Ns/m 2, the second term on the right hand side of Equation (l) can be dropped. This equation is thus become explicit and much easier to use. Figure 4 shows the comparison between the experimental drop volumes of various aqueous solutions emerged from fiat tip nozzles of different sizes with the calculated values by the correlation of Scheele and Meister. The mean deviations of the calculated drop sizes by using of the correlations of Scheele and Meister (Eq. 1) and Kagan e~ al. (Eq. 2) from their original experimental values are +6.3% and +3.7%, respectively. Both tend to overestimate the drop sizes, quite different from the large negative deviations in Tables 3 and 4 and Figures 3 and 4 of this work. This is because nozzles of flat tip are used in this work,
Vol. 28, No. 5
DROP FORMATION FROM FLAT TIP NOZZLES
687
the edges of the opening of the nozzles were not filed down to sharp or bevel, the wetting effect of the drop liquid causes the liquid-liquid-solid contact line moves outward and consequently, the drop sizes become larger.
TABLE 3 Deviations between the Estimated Drop Volumes by the Scheele and Meister's Correlation and the Experimental Values :l.=l.D.(cm)
0.018
0.026
0.041
0.069
0.107
-52.49 -52.45 -52.23 -50.95 -51.29 -51.55 -51.99 -52.08 -55.09 -52.24
.50.21 .50.30 -50.52 -49.38 .49.10 .50.27 .50.45 .52.34 -51.46 -50.45
-46.34 -46.91 -47.34 -46.38 -47.17 -46.23 -48.54 -49.24 -48.99 -47.46
-39.83 -40.49 -40.97 -40.30 -34.53 -40.80 -40.01 1-41.55 -42.00 -42.51 -40.94 -34.53 -39.50
0.137
0.216
0.269
0.434
0.680
0.932
-32.62 -33.06 -33.63 -31.88 -33.33 -32.52 -33.74 -33.18 -33.61 -33.06
-26.44 -28.22 -26.99 -24.88 -28.90 -29.01 -29.06 -28.29 -29.42 -27.91
-29.80 -29.08 -29.65 -28.88 -29.64 -29.50 -29.92 -28.34 -30.23 -29.45
-30.36 -29.59 -19.53 -24.04 -29.84 -29.87 -30.44 -28.68 -29.83 -28.02
-27.96 -25.39 -21.34 -28.62 -30.47 -30.46 -30.05 -29.81 -29.43 -28.17 -26.95
-22.83 -27.63 -23.89 -20.91 -27.09 -23.80 -18.88 -29.16 -27.62 -24.65
Devi.(%) \
Pure water
10-2(M)NaCI
I 0-t(M)NaCI I(M)NaCI 2(M)NaCl 10-2(M)A1CI3 10-1(M)A1CI3 1(M)AICI3 2(M)A1CI3 Average
-36.08
TABLE 4 Deviations between the Estimated Drop Volumes by the Kagan's Equation and the Experimental Values d,=l.D.(cm)
0.018
0.026
0.041
0.069
Pure water 10-2(M)NaCI 10"l(M)NaCl I(M)NaCI
-53.62 -53.49 -53.24 -51.90 -52.20 -52.62 -53.10 -53.09 -55.75 -53.22
-51.36 -51.45 -51.60 -50.41 -50.15 -51.36 -51.64 -53.39 -52.34 -51.52
-47.51 -48.01 -48.41 -47.57 -48.32 -47.47 -49.81 -50.31 -49.89 -48.59
-41.23 -41.69 -42.11 -41.42 -35.79 -42.13 -41.38 -42.99 -43.40 -43.45 -42.20 -35.79 -40.67
2(M)NaO I 02(M)AICI3
10-~(M)AICI3 I(M)AICI3 2(M)AICI3 Average
0.107
0.137
0.216
0.269
0.434
-33.95 -27.82 -31.01 -31.46 -34.35 -29.37 -30.02 -30.62 -34.77 -28.14 -30.75 -20.61 -33.23 -26.12 -29.96 -24.82 -34.49 -29.98 -30.58 -30.76 -33.94 -30.36 -30.90 -30.87 -35.28 -30.45 -31.32 -31.53 -34.37 -29.40 -29.38 -29.65 -34.81 -30.49 -31.15 -30.63 -34.35 -29.13 -30.56 -28.99 -37.13
C).680 0.932
-28.70 -26.19 -22.14 -29.29 -31.12 -31.32 -30.96 -30.45 -30.07 -28.92 -27.68
-23.46 -28.14 -24.39 -21.37 -27.54 -24.31 -19.49 -29.50 -27.94 -25.13
688
C.-T. Chen et al.
Vol. 28, No. 5
0
-10
7
--<3- Scheele and Meister] Kagan et al. /
-20
-40 o
0.01
0.1
I
!. D. of nnzzles (era)
FIG. 3 Predicted Deviations of Drop Sizes by Different Authors as Functions of I.D. of the Nozzles.
0.5
(b) AICI3
(a)NaCI 0.4
,d <
2(M)
/
li!i ! /
•
,X'(M) /
0.3
/
0 Purewater
0 Purewater] + O.Ol(M) | AO.I(M) / |
.".
0.2
0.1 / 0
~ 0.1
'
0 0.2
/ ~ 1
I 0.3
0.4
0
0.1
0.2
t
t
0.3
0.4
0.5
V d EXP (cm 3) FIG. 4 Comparison between the Experimental Drop Volumes and the Calculated Values by the Scheele and Meister's Correlation (d,yl.D.).
Haynes et al. [8] pointed out that if the external phase preferentially wets the material used to construct the nozzle, the inside diameter of the nozzle is used as the characteristic dimension, if not, the outside diameter is taken as characteristic. When the drop liquid wets the fiat tip of the nozzle, an additional adhesion force exists on the base of the drop influencing the attachment area. Since metals could be wetted by either phase, the difference in adhesion tensions between metal and the dispersed and
Vol. 28, No. 5
DROP FORMATION FROM FLAT TIP NOZZLES
689
continuous liquids determines the position of three phase contact line and the attachment area, and consequently, the drop size. The mean deviations of drop volumes calculated by the Scheele and Meister's equation using the outside diameter of the nozzles as the characteristic dimension, d,, are listed in Table 5. This table shows that the Scheele and Meister's equation thus modified gives good estimation of sizes of drops emerged from relatively large nozzles of wall thickness > 0.1cm. But it results a 9-14% underestimation for small nozzles of wall thickness < 0.04em. This is because that for the thin wall small nozzles, the three phase contact lines move beyond the outer circumferences of the nozzle tips and up the outside wall, and consequently, make the hanging drops larger. This phenomenon is not observed in the case of fiat tip nozzles of relatively large diameter and thicker wail. Therefore, larger characteristic diameters should be used for estimating the size of drops emerged from thin wall fiat tip nozzles of relatively small diameter. Table 6 shows that when characteristic diameters of d~--1.15xO.D. are used, the agreement between the experimentally determined sizes of drops emerged from these nozzles and the estimated values by the Scheele and Meister's equation is reasonably good. Significant improvement in the agreement between the estimated and experimental drop sizes is also shown in Figure 5. The estimated values in this figure are based on d,--O.D, for thick wall nozzles as listed in the right portion of Table 5, and d~= 1.15xO.D. for the thin wall nozzles as listed in Table 6. This is perhaps a rule of thumb for the selection of the characteristic diameter, d~, for the estimation of the sizes of drops emerged from flat tip nozzles preferentially wetted by the drop liquid.
TABLE 5 Deviations between the Estimated Drop Volumes by the Scheele and Meister's Correlation Using d~=O.D, and the Experimental Values l.D,(cm) d~=O.D.(cm)
0.018 0.026 0.034 0.046
Pure water
-10.90 -10.96 -10.59 8.41 9.16 9.26 -10.03 •10.47 -16.76 -10.73
.~(M)NaCl I0t(M)NaCI
I(M)NaCl 2(M)NaCI .IO'2(M)AIC1,
,,I,O-:(M)AICI3 I(M)AICI3 2(M)AICI, Average
0.041 0.069 0.072 0.107
9.107 0.137 9.147 0.183
-12.88 7.56 - 8.64 -13.05 8.63 - 9.85 -13.54 9.43 -10.68 -11.74 7.68 -9.75 -12.06 -!1.27 9.16 -10.32 -13.09 7.27 - 8.93 -13.27 -11.14 -11.18 -16.88 -12.86 -12.04 -15.79 -12.89 -13.53 -13.50 9.62 -10.55 -12.06
-11.93 -12.53 -13.39 -11.00 -13.06 -11.74 -13.23 -12.86 -13.46 -12.58
- 11.42
-8.04
~).216 0.269 0.277 0.340
7.63 -10.01 8.50 5.82 -10.93 -10.84 -10.87 -10.15 -11.59 9.59
1.434 0.680 ~).630 0.952
-13.07 1 . 4 8 -12.39 0.56 -12.97 13.50 -12.05 6.78 -13.08 0.88 -12.57 1 . 0 0 -13.08 1 . 5 7 -11.40 0.93 -13.78 0.73 -12.71 1 . 6 7
0.88 2.77 8.26 - 1.71 - 4.08 - 3.94 -3.15 -
- 3.03
-2.13 - 0.88 0.96
0.932 1.270
4.69 2.11 2.90 6.93 1.00 2.99 10.03 - 4.04 - 1.50 2.10
690
C.-T. Chen et al.
Vol. 28, No. 5
TABLE 6 Deviations between the Estimated Drop Volumes by the Scheele and Meister's Correlation Using d,=l. 15×O.D. and the Experimental Values for Thin Wall Small Nozzles l.D.(cm) O.D.(cm) n dffO.D.
~).018 0.026 0.041 0.069 D.034 0.046 0.072 0.107 1.15 1.15 1.15 1.15
Pure water 10-2(M)NaCI 10-1(M)NaCI 1(M)NaCI 2(M)NaCI 10-2(M)AICIs I 0-t(M)AICI3 I(M)AICIs 2(M)AICI3 Average
2.36 2.26 2.66 5.10 4.19 4.21 3.35 2.75 - 4.70 2.46
- 0.04 - 0.25 - 0.85 1.16 1.69 - 0.31 -0.48 - 4.71 3.59 0.82
5.83 4.57 3.63 5.68 3.94 6.20 1.81 - 0.33 - 0.53 3.42
4.39 2.91 1.91 2.94 2.39 4.04 1.53 0.47 1.54 2.12
0,107 0.147 1.15
0.14
0.14 1.10
0.137 0.216 0,269 0.183 0.277 0.340 1.15 1.15 1.15
0.25 0.44 1.50 1.30 1.14 0.51 1.12 0.91 1.60 0.52
5.06 2.24 3.95 7.03 1.18 1.41 1.41 2.08 0.44 2.76
1.14 0.54 1.10 0.06 1.29 0.46 1.02 0.68 2.04 0.77
0.5 (a)NaC! 0.4 0.3 <
(b) AICI3
/ ~
0 Purewater + 0.01(M] a 0. t(M) XI(M) I 2(M)
~/~/
o Purewater +0.01(M) ~ 0.1(M) I
,
/ , 0 ~
/"
0.2 0.1
0 0.1
0.2
0.3
0.4
0
0.1
0.2
0.3
0.4
0.5
V d EXP ( c m 3) FIG. 5 Comparison between the Experimental Drop Volumes and the Calculated Values by the Scheele and Meister's Correlation (d,=l. 15xO.D. for Thin Wall Small Nozzles, d,=O.D, for Thick Wall Large Nozzles).
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DROP FORMATION FROM FLAT TIP NOZZLES
691
Conclusions
Correct estimation of drop sizes is important to the design of various liquid-liquid contact equipments. Measurements of the sizes of aqueous drops emerged from stainless steel flat tip nozzles were carried out in this work. It is shown that, since the drop liquid wets the nozzle surface preferentially, the existing correlations reported in the literature, such as the equations of Scheele and Meister, and Kagan et al. usually underestimate the drop size by as much as 55%. This is because that these correlations were based on experimental measurements using nozzles with tips filed down to sharp or bevel or a very thin thickness. The deviation of the estimated sizes by the correlation of Kagan et al. differs very little from that of Scheele and Meister. These deviations are not affected by the dissolved salts within the range of concentrations studied. It is also shown in this work that after some adjustment of the value of the characteristic diameter, d,, the correlation of Scheele and Meister can be used to estimate the sizes of aqueous drops emerged from fiat tip stainless steel nozzles within an error of a few percents. This modified correlation of Scheele and Meister covers a much wider range of nozzle size than the original one. For relatively large nozzles of about l cm O.D. with wall thickness between 0.098 and 0.170era, the d, value is taken to be the outside diameter; for small thin wall nozzles of O.D. less than 0.35cm with wall thickness < 0.036cm, the d, value is taken to be 1.15xO.D..
d. F g I.D. i n O.D. R U, Vd /zc Pc Pd Ap o
Characteristic diameter of the nozzle (cm) Drop diameter (cm) Harkins and Brown's correction factor Gravitational acceleration (cm/sec2), 980.665cm/sec 2 Inside diameter of the nozzle (cm) Number of runs Ratio of characteristic diameter to the O.D. of the nozzle Outside diameter of the nozzle (cm) Dimensionless inside radius of the nozzle Dispersed (drop) phase average velocity through the nozzle (cm/sec) Drop volume (cm3) Viscosity of continuous phase (g/cm see, poise) Density of continuous phase (g/cm3) Density of dispersed phase (g/cm3) Density difference (g/era3) lnterfaeial tension (dyne/cm)
Dimensionless grouns
We
Weber number, (Pc + pd,_,__n 2"~dU 2or
692
C.-T. Chen et al.
Vol. 28, No. 5
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