EFFECTS OF KINEMATIC VISCOSITY AND SURFACE TENSION ON GAS ENTRAPMENT RATE OF AN IMPINGING LIQUID JET

EFFECTS OF KINEMATIC VISCOSITY AND SURFACE TENSION ON GAS ENTRAPMENT RATE OF AN IMPINGING LIQUID JET Minoru KUMAGAIand Kazuo ENDOH Department of Chemical Process Engineering, Hokkaido University, Sapporo 060 The effects of the kinematic viscosity and the surface tension of aqueous solution on the gas entrainment rate of an impinging liquid jet were studied experimentally, using a straight cylindrical nozzle with a nozzle cap. The three critical jet velocities at three transition points, respectively, on the gas entrainment curve increase with an increase of kinematic viscosity of the liquid. The gas entrainment rate of an impinging liquid jet tends to decrease in the initial entrainment region, while it tends to increase in the low jet velocity region, as kinematic viscosity increases. In the high jet velocity region, the effect of kinematic viscosity on gas entrainment rate is insignificant. The effect of the surface tension of the liquid on the gas entrainment rate and the three transition points is negligible. Intro duction The liquid jet can be considered to be usable for gas-liquid contactors because a number of fine bubbles are generated by impinging the liquid jet on the liquid surface. From this point of view, several experimental studies have been madeto measure the gas entrainment rate of a water jet in recent years1'2-5"75. Gas-liquid contact is generally conducted using a liquid with higher kinematic viscosity or lower surface tension than those of tap-water, i.e., NaOH- CO2, and Na2CO3-NaHCO3-CO2 systems. In such a case, it is necessary to measure the gas entrainment rate of the liquid jet. Nevertheless, when using such impinging liquid jets, it can be observed that a great number of fine bubbles are generated, and they travel around inside the bath. Consequently, it is not easy to measure the gas entrainment rate by use of a "bubble trap"5'6! to collect bubbles. It follows from the above reasons that experimental studies on the gas entrainment rate of such a liquid jet have rarely been reported. Our previous paper3) dealt with the gas entrainment rate of an impinging water jet. In the present work we have measured the gas entrainment rate of an impinging liquid jet with higher kinematic viscosity or lower surface tension by use of the same apparatus as in the previous work3). The purpose of this investigation is to make clear the effects of kinematic viscosity and surface tension Received February 3, 1982. Correspondence concerning this article should be addressed to M. Kumagai. of the liquid on the gas entrainment rate. 1. Experimental Procedure The detailed arrangement of the experimental apparatus was presented in our previous paper3}. The apparatus consisted of a plunger pump, a compressor, a tank, straight cylindrical nozzles (LJD=50) over a range of inside diameters between 2.00-10~3 and 5.75-10~3 m with a nozzle-cap, and a bath of height 0.73 m and section 1.0m by 0.3 m. The surface tension of liquid (aqueous solution) was decreased by adding a surface-active agent, Tween 80 (Wako Pure Chemical Industries, Ltd.), to tap-water. The values of surface tension ranged from 7.33à"10~2 to 4.562-10~2 N/m. The viscosity of liquid was increased by adding corn-syrup to tapwater. The values of kinematic viscosity ranged from 1.01-10-6 to 6.04-10"6m2/s. The surface tension and viscosity of the liquids were measured with a Du Noiiy Tensiometer and an Ostwald Viscometer, respectively. The entrained gas was air at room temperature. The measurements of liquid and gas flow rates were madeby orifice meters. For each run the temperature of liquid was 23dz2 C, and that of tap-water was 18±1 C. The measurements of gas entrainment rate were conducted by the following procedure. As the liquid jet entrained gas inside the nozzle-cap, the liquid level inside the nozzle-cap became higher than that in the bath. Then it was necessary to supply the same amount of gas as the entrained gas into the nozzle-cap in order to keep the liquid level inside the nozzle- VOL. 15 NO. 6 1982 427

Pi, P2 and P3 indicate transition point on each gas entrainment curve. Definition of transition point (Pi, P2, P3) is also show in this figure. Surface tension 0) is 7.33à"10~2 N/m at vi=1.01-10-8m2/s, 6.85-10"-2 N/m at ^=3.17-10-6m2/s, and 6.265-lO"2 N/m at ^=6.04-10-6 m2/s. Fig. 1 Dependence of gas entrainment rate (G) on kinematic viscosity (vl) of liquid at >=3.02 10~3 m cap equal to that in the bath3). The amount of gas supplied into the nozzle-cap in a unit time was defined as the gas entrainment rate (G). 2. Results and Discussion 2. 1 The effect of kinematic viscosity on gas entrainment rate Figures 1 and 2 show the dependence of the gas entrainment rate on the kinematic viscosity (vt) of liquid, at constant nozzle diameter (D), constant jet length (Lj) and constant angle (a) between liquid jet discharge and bath surface. As the velocity of the liquid jet increases, the slope of the gas entrainment curve varies and the curve can be devided into four distinct regions3\ as follows: I) initial entrainment region, II) low jet veolocity region, III) transition region and IV) high jet velocity region at three transition points, Pl5 P2 and P3 as shown in Fig. 1. The definition of the three transition points is also shown in Fig. 1. Similarly, from Fig. 2 the gas entrainment curves obtained by use of the viscous liquid jets consist of four distinct regions. It can be seen from these figures that the three transition points (Pi, P2, P3) on the gas entrainment curve tend to shift in the direction of the high jet velocity with an increase of kinematic viscosity. Consequently, in region I the gas entrainment rate decreases, and in region II it increases with an in- Fig. 2 Dependence of gas entrainment rate (G) on kinematic viscosity (vt) of liquid at Z)=2.00 10"3 m crease of kinematic viscosity. In region IV, each of the gas entrainment curves gives almost the same value at the constant liquid jet velocity. Hence, the effect of kinematic viscosity on them is insignificant in region IV. It was noted in our previous paper3) that a gas entrainment curve with the form of an "S" curve was obtained where the water jet length (L3) was short and the angle (a) was small. In this work, using viscous liquid jets, this result was clearly obtained under most experimental conditions. The gas entrainment rate tends to increase as the liquid jet length (L3) increases and as the angle (a) decreases. These effects are shown in Figs. 3 and 4, respectively. The forms of these curves are almost the same. 2. 2 The effect of surface tension on gas entrainment rate Figure 5 shows the experimental results for the gas entrainment rate obtained by use of liquids containing the surface-active agent. The dependences of the gas entrainment rate and the three transition points on surface tension are inconsiderable from this figure, although the value of the surface tension of liquid was up to about 40 per cent lower than that of tap-water at 18 C. However,the gas entrainment rate increases somewhatwith surface tension at liquid jet velocities below about 2m/s. Each equation of Ohyama et a/.6>, gas Ciborowski entrainment et al^ rate and De Frate et al2) for the comprises the dimensionless groups {We, Oh) associated of liquid. Consequently, with the surface it is concluded tension that our experimental result is different from those of other authors1'2'5). JOURNAL OF CHEMICAL ENGINEERING OF JAPAN

Fig. 3 Effect of jet length (Lj) on gas entrainment rate (G) at vz=3.17 10 6 m2/s 2. 3 Transition points on the gas entrainment curve Three transition points tend to shift in the direction of the high jet velocity with an increase of kinematic viscosity of liquid, as can be seen from Figs. 1 and 2. The influence of surface tension on these points is inconsiderable, as shown in Fig. 5. Van de Sande et al.7) reported that the value of starting velocity of gas entrainment is nearly 2 m/s, and hence they determined the range of velocities in region II from 2 to 5m/s. However, it can be seen from the present result and our previous paper3] that two critical velocities (Vj*, K,*) are not held constant, but depend on the experimental conditions (D, Lj9 a, vi). Consequently, we cannot locate the range of velocities in region II between 2 and 5 m/s. Van de Sande et al.6) also reported that the transition point P3, the transition point from region III to IV, corresponded to the velue of the Weber number (pav2d/a) of 10, based on the air density. Table 1 gives a list of the values of the Webernumbers at the transition point P3. It is obvious from Table 1 that each value of the Webernumbersat the transition point P3 deviates from 10 with the variation of experimental conditions. The effect of surface tension on the Weber number at transition point P3 is shown in Table 2. The value of the surface tension of liquid was decreased by adding the surface-active agent to tap-water. When the kinematic viscosity of liquid was increased, the surface tension decreased. The two sets of data obtained by use of these liquids are given in Table 3. The values of the Weber numbers in Tables 2 and 3 increase with decreasing surface tension, and no value is equal to the constant value of 10. Defining the value of the Weber number at the transition point P3 as 10 is questionable. We have VOL. 15 NO. 6 1982 Fig. 4 Effect of angle (a) between liquid jet discharge and bath surface on G at Vi=6.04-10-6 m2/s Fig. 5 Dependence of gas entrainment rate (G) on surface tension (a) of liquid at D=5.75 10~3 m and D=3.02 10-3m examined the effects of kinematic viscosity and surfao tension of liquid on the three transition points. Th< following correlations were derived from the least squares fits of the data. These expressions correlat< the critical Reynolds number, defined as Re*= V*D/vi, with the nozzle inside diameter (D), th< liquid jet length (L,-), the angle (a) and the kinemati< viscosity (yi) of liquid. 42<

Table 1 Comparison between our and Van de Sande's data on Weber number at transition point P3 (surface tension is 7.33 à" 10"2 N/m) Z)=2.00-10-3m Z>=3.02-10-3m D=5.75-10-3m D=8.04-10-3m Lj [m] a [ ] We [~] Lj [m] a [ ] We L, [m] a [ ] 0^, [m] a [ ] ^ 0.02 60 6.66 0.06 20 6.03 0.06 20 ll.49 0.08 20 22.09 0.06 20 5.16 30 4.98 30 7.52 30 10.28 30 4.37 45 6.03 45 7.69 45 9.59 45 8.45 60 ll.21 60 7.35 60 8.49 60 7.43 0.09 20 6.03 0.115 20 13.22 0.16 20 16.95 0.10 20 5.41 30 8.55 30 7.35 30 13.27 30 5.16 45 9.08 45 6.07 45 8.75 45 6.47 60 8.42 60 7.69 60 7.67 60 6.94 0.15 20 5.28 0.175 20 10.46 0.24 20 13.81 0.14 20 5.58 30 6.25 30 10.46 30 10.75 30 5.58 45 7.79 45 9.49 45 ll.48 45 6.47 60 6.94 60 10.46 60 8.49 60 8.45 0.21 20 6.59 0.29 20 10.46 0.40 60 10.28 0.20 20 5.49 30 7.79 30 ll.49 30 5.84 45 8.16 45 8.57 45 5.16 60 9.09 60 13.67 60 6.29 0.30 20 7.42 0.40 20 13.67 Vq a Qa, ~7^ 0.23 20 5.32 30 7.06 30 12.55 j^f*******1> 30 5.58 45 8.41 45 ll.49 L>~ r'\m> ^; 1 45 4.75 60 7.79 60 ll.91 D [m] We ^ 60 5.58 0.40 60 7.42 0.575 60 12.55 3.0-10~3 9.7 0.30 60 7.93 0.50 60 9.09 3.8-1O"3 9.0 0.40 60 6.47 0.60 60 8.17 4.9-10"3 9.0 0.50 60 6.02 0.70 60 6.94 6.8-10"3 9.1 0.60 60 6.47 0.80 60 5.92 1.0-10"2 10.5 Table 2 Effect of surface tension on Weber number at transition point P3 D[m] Lj[m) a[ ] <j-102[n/m] We 3.02-10"3 0.06 60 7.33 ll.21 6.151 13.37 5.840 14.08 5.589 14.71 5.003 16.43 4.562 18.02 5.75-10"3 0.06 30 7.33 7.52 4.562 ll.28 5.75-10"3 0.29 30 7.33 ll.49 4.562 15.25 Jf^ef=3.ll X lo1^0-63^0-091^!! a)-0.187j,r0.628 (^ Re*=3.21 X 102Z) -832L5-128(sin ^-o.soi^-o^ (2] Re*=1.ll X 10\D -70^L5-053(sin a)-0-052vr0-890 (3; The three sets of the critical Reynolds number (Re? Ref, Re$) are plotted against each of the parametei groups in Figs. 6, 7 and 8, respectively. Solid lines in these figures show the results of correlations (1) (2) and (3). From these figures, each correlation oj our own data with Eqs. (1), (2) and (3) seems to be reasonable. If the value of the Reynolds number (V-D/vt) h lower than that of the critical Reynolds numbei Re? calculated from Eq. (1), the gas entrainment rate exists in region I. If the value is between those oi Re? and Ref calculated from Eqs. (1) and (2), respectively, it exists in region II. If the value is between those of Ref and Ref calculated from Eqs. (2) and (3), respectively, it exists in region III, and if the 430 Surface tension (a) is 7.33-10-2N/m at vz=1.0m0-6m2/s, 6.85-10-2N/m at vt= 3.17-10-6m2/s and 6.265à"10~2N/m at Vl= 6.04-10-6 m2/s. Fig. 6 Critical Reynolds number Re^ as a function of nozzle inside diameter (Z>), liquid jet length (L^, angle (a) and kinematic viscosity (vl) at transition point P1# value is greater than that of Ref calculated from Eq. (3), it exists in region IV. 2. 4 Experimental equations for gas entrainment rate It can be generally assumed that the factors which influence the gas entrainment rate are the liquid jet velocity (F), the nozzle diameter (D), the liquid jet length (Lj), the angle (a) between liquid jet discharge and bath surface, the kinematic viscosities of gas (vg) and liquid fa), the densities of gas (pg) and liquid (pi) and the surface tension of liquid (a). Therefore, we assumed the following dependence. JOURNAL OF CHEMICAL ENGINEERING OF JAPAN

Table 3 Weber number at transition point P3 obtained using viscous liquid (7=6.85-10-2 N/m <T=6.265-10-2N/m!,=3.17-10-6 m2/s v=6.04-10-6 m2/s D [m] Lj [m] a [ ] We D [m] Lj [m] a [ ] JFe 5.75-10"8 0.06 30 8.59 5.75-10"3 0.06 30 12.01 60 7.69 0.06 60 7.83 0.115 30 ll.63 0.115 30 12.95 60 8.59 0.175 30 12.95 0.175 30 13.19 0.29 30 14.69 0.29 30 13.67 3.02-10"3 0.06 30 10.16 3.02 10"8 0.06 30 17.86 0.09 30 12.49 0.09 30 21.06 0.15 30 ll.21 0.15 30 21.06 0.21 30 12.82 0.21 30 25.72 2.00-10"3 0.06 20 6.44 2.00-10"3 0.06 20 ll.29 30 5.69 30 ll.97 45 5.26 45 10.52 60 5.17 60 12.65 0.10 30 6.16 0.10 30 ll.16 60 6.73 60 ll.97 0.14 30 6.15 0.14 30 13.79 Fig, 7 Critical Reynolds number Re2* at transition point P2 G=f(V, D, L3, sina, vg, vu pg9 pu a) (4) The effects of F, D, L3- and sin a on the gas entrainment rate were already examined using the water jet3) and the effects of vx and a are discussed in this paper. According to the previous discussions for regions I and II, we have derived the dependences of the gas entrainment rate as a function of experimental conditions from the least-squares fits of the data, as follows : Region I : G=1.0x lo-5(102 - F)1-e5I)"0-17DB-85LJ--15(sin a)-0-27yr0-95 Region II : G=1.58 X lo-2^1-67^1-06^-3^^ a)-o.8ovo.ii (6) Figure 9 shows our experimental data in region I together with the solid line calculated from Eq. (5). Figure 10 shows the experimental data of the present VOL 15 NO. 6 1982 (5) Fig. 8 Critical Reynolds number ReB* at transition point P3 authors and those of Van de Sande6>7) in region II together with Eq. (6). Since the data points in Figs. 9 and 10 follow each solid line, the agreement between experimental results and calculated values from Eqs. (5) and (6) is reasonable. In region IV, the effects of kinematic viscosity and surface tension of liquid on the gas entrainment rate were negligible. Consequently, the gas entrainment rate can be evaluated from the following two equations, determined with respect to the water jet in our previous paper3}. Region IV: L3fD<70: G-3.0X lo-^^f2)-^//))0-35 X (sin a)-0-3 (7) Lj/D>70: G=5Ax 10~'(p^VtyiLJD)0'7* X (sin a)-0'2 (8) The comparison of Eq. (7) with the data of the present authors and Van de Sande6) is shown in Fig. ll 431

Surface tension 0) is 7.33à"10~2 N/m at Vl= 1.0M0-6m2/s, 6.85à"10-2 N/m at w=3.17-10-6m2/s and 6.265 10"2 N/m at Vl=6.04-10-6 m2/s. Fig. 9 Correlation of gas entrapment rate (G) with Eq. (5) in region I Surface tension (a) is 7.33à" 10~2 N/m at Vi= 1.0M0-8m2/s, 6.85-10"2N/m at ^=3.17-10-6 m2/s and 6.265-10"2 N/m at ^=6.04-10"6 m2/s. Fig. 10 Correlation of gas entrainment rate (G) with Eq. (6) in region II to examine the fitness of the experimental result with Eq. (7). Since the correspondence is very good, the gas entrainment rate in region IV can be evaluated from Eqs. (7) and (8), respectively, depending upon the ratio of jet length to nozzle inside diameter. Also, the influence of kinematic viscosity and surface tension of liquid is insignificant. From the viewpoint of industrial application it must be more valid to operate the gas-liquid contactor in region IV than in other regions since a large number 432 Surface tension (a) is 7.33à"10 2 N/m at vi= 1.01-10-8m2/s, 6.85-lO"2N/m at ^=3.17-10-6m2/s and 6.265à"10"2 N/m at y =6.04-10-6 m2/s. Fig. ll Correlation of gas entrainment rate (G) with Eq. (7) in region IV at Lj/D^70 of fine bubbles are generated by plunging the turbulent liquid jet into liquid. Photographs of the gas entrainment phenomenaof an impinging water jet were shown in our previous paper4). Whenthe kinematic viscosity of liquid increases or the surface tension of liquid decreases in comparison with those of tap-water, it is difficult to measure the gas entrainment rate by use of a "bubble trap" collecting bubbles because a large number of fine bubbles are generated in the bath. In the present study measurement of the gas entrainment rate of an impinging liquid jet was made possible by use of the nozzle with a nozzle cap. Conclusions The gas entrainment rate of an impinging liquid jet was measured under experimental conditions in which the increased kinematic viscosity of aqueous solution was or the surface tension of aqueous solution was decreased, respectively. The experimental results are summarized as follows: 1) The gas entrainment curve consists of four regions. The three critical Reynolds numbers on that curve were correlated with the experimental conditions, and Eqs. (1), (2) and (3) were obtained. 2) The influence of kinematic viscosity on the critical Reynolds numbers was significant, but that of surface tension was negligible. 3) The gas entrainment rate decreased in region I but increased in region II with an increasing kinematic JOURNAL OF CHEMICAL ENGINEERING OF JAPAN

viscosity. In region IV the influence of kinematic viscosity on the gas entrainment rate was negligible. 4) The influence of surface tension on the gas entrainment rate was negligible all over the whole range of liquid jet velocities. Nomenclature D = nozzle inside diameter G = volume flow rate of entrained gas Lj = length of liquid jet Ln = length of nozzle Oh = Ohnesorge number, vi/vpida [m] [ms/s] [m] [m] Pi, P2 P3 = transition points on gas entrainment curve Re = Reynolds number, VD/vi itei*, Re2*, Re$* = critical Reynolds numbers V^DIvu V2*D/vi and VB*D!vi corresponding to Pi, P2 and P3, respectively [m/s] V = liquid jet velocity at nozzle exit Vi*, V**, Vz* = critical jet velocities at transition points, [m/s] Pl5 P2 and P3, respectively We = Weber number, pav2d/a a = angle between liquid jet discharge and bath surface ==viscosity =density =surface tension = kinematic viscosity <Subscripts> a =air / = liquid [Pa-s] [kg/m 3] [N/m] [m2/s] Literature Cited 1) Ciborowski, (1972). J. and A. Bin: Inzynieria Chemiczna, 2, 557 2) De Frate, L. and F. Rush: Selected Papers, Symposium- Part II, 64th National Meeting of AIChE., New Orleans, Louisiana, March (1969). 3) Kumagai, M. and H. Imai: Kagaku Kogaku Ronbunshu, 8, 1 (1982). 4) idem: ibid., 8, 510 (1982). 5) Ohyama, Y., Y. Takashima and H. Idemura: Kagaku Kenkyusho 6) Van de Hokoku, Sande, E. 29, and 344 (1953). J. M. Smith: Chem. Eng. Sci., 28, 1161 (1973). 7) idem: ibid., 31, 219 (1976). (Presented at Toyama Meeting of The Soc. of Chem. Engrs., Japan, July, 1980.) VOL, \5 NO. 6 1982 433