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Coalescence Phenomena and Marangoni Instabilities in Distillation The sizes of satellite droplets which are produced when a surface tension negative system, where the more votatile component has the higher surface tension, is distilled, are reported. A coalescence mechanism is observed, and in some cases secondary droplets are formed. The surface tension driving forces responsible for the initial ejections of the drops into the vapor phase are qualitatively evaluated.
tems, both a t equilibrium and total reflux conditions in an apparatus previously described (Boyes and Ponter, 1970), it was observed that surface tension positive systems exhibited no interfacial turbulence. However, for surface tension negative systems, Le., where the more volatile component has the greater surface tension, satellite droplets were ejected from the liquid surface into the gas phase as a result of hlarangoni instabilities which arise from surface tension differences along the interface, produced by local variations in concentration. The mists produced caused higher mass transfer with accompanying higher efficiencies because of the increase of interfacial area. It was expected that the liquid droplets would fall back into the bulk phase and be assimilated, but photographic studies now show that the returning droplet often bounces on the interface for appreciable periods of time before coalescing into the main body of the liquid. For the surface tension negative system benzene-n-heptane a series of high-speed photographs have been taken showing droplet sizes, heights attained, and times for the droplets to fall back
T h e design of liquid-liquid extraction equipment is most often limited by the rate-controlling drop coalescence. Recently, Spielman and Goren (1970)have carefully reviewed this field and have discussed the methods available, together with the mathematical description, to induce rapid coalescence and separation of the dispersed phase. hlost of the models developed to predict the behavior of single drops and multidrops assume that pure states exist with no interference from stabilizing surfactant agents. This of course precludes any real comparison between these systems and those encountered in industrial operations. A step to remedy this was recently made by Komasawa and Otake (1970),who showed that there was little difference between stabilities of a single drop and of multidrops in a layer in the absence of stabilizing agents, but that stability of drops in a layer was far less than that of a single drop in the presence of the agent. We now wish to show that an analogous mechanism accounts for increased efficiencies of some systems undergoing distillation. When measuring contact angles of binary liquid sys-
Table I Drop diameter, m m
1 2 3 4a 4b
5 6a 6b 7a
7b 7c 8 9a 9b 1Oa 10b 1oc 10d
11
1.024 0.622 0.145 0,622 0.702 0.496 0.66 0.666 0.383 0.465 0.238 0.279 0.228 0.124 0.362 0.362 0.372 0.186 0.560
Angle of ejection, deg
80 70 70 80 80 65 87 85 75 75 75 85 85 30 60 63 65 65 75
Initial velocity, u , cmfsec
24.9 36.54 15.66 44.38 14.94 32.48 24.56 24,56 40.63 15.23 15.23 34.47 39.39 39.24 22.66 18.14 16.24 21.66 45.7
Ma55 of drop, g
x
104
4.16 0.73 0.012 0.642 1.1 0.4 1.05 1.05 0.15 0.37 0.053 0.083 0,047 0.0075 0.19 0.19 0.2 0.02 0.65
Area of initial disturbance, cm2
Surface tension difference, dynfcm
Mode of coalescence
0,264 0.222 0.0755 0.3029
0.485 0.218 0.02
b b b
0,1093 0.1251 0.1346
o,2081 0,2531 0.188
0'1°
0,0765 0.0594
t
0.064
O.O6l1: 0.0145
b a
b bl c a C
0.107 b, c
0.246
0,279
b
Ind. Eng. Chem. Fundom., Vol. 10, No. 4, 1971
641
P
0
5
2 DROPLET M A I S
I
10.
l
'imr.
Figure 1 . Plot of surface tension differences vs. droplet mass
(magnification X Z O ~
Figure 2. Multiple bouncing of droplet on surface without coalescence (benzene-n-heptane; magnification X5)
Figure 3. Droplet bouncing once on surface before assimilation (magnification X 10)
to the liquid surface which enables the initial velocity to be computed. T o date there are no methods available for determining the surface tension of binary systems under distillation conditions, ie., for a boiling liquid undergoing mass transfer. This information is necessary if a complete analysis of the phenomenon is to he made. However, an approximate value of 642 Ind.Eng. Chem.Fundom.,Vol. 10, No. 4, 1971
the surface tension differences causing the drop ejection can he calculated, if it is assumed that the kinetic energy comes from the surface forces and that none comes from the gas and liquid motions. The initial velocity of the drop, u, can be calculated knowing the angle of ejection, e,the vertical height attained, h, with the corresponding time, t, by the equation
The energy requirement for the droplet t o leave the interface will he muz//2, which will be supplied to produce the surface tension engine via the Marangoni effect; this is equivalent to A . A
