Oscillating Drops

O. Liquid drops in immiscible liquid, free rise or fall, discontinuous phase coefficient, oscillating drops... 

Fig. 9.13 Flooding point diagram of countercurrent extractors. The drawn lines for six different Ar values are valid for circulating drops. The dotted lines for three different values are valid for oscillating drops. (From Ref. 2.)... 

For the mass transfer on the inside of the drop the equation by Handlos and Baron [20] for oscillating drops ... 

The mean drop diameter should be fixed in the range of the transition region of circulating to oscillating drop, since this gives the most favorable compromise between the possible transfer area per unit volume of the column and mass transfer intensity. 

In order to allow for a variation of interfacial area from that of an equivalent sphere, the eccentricity of the ellipsoidal drop must be taken into account. The area ratio of Eq. (44) does not exceed unity by a serious amount until an eccentricity of 1.5 is attained. An experimental plot of eccentricity as ordinate vs. equivalent spherical drop diameter as abscissa may result in a straight line (G7, Kl, K3, S12). A parameter is yet to be developed by which the lines can be predicted without recourse to experiment. Eccentricity is not an accurate shape description of violently oscillating drops and should therefore be used only for drop size below the peak diameter (region B of Fig. 5). 

With all three types of oscillations superimposed, the final result has a random appearance. Since a sphere has the smallest area per unit volume, all oscillatory movements cause an alternate creation and destruction of interfacial area. The rate of mass transfer is thereby enhanced for oscillating drops. Since surface stretch due to oscillations is not uniformly distributed, all such oscillations produce interfacial turbulence (see Section VII, E). 

Violent oscillations of the axially symmetric type can be induced in single drops formed at a nozzle. Drops of chlorobenzene (Dg = 0.985 cm) were so formed, and allowed to fall in water. At about five inches below the nozzle two types of rupture were observed. A small droplet was formed at the front and hurled ahead of the drop by the next oscillation. A second mode of formation caused a droplet to be formed by inertial pinch at the rear of the oscillating drop. This rear-formed droplet was always larger than the very small one formed in front. There were, on occasion, two successive pinch-formed droplets from the rear. In a few instances both front and rear formation occurred, as shown in Fig. 13 in selected... 

Many investigators base mass transfer coefficients upon the area of the volume-equivalent sphere, especially for oscillating drops ... 

Fig. 7.16 Fractional approach to equilibrium for circulating and oscillating drops in gases. Data of Garner and Lane (G4).

The assumption of transfer by a purely turbulent mechanism in the Handlos-Baron model leads to the prediction that the internal resistance is independent of molecular diffusivity. However, such independence has not been found experimentally, even for transfer in well-stirred cells or submerged turbulent jets (D4). In view of this fact and the neglect of shape and area oscillations, models based upon the surface stretch or fresh surface mechanism appear more realistic. For rapid oscillations in systems with Sc 1, mass transfer rates are described by identical equations on either side of the drop surface, so that the mass transfer results embodied in Eqs. (7-54) and (7-55) are valid for the internal resistance if is replaced by p. Measurements of the internal resistance of oscillating drops show that the surface stretch model predicts the internal resistance with an average error of about 20% (B16, Yl). Agreement of the data for drops in liquids with Eq. (7-56) considerably improves if the constant is increased to 1.4, i.e.. 

P. Liquid drops in immiscible liquid, free rise or fall, discontinuous phase coefficient, oscillating drops T L,d,0icdp Nsh- 032(pA (a3g ph010 [E] Used with a log mean mole fraction difference. Based on ends of extraction column. Nfedrop = 411 < < 3114 dp = diameter of sphere with volume of drop. Average absolute deviation from data, 10.5%. Low interfacial tension (3.5-5.8 dyn), [ic < 1.35 centipoise. [141] p. 406 [144] p. 435 [145]... 

The mass-transfer coefficient in each film is expected to depend upon molecular diffusivity, and this behavior often is represented by a power-law function k . For two-film theory, n = 1 as discussed above [(Eq. (15-62)]. Subsequent theories introduced by Higbie [Trans. AIChE, 31, p. 365 (1935)] and by Dankwerts [Ind. Eng. Chem., 43, pp. 1460-1467 (1951)] allow for surface renewal or penetration of the stagnant film. These theories indicate a 0.5 power-law relationship. Numerous models have been developed since then where 0.5 < n < 1.0 the results depend upon such things as whether the dispersed drop is treated as a rigid sphere, as a sphere with internal circulation, or as oscillating drops. These theories are discussed by Skelland [ Tnterphase Mass Transfer, Chap. 2 in Science and Practice of Liquid-Liquid Extraction, vol. 1, Thornton, ed. (Oxford, 1992)]. 

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