Mass transfer oscillating drops

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. 

Finally, it must be noted that tensides that are adsorbed at the interface cause a stiffening of the interface. They hinder or even stop the inner circulation and oscillation of drops, and reduce the mass transfer intensity. Moreover, they form a barrier against the mass transfer, so that a further resistance term should be considered in the overall mass transfer process [28] in Eq. (9.33). Since the nature and concentration of tensides in industrial processes cannot be predicted, such phenomena cannot be taken into consideration during equipment calculations. 

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). 

Secondary motion plays an important role in increasing drag (L7) and in promoting heat and mass transfer from bubbles or drops. The onset of oscillations corresponds approximately to the maximum in Uj d ) and minimum in... 

C )(Re) curves for drops and bubbles (Bll, El, E2, T4). The influence of oscillations on heat and mass transfer is discussed in Section III. 

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

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.. 

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)]. 

Drop circulation plus oscillation Empirical, mass transfer liquid-liquid... 

By viscous interaction with the continuous phase, oscillating shape variations of liquid drops and gas bubbles occur, and for Re 1. mobile surface fluid particles in free-rising or falling conditions move in a wobbling or spirial-like manner, which has a marked influence on mass transfer rates. As before, we can arrive at different correlations for different bulk flow regions. These are summarized below ... 

A decisive parameter is the time of contact. In pulsed sieve tray colunms the time of instationary mass transfer is equal to the residence time of the dispersed phase in the space between two trays. In agitated colunms, the residence time in an agitation cell has to be taken. However, the application of the above equations to packed columns is difficult. Often recommended is the correlation of Handlos and Baron (1957) which has been developed and verified for oscillating drops ... 

By comparison to solid particles, drops are not only subject to deformation but also to internal circulation and oscillation. This affects not only the values of the continuous but also of the dispersed phase mass transfer coefficients. Relevant theoretical and empirical correlations are collected in literature (24, 25). For oscillating drops the equations of Clift et al. (26) give usually a good prediction (27)... 

The correlations currendy preferred for predicting the individnal mass transfer coefficients in Eq. (7.4-13) are listed in Table 7.4-1 for systems nominally free from surface-active contamination. Criteria are available for detecting whether drops of a given qratem are str nant, drcuhting, or oscillating. 

Figure 12.2 Schematic diagram of an apparatus consisting of two CSTRs for studying physically coupled oscillating reactions. A needle valve controls the flow between the reactors. Inputs to the reactors are independently controlled. Drop detectors ensure that liquid flows out of the two reactors at the same rate so that there is no net mass transfer from one to the other. Reprinted, in part, with permission from Crowley, M. F. Epstein, I. R. 1989. Experimental and Theoretical Studies of a Coupled Chemical Oscillator Phase Death, Multistability, and In-Phase and Out-Of-Phase Entrainment, J. Phys. Chem. 93, 2496-2502. CC 1989 American Chemical Society.)...

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