Mass transfer from large oscillating drops

Abstract

A mass transfer model for vigorously oscillating single liquid drops moving in a liquid field has been developed with the concepts of interfacial stretch and internal droplet mixing. The model takes into account both amplitude and frequency of drop oscillations. Experimental values of fraction extracted were predicted with an average deviation of 15%. Oscillations break up internal circulation streamlines and a type of turbulent internal mixing is achieved.The contact of large drops of a dispersed liquid phase with a continuous liquid phase roceeds in fain distinct fect the extraction operation. These four major zones for mass transfer in the lifetime of such Iarge drops are: formation of the discrete drops while they are still resident on the drop-forming device, an acceleration period immediately after the drops leave the nozzle or orifice, during the free rise (or fall) of the drops at a steady state slip velocity, and in a zone of flocculation and coalescence at the end of their vertical travel through the equipment (or stage) under consideration.We are concerned here only with drops in the freely falling zone and of such a size that they will exhibit a cyclic, oscillatory motion as they move through the continuous phase.The literature dealing with mass and heat transfer between fluid particles and their fluid surroundings is very extensive (9, 15, 18, 19). Most studies have tried to isolate the resistances to such transfer into an internal and an external one, relative to the phase interface. The resistance to transfer, whether internal or external to the droplet surface, depends upon the motion of the fluid particle. Widely ranging magnitudes of resistance have been reported for drops which behave as rigid spheres, those performing like nonoscillating fluid ( circulating) bodies, and those exhibiting a fully oscillating regime. Oscillating drops show a far greater rate of transfer than any other type. Summaries of the published work on the continuous (external) phase resistance are readily available (4, 13, 17, 18). Garner and Tayeban (3) studied the effect that droplet oscillation had on the continuous phase resistance.The dispersed phase resistance has been analyzed on the basis of three mathematical models. One of these, developed by Newman (14), is based upon a rigid sphere with no internal motion and leads to the expression stages if a spray or perforated p P ate tower is used to efWhen resistance to transfer in the continuous phase is zero and laminar circulation patterns which can be described by the Hadamard ( 5 ) streamlines are present, the result of Kronig and Brink (10) can be applied:Handlos and Baron (6) superimposed a turbulence due to random radial motion upon a circulatory pattern; this model yields, for zero resistance in the continuous phaseThe numerical values of An and 1 , in Equations (2) and ( 3 ) are not identical. Previous workers (1, 3, 8, 12, 19) have used these three theoretical models, combined with one of the various empirical equations for the continuous phase resistance, to...

Handlos and Baron model: Short contact times

“…On the basis of their observations, Rose and Kintner have proposed an extraction model for vigorously oscillating droplets which assumes complete mixing in the droplet for every oscillation cycle and which also considers the effect of interfacial stretch (11 ) . Angelo et al.…”

“…The partial differential equation and boundary conditions describing the Handlos and Baron model with continuous phase resistance [see Equations ( l o ) , ( 11) , and (12) of reference 21 were solved b using the implicit Olson (7). All computational details are given in reference 16.…”

A study of mass transfer from single large oscillating drops

“…The Garner and Tayeban [8] correlation has been widely used for the prediction of the continuous phase mass transfer coefficient [3,51 and is believed to be valid for this study.…”

“…Rose and Kintner [3] assumed that film theory and surface renewal criteria apply to the droplet/continuous phase boundary. They also used Garner and Tayeban's [8] em-pirical correlation for non-oscillating droplets to calculate the continuous phase mass transfer coefficient.…”

Stability analysis of interfacial circulation on a static liquid drop with forced internal circulation

“…This does not permit the neglect of either viscous or inertial terms in solving the equations of motion. Interestingly enough» however, Hadamard's solution which does not consider the inertial terms, nevertheless describes flow patterns observed within falling drops at Reynolds numbers well above 200 (69). Combining these features in a single problem makes the problem too difficult to be manageable.…”