Handlos and Baron have proposed a mathematical model which describes the internal mass transfer mechanism for droplets that have a special type of turbulent internal circulation ( 1 ) . The turbulence is in the form of random radial vibrations superimposed upon internal streamlines which are in the form of a system of tori. These fluid dynamic conditions are most likely to be encountered in the high-droplet Reynolds number-nonoscillating region. A detailed description of the model and the assumptions involved are given elsewhere (1, 2 ) . The model has been compared (with approximate solutions used) with experimental data for single droplet systems (1 to 4 ) , and its use has also been suggested for multiple droplet systems (5, 6). The object of this work is to obtain a more exact solution to the Handlos and Baron model which is rigorously applicable for short (and long) contact times and finite continuous phase resistances. This more exact solution (along with various approximate solutions) will then be compared with some of the single droplet extraction data which have been presented in the literature.Solutions to droplet extraction models can be presented either in terms of droplet extraction efficiencies or in terms of mass transfer coefficients. These two performance indices for extraction are related by the following expression APPROXIMATIONS FOR LARGE CONTACT TIMESThe approximate solutions of Handlos and Baron (1) and Wellek and Skelland ( 2 ) , consider only the first term in the above series summation; thus their solutions are limited to large contact times when only the first term is dominant. Furthermore, in both papers (1, 2 ) it is tacitly assumed that 2B12 is equal to unity. Thus, Equations (1) and (2) ma be solved for K d , subject to the above assumptions a n l therefore, for large contact times In terms of the droplet extraction efficiency, these large contact time solutions are expressed asThe Rayleigh-Ritz variational method was used in references 1 and 2 to solve for values of Handlos and Baron considered the case of zero continuous hase resistance and found A1 = 2.88. Wellek and Skel P and considered the effect of various finite continuous phase resistances on the value of hl (see Table 1