The mechanism of mass transfer in agitated liquid-liquid systems has been considered, and it was found that existing procedures for calculating stage efficiencies were deficient in that they did not take two aspects of droplet behaviour into account. Firstly that in flow systems the drops would exhibit a residence time distribution similar to that observed for liquid particles in well mixed homogeneous systems. Secondly, that the mechanism of mass transfer could be altered by repeated coalescences and redispersion of the drops. For the case when coalescence did not occur, design equations were obtained by assuming that mass transfer took place by molecular diffusion inside the drops, which behaved like rigid spheres, with a resistance to mass transfer in the continuous phase. The drops were assumed to exhibit the residence time distribution characteristic of a perfectly mixed system. When coalescence took place, it was shown that the mechanism of mass transfer was altered. Design equations were obtained under the assumptions that the free time between coalescences was small compared to the nominal residence time for the system, and was sufficiently short to enable application of the penetration theory. Stage efficiencies calculated from these equations were compared with experimental data, taken from the literature, for the extraction of benzoic acid from water with kerosine dispersed in continuous-flow agitated tanks. It was necessary to estimate coalescence frequency for application of the equation derived for rapid coalescence. It was concluded that the experimental results exhibited a behaviour intermediate between the two extreme conditions of rapid coalescence and no coalescence.
A theoretical study was made of the coalescence of drops suspended in a liquid in a homogeneous isotropic turbulent flow. It was assumed that the frequency of coalescence could be calculated from the product of two independent terms, one giving the collision frequency, the other the fraction of collisions resulting in coalescence. For the first, it was assumed that the motions of droplets suspended in a turbulent flow field could be described as a diffusion process, and that an equation derived by Smoluchowski for the rate of coagulation of colloidal particles could be applied by inclusion of the turbulent coefficient of self-diffusion of the drops. It was shown that the diffusion time was likely to be short in relation to the Lagrangian integral time'", scale for the turbulent flow. It was assumed that since the densities of drop and field phases were similar, the turbulent diffusion coefficient for dispersed particles was the same as that for elements of the continuous phase itself, and the appropriate relations were obtained from the theory of diffusion in turbulent flow. These were inserted into the Smoluchowski equation to obtain a relation for the collision frequency. A model for coalescence behaviour was developed to enable prediction of the fraction of collisions resulting in coalescence. In the simplest case it was assumed that coalescence occurred if the relative velocities along the line of centres of two drops at the instant of collision exceeded a critical value. On this basis, and making use of techniques developed in the field of statistical mechanics, an equation was derived for the fraction of collisions resulting in coalescence. The equation for coalescence frequency on the basis of the simple model was
Ð =(24Øû2 / Ó2 )1/2 exp( - 3w2 / 4û-2)
On the basis of observations of recent workers that coalescence of drops impacting on plane surfaces only occurred for velocities in discrete intervals, more complex models for coalescence were proposed, resulting in alternative expressions for coalescence frequency. Although there appeared to be qualitative support from the literature for one of these equations, it was not possible to apply them in practice because there was no way of predicting the magnitude of the parameters involved. A preliminary test of the equation based on the simple mddel, against data on coalescence frequencies in agitated tanks from the literature, indicated that the theory and experiment were not inconsistent.
An experimental method for measuring coalescence frequency was devised. This was different from methods proposed by other workers, in that the rate of coalescence was not measured by observing the rate of spread of a tracer in the dispersed phase, but rather was based on following transients in the mean drop size after a disturbance to the intensity of agitation. It was argued that the rate of increase of mean drop size following a sudden reduction in impeller speed was directly related to coalescence frequency if certain assumed conditions were met. A major requirement was that the turbulence decay rate following the change in impeller speed should be rapid compared to the rate of coalescence. Subsequent testing showed that this condition was met, provided the magnitude of the change in impeller speed was restricted to moderate values. Coalescence frequency was measured for a mixture of carbon tetrachloride and benzene, with density adjusted to be close to that of the continuous phase, dispersed in water, A.R, grade organic reagents, and once distilled water were used for most of the measurements, but some were made with the materials further purified by distillation. It was found that coalescence frequency varied as impeller speed raised to a power in the range 1.3 - 1.65, as the square root of the volume fraction of dispersed phase, and as the inverse of drop size. It was found that coalescence frequency increased with temperature of the dispersion, and increased with decrease in density difference. It was deduced that the effect of temperature was likely to have resulted from it's effect in turn on the density difference ( þd - þc ), as the latter decreased with increase in temperature. The addition of simple electrolytes (sodium chloride and sodium sulphate) to the continuous phase produce a marked reduction in coalescence frequency. The reason for this effect was not clear; although possible causes of the reduction were suggested, they were not verified. There was excellent agreement between the values of coalescence frequency, and their dependence on impeller speed and volume fraction dispersed phase, observed in these experiments and reported by previous workers, and this was taken as confirmation of the validity of the method of measurement.
Comparison of the experimental results with the theory indicated that the latter appeared to predict correctly the dependence of coalescence frequency on volume fraction of dispersed phase and drop size. Although the observed dependence on! impeller speed appeared to be consistent with the theory for a single set of data, comparison between sets of data thought to differ only in the fraction of collisions resulting in coalescence indicated that the theory did not appear to be adequate to explain this aspect of coalescence behaviour. The theory predicted a much stronger dependence of the fractions of collisions resulting in coalescence than was observed experimentally. According to the theory this quantity was given by exp (- const./N2), whereas the observed behaviour was more in keeping with a term such as exp(- const./N1/2)if the original equation for collision frequency was retained. No simple model for coalescence which resulted in such a term could be proposed, and the more complex models could not be used because of an absence of suitable information as to the magnitude of the parameters involved.