Numerical Simulation of Ostwald Ripening in Emulsions

Ostwald ripening at finite dispersed phase volumes was modeled successfully using linearized analytical solutions of the ripening equations and an explicit numerical routine. The numerical approach incorporated a number frequency distribution of drop radii rather than using a discrete number of drops. The effect of finite dispersed phase volume fraction was accounted for by using half the average separation distance between drops as the mass transfer boundary. The numerical predictions matched analytical predictions for infinitely dilute systems almost exactly and were in qualitative agreement with analytical predictions for infinitely concentrated systems. The numerical model was applied to the full range of dispersed phase concentrations and successfully predicted experimental cumulative frequency distributions. The growth rate, i.e. the change in the cube of the mean radius with time, was confirmed to be constant at any dispersed phase volume fraction. A simple expression was developed relating growth rate to dispersed phase volume fraction. Predicted growth rates at dispersed phase volume fractions less than 0.2 matched those found experimentally and by other numerical methods. Predicted growth rates at higher dispersed phase volume fractions agreed well with experimental data from the literature but were significantly higher than predictions from other numerical methods.