A novel approach for determining the droplet size distribution in emulsion systems by generating function

We present a novel approach that allows us to figure out the size distribution of an isolated collection of droplets of a liquid dispersed in another one (emulsion) using NMR pulsed gradient spin echo (PGSE) measurements. The echo decay coming from the ensemble of droplets with different radii was related to the particle size distribution function and to the echo attenuation of an isolated sphere. This latter term was evaluated according to the second cumulant approximation, while the unknown distribution was approximated using a generating function series. The coefficients of the series are evaluated, using a least squares procedure, fitting the obtained relationship to the experimental data. We find that when the volume fraction distribution is contained in the range of lengths determined by the parameters of the PGSE measurement, the experimental data (echo attenuation) contain enough information to describe the distribution function in all the details. The method has been tested on both experimental and simulated data and appears to be powerful and flexible. It is able to work with highly asymmetric distributions, still giving accurate results.