Spatially resolved emulsion droplet sizing using inverse Abel transforms

Pulsed field gradient (PFG) nuclear magnetic resonance (NMR) is well established as a tool for determining emulsion droplet-size distributions via measurement of restricted self-diffusion. Most measurements made to date have not been spatially resolved, but have measured an average size distribution for a certain volume of emulsion. This paper demonstrates a rapid method of performing spatially resolved, restricted diffusion measurements, which enables emulsion droplet sizing to be spatially resolved as a function of radius in cylindrical geometries or pipes. This is achieved by the use of an Abel transform. The technique is demonstrated in various annular systems containing two emulsions, with different droplet-size distributions, and/or a pure fluid. It is also shown that by modifying the pulse sequence by the inclusion of flow-compensating magnetic field gradients, the technique can measure spatially resolved droplet-size distributions in flowing emulsions, with potential applications in spatially resolved on-line droplet-size analysis.