Robust Characterisation of Flowing Emulsions using Regularisation and Velocity-compensating Pulsed Field Gradient (PFG) Techniques

Abstract

The use of nuclear magnetic resonance (NMR) pulsed field gradient (PFG) techniques to produce emulsion droplet-size distributions, is well established. This is accomplished by employing a description of restricted self-diffusion in spherical cavities to interpret the PFG data. We present two improvements of this droplet sizing technique in order to increase its robustness. The droplet size distribution is generally assumed to be a log-normal shape, which both stabilises and simplifies the mathematical extraction of the droplet-size distribution from the PFG data. An alternative technique is reported here, which employs Tikonov regularisation theory to perform this extraction. Consequently no assumptions are made with respect to the shape of the droplet-size distribution. The technique is also developed to be able to characterise an emulsion under flowing conditions. Conventional PFG is unable to distinguish between self- diffusion and a distribution of velocities. We introduce a flow-compensated PFG technique to enable self-diffusion alone to be detected, hence enabling measurements of droplet-size distributions for flowing emulsions.