An analytical solution to the fixed pivot fragmentation population balance equation

Towards a Standard Method for Estimating Fragmentation Rates in Emulsification Experiments

The fragmentation rate function connects the fundamental drop breakup process with the resulting drop size distribution and is central to understanding or modeling emulsification processes. There is a large interest in being able to reliably measure it from an emulsification experiment, both for generating data for validating theoretical fragmentation rate function suggestions and as a tool for studying emulsification processes. Consequently, several methods have been suggested for measuring fragmentation rates based on emulsion experiments. Typically, each study suggests a new method that is rarely used again. The lack of an agreement on a standard method has become a substantial challenge. This contribution critically and systematically analyses four influential suggestions of how to measure fragmentation rate in terms of validity, reliability, and sensitivity to method assumptions. The back-calculation method is identified as the most promising—high reliability and low sensitivity to assumption—whereas performing a non-linear regression on a parameterized model (as commonly suggested) is unsuitable due to its high sensitivity. The simplistic zero-order method is identified as an interesting supplemental tool that could be used for qualitative comparisons but not for quantification.