Experimental Methods for Measuring the Breakup Frequency in Turbulent Emulsification: A Critical Review

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.

Estimating Breakup Frequencies in Industrial Emulsification Devices: The Challenge of Inferring Local Frequencies from Global Methods

Experimental methods to study the breakup frequency in industrial devices are increasingly important. Since industrial production-scale devices are often inaccessible to single-drop experiments, breakup frequencies for these devices can only be studied with “global methods”; i.e., breakup frequency estimated from analyzing emulsification-experiment data. However, how much can be said about the local breakup frequencies (e.g., needed in modelling) from these global estimates? This question is discussed based on insights from a numerical validation procedure where set local frequencies are compared to global estimates. It is concluded that the global methods provide a valid estimate of local frequencies as long as the dissipation rate of turbulent kinetic energy is fairly homogenous throughout the device (although a residence-time-correction, suggested in this contribution, is needed as long as the flow is not uniform in the device). For the more realistic case of an inhomogeneous breakup frequency, the global estimate underestimates the local frequency (at the volume-averaged dissipation rate of turbulent kinetic energy). However, the relative error between local frequencies and global estimates is approximately constant when comparing between conditions. This suggest that the global methods are still valuable for studying how local breakup frequencies scale across operating conditions, geometries and fluid properties.