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.

Automated summary

The use of global methods in estimating local breakup frequencies in industrial devices is discussed in this study. The results show that global methods provide valid estimates as long as the dissipation rate of turbulent kinetic energy is fairly homogenous. However, in cases of inhomogeneous breakup frequencies, global estimates may underestimate local frequencies, with a constant relative error observed across conditions. This suggests that global methods are still valuable for studying how local breakup frequencies scale across different operating conditions, geometries, and fluid properties.