Abstract
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.
Highlights
Designing equipment and processes that allow for controlled and resource-efficient emulsification has a large relevance for chemical engineering processing
This study is part of an ongoing research project attempting to find methods for measuring breakup frequencies in industrial turbulent emulsification processes. The aim of this contribution is to determine under which conditions the previously suggested breakup frequency estimation methods based on emulsification data can be used to obtain quantitative information about the local frequencies
The amplification of uncertainty seen from the method used in this study (Appendix A), comes from the specific form taken by Equation (8), and it is not expected to generalize to different methods. The aim of this contribution was to determine under which conditions the previously suggested breakup frequency estimation methods based on emulsification data can be used to obtain quantitative information about the local frequencies
Summary
Designing equipment and processes that allow for controlled and resource-efficient emulsification has a large relevance for chemical engineering processing. Since the only experimental input required by these methods is the emulsion drop-size distribution, they can be applied to any emulsification device, which makes them promising for studying full-scale industrial devices These emulsification-experiment based methods do, by necessity, result in a global breakup frequency, averaged across the entire emulsification device (e.g., averaged across the entire homogenizer valve in the case of high-pressure homogenization, across the whole mixer head of an inline mixer or averaged across the entire tank for a stirred batch tank), as opposed to a local breakup frequency specified at each point in the domain. The aim of this contribution is to determine under which conditions the previously suggested breakup frequency estimation methods based on emulsification data (the “global methods”) can be used to obtain quantitative information about the local frequencies
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