Predicting phase inversion in agitated dispersions with machine learning algorithms

Abstract

In agitated systems, the phase inversion (PI) phenomenon – the mechanism by which a dispersed phase becomes the continuous one – has been studied extensively in an empirical manner, and few models have been put forward through the years. The underlying physics are still to be fully understood. In this work, the experimental evidence published in literature is used to train machine learning models that may infer the inherent rules that lead to a given dispersion type (O/W or W/O), as well as predict the value of the dispersed phase volume fraction at the edge of the inversion point. Decision trees, bagged decision trees, support-vector machines, and multiple perceptrons are implemented and compared. Results show that it is possible to infer an ensemble of physical rules that explain why a given dispersion is O/W or W/O, where a strong “turbulence constraint” is identified. The intuitive rule that PI occurs at 50% dispersed phase almost never holds. Moreover, neural networks have shown a better performance at predicting the PI point than the other algorithms tested. Finally, a theoretical study is performed in an effort to produce a phase inversion map with the relevant operating variables. This study showed a strong nonlinear effect of the impeller-to-vessel size ratio and an asymmetrical behavior of the interfacial tension on the phase inversion points.

Keywords:

• Liquid–liquid dispersions
• machine learning
• neural network
• phase behavior

Acknowledgments

The authors are grateful to Mrs. Mercedes Alais, Mrs. Catalina Swinnen, and Mrs. Paloma Aqueveque Cuetos for their contributions to this work, to CONICET for the doctoral fellowship granted to Juan M. Maffi, and to ITBA for its support.

Nomenclature

Greek letters
γ	=	Interfacial tension N/m
μ	=	Viscosity Pa·s
ρ	=	Density kg/m3
σ	=	Surface tension N/m
$\varphi$	=	Phase volume fraction

Latin letters

N	=	Stirring speed min−1
D/T	=	Impeller-to-vessel diameter ratio
D	=	Impeller diameter m

Subscripts

c	=	Continuous phase
d	=	Dispersed phase
o	=	Oil phase
w	=	Aqueous phase