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\begin{document}

\title{Predicting the Diameters of Droplets Produced in Turbulent Liquid-Liquid
Dispersion}



\author[1]{John  Thomas }%
\author[1]{Brian DeVincentis}%
\author[2]{Johannes Wutz}%
\author[3]{Francesco Ricci}%
\affil[1]{M-Star Simulations}%
\affil[2]{M-Star Center Europe}%
\affil[3]{Boehringer Ingelheim Corp USA}%


\vspace{-1em}



  
  \date{May 18, 2024}


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\begin{abstract}
The droplet size distribution in liquid-liquid dispersions is a complex
convolution of impeller speed, impeller type, fluid properties, and flow
conditions. In this work, we present three a priori modeling approaches
for predicting the droplet diameter distributions as a function of
system operating conditions. In the first approach, called the two-fluid
approach, we use high-resolution solutions to the Navier-Stokes
equations to directly model the flow of each phase and the corresponding
droplet breakup/coalescence events. In the second approach, based on an
Eulerian-Lagrangian model, we describe the dispersed fluid as individual
spheres undergoing ongoing breakup and coalescence events per
user-defined interaction kernels. In the third approach, called the
Eulerian-Parcel model, we model a sub-set of the droplets in the
Eulerian-Lagrangian model to estimate the overall behavior of the entire
droplet population. We discuss output from each model within the context
of predictions from first principles turbulence theory and measured
data.%
\end{abstract}%



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