# Modeling the excess velocity of low-viscous Taylor droplets in square microchannels

## TL;DR

This paper presents a new model to predict the excess velocity of Taylor droplets in square microchannels, linking droplet shape deformation, bypass flow, and flow parameters, validated with experimental data.

## Contribution

The work introduces a novel model for droplet excess velocity considering cap deformation and bypass flow, validated with empirical data and optimized via metaheuristic methods.

## Key findings

- Model accurately predicts droplet excess velocity.
- Parameters like bypass length and viscosity ratio are key.
- Validated against published experimental data.

## Abstract

Microscopic multiphase flows have gained broad interest due to their capability to transfer processes into new operational windows and achieving significant process intensification. However, the hydrodynamic behavior of Taylor droplets is not yet entirely understood. In this work, we introduce a model to determine the excess velocity of Taylor droplets in square microchannels. This velocity difference between the droplet and the total superficial velocity of the flow has a direct influence on the droplet residence time and is linked to the pressure drop. Since the droplet does not occupy the entire channel cross section, it enables the continuous phase to bypass the droplet through the corners. A consideration of the continuity equation generally relates the excess velocity to the mean flow velocity. We base the quantification of the bypass flow on a correlation for the droplet cap deformation from its static shape. The cap deformation reveals the forces of the flowing liquids exerted onto the interface and allows estimating the local driving pressure gradient for the bypass flow. The characterizing parameters are identified as the bypass length, the wall film thickness, the viscosity ratio between both phases and the Ca-number. The proposed model is adapted with a stochastic, metaheuristic optimization approach based on high-speed camera measurements. In addition, our model is successfully verified with published empirical data.