A one-dimensional mathematical model for shear-induced droplet formation in co-flowing fluids
Abstract
Shear-induced droplet formation is important in many industrial applications, primarily focusing on droplet sizes and pinch-off frequency. We propose a one-dimensional mathematical model that describes the effect of shear forces on the droplet interface evolution. The aim of this paper is to simulate paraffin wax droplets in a co-flowing fluid using the proposed model to estimate the droplet volume rate for different flow velocities. Thus, the study focuses only on the dripping regime. This one-dimensional model has a single parameter that arises from the force balance on the interface. We use PETSc, an open-source solver toolkit, to implement our model using a mixed finite element discretization. The parameter is defined by cross-validation from previous computational and experimental data. We present the simulation results for liquid paraffin wax under fast-moving airflow with a range of velocities.
Keywords
Cite
@article{arxiv.2307.01308,
title = {A one-dimensional mathematical model for shear-induced droplet formation in co-flowing fluids},
author = {Darsh Nathawani and Matthew Knepley},
journal= {arXiv preprint arXiv:2307.01308},
year = {2024}
}