A one-dimensional mathematical model for shear-induced droplet formation in co-flowing fluids

TL;DR

This paper introduces a one-dimensional mathematical model to simulate shear-induced droplet formation in co-flowing fluids, focusing on droplet volume rate estimation in the dripping regime using computational methods.

Contribution

The paper presents a novel one-dimensional model incorporating shear forces and implements it with PETSc for simulating droplet formation in co-flowing fluids.

Findings

Model accurately predicts droplet volume rate under various flow velocities.

Simulation results align with experimental data for paraffin wax droplets.

The model simplifies complex dynamics with a single force balance parameter.

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.