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

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. This parameter is related to the shear layer thickness and hence influenced by the change in quantities like velocity, viscosity, and surface tension. The correlation describing the dependence of the parameter on these quantities using non-dimensional numbers is presented. The model is then cross-validated with the previous computational and experimental data. We use PETSc, an open-source solver toolkit, to implement our model using a mixed finite element discretization. We present the simulation results for liquid paraffin wax under fast-moving airflow with a range of velocities.