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

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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. 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.

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Acknowledgements

This study was funded by the United States Department of Energy’s (DoE) National Nuclear Security Administration (NNSA) under the Predictive Science Academic Alliance Program III (PSAAP III) at the University at Buffalo, under contract number DE-NA0003961. This work was partially supported by the National Science Foundation under Grant No. NSF SI2-SSI: 1450339.

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  1. Department of Computer Science and Engineering, University at Buffalo, Buffalo, NY, 14260, USA

    Darsh Nathawani & Matthew Knepley

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  1. Darsh Nathawani
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Correspondence to Darsh Nathawani.

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D.N. wrote the main manuscript text and prepared all figures. All authors contributed to the development of the computer code used for the research. All authors reviewed the manuscript.

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Communicated by Peter Duck.

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Nathawani, D., Knepley, M. A one-dimensional mathematical model for shear-induced droplet formation in co-flowing fluids. Theor. Comput. Fluid Dyn. (2024). https://doi.org/10.1007/s00162-024-00690-5

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