Journal of Materials & Metallurgical Engineering Review Article
A Nonlinear Galerkin Reduced-Order Model for Liquid Jet Breakup Dynamics and Satellite Droplet Formation
Abstract
Liquid jet breakup is a complex nonlinear free-surface phenomenon governed by the coupled effects of inertia, viscosity, and surface tension. Accurate prediction of jet evolution and satellite droplet formation remains challenging due to the computational cost associated with resolving rapidly evolving interfaces and multiscale breakup dynamics. In this work, a physics-based Galerkin reduced-order model is developed to describe the nonlinear dynamics of liquid jets using a low-dimensional representation of the interface deformation and axial velocity fields. The governing slender-jet equations are nondimensionalized and projected onto a finite set of spatial modes, yielding a six-state nonlinear dynamical system comprising three radius-deformation modes and three velocity modes. The formulation preserves the essential physical mechanisms of capillary restoration, viscous dissipation, nonlinear geometric deformation, and mode-to-mode interaction responsible for the evolution of jet instabilities. The reduced-order model provides an efficient framework for analyzing the nonlinear behavior of liquid jets while maintaining a direct connection with the underlying fluid mechanics. The model captures the coupled evolution of interface and velocity fluctuations and provides a computationally efficient alternative to high-fidelity simulations for exploring breakup dynamics. The proposed framework establishes a foundation for advanced stability analysis and physics-based manipulation of liquid jet breakup and satellite droplet formation.
Keywords
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