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    Energy conversion and cavity depth model in droplet impact on an immiscible deep pool: A generalized analysis approach

    Sihang Liu1, Ran Gao1, Shuai Yin2, Zhi Tao1, Haiwang Li1, and Yi Huang1,*

    • 1National Key Laboratory of Science and Technology on Aero-Engine Aero-Thermodynamics, Research Institute of Aero-Engine, Beihang University, Beijing 100191, China
    • 2School of Mechanical and Power Engineering, Nanjing Tech University, Nanjing 211816, China

    • *Contact author: huangyi_buaa@buaa.edu.cn

    Phys. Rev. Fluids 11, 014004 – Published 23 January, 2026

    DOI: https://doi.org/10.1103/qp89-xhm3

    Abstract

    Droplet impact onto immiscible liquid pools is frequently observed in both natural and industrial processes. A detailed understanding of the interfacial dynamics and energy transfer mechanisms involved in such impacts is essential for advancing applications such as chemical synthesis, additive manufacturing, and pharmaceutical formulation. However, within the range of impact velocities relevant to these processes, the spatiotemporal evolution of the immiscible interface and the associated energy pathways remain insufficiently characterized. Previous models have predominantly attributed energy conversion to the formation of cavity potential energy, often neglecting other important components. In this study, we experimentally investigate the formation and evolution of cavities induced by millimeter-sized droplet impact on immiscible deep pools over a Froude number (Fr) range of 101–103. Our results reveal that, in addition to cavity potential energy, cavity surface energy plays a nonnegligible role, and a substantial fraction of the droplet's initial kinetic energy is dissipated via viscous effects. To improve the accuracy of the cavity energy estimation, we introduce a shape factor k to account for variations in cavity geometry under different impact conditions. We also propose a dissipation coefficient α that quantifies the relationship between viscous energy loss and the pool-droplet viscosity ratio. Based on the refined energy balance, we derive a dimensionless expression for the maximum cavity penetration depth. This model is semiempirical, with all variables retaining clear physical meaning. The findings offer new theoretical insights into the fluid dynamics of droplet impact on immiscible liquid interfaces.

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