A causal model of drop breakup in turbulence
Abstract
Fragmentation of drops and bubbles in turbulence controls interfacial area generation, mixing, and transport in environmental and engineering flows. Reduced-order models of breakup are highly sought after, but the bidirectional, nonlinear coupling between the interfacial and hydrodynamic stresses is an obstacle to their development. By leveraging a decomposition of the flow into outer and inner regions introduced by Vela-Martín & Avila (2021), we demonstrate that at low Weber numbers breakup is caused by outer eddies that produce extreme events of interfacial stretching. Capillary forces oppose stretching and transfer the interfacial energy back to the velocity field by generating inner eddies as the drop relaxes. Hence, for breakup to occur, outer stretching events must inject energy faster than the interface can convert it into inner eddies. Numerical simulations initialized with ellipsoidal drops reveal that the energy transfer to the inner eddies is governed by the capillary time, whereas the outer forcing acts on the eddy-turnover time scale. Building on these observations and the governing equations, we derive a simple model for the breakup rate. Although the underlying assumptions are strictly valid only in the limit of large surface tension, the resulting equation quantitatively captures both drop and bubble breakup rates over a wide range of Weber numbers using only a single fitting parameter. Our results establish a direct causal link between turbulent intermittency and the memoryless nature of breakup, and suggest a universal mechanism governing drop and bubble breakup at low Weber numbers.
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BibTeX
@misc{moron2026causal,
title = {{A causal model of drop breakup in turbulence}},
author = {Daniel Morón and Ianto Cannon and Alberto Vela-Martín and Marc Avila},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2605.07504},
eprint = {2605.07504},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.07504},
}
RIS
TY - UNPB
TI - A causal model of drop breakup in turbulence
AU - Daniel Morón
AU - Ianto Cannon
AU - Alberto Vela-Martín
AU - Marc Avila
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2605.07504
UR - https://arxiv.org/abs/2605.07504
AB - Fragmentation of drops and bubbles in turbulence controls interfacial area generation, mixing, and transport in environmental and engineering flows. Reduced-order models of breakup are highly sought after, but the bidirectional, nonlinear coupling between the interfacial and hydrodynamic stresses is an obstacle to their development. By leveraging a decomposition of the flow into outer and inner regions introduced by Vela-Martín & Avila (2021), we demonstrate that at low Weber numbers breakup is caused by outer eddies that produce extreme events of interfacial stretching. Capillary forces oppose stretching and transfer the interfacial energy back to the velocity field by generating inner eddies as the drop relaxes. Hence, for breakup to occur, outer stretching events must inject energy faster than the interface can convert it into inner eddies. Numerical simulations initialized with ellipsoidal drops reveal that the energy transfer to the inner eddies is governed by the capillary time, whereas the outer forcing acts on the eddy-turnover time scale. Building on these observations and the governing equations, we derive a simple model for the breakup rate. Although the underlying assumptions are strictly valid only in the limit of large surface tension, the resulting equation quantitatively captures both drop and bubble breakup rates over a wide range of Weber numbers using only a single fitting parameter. Our results establish a direct causal link between turbulent intermittency and the memoryless nature of breakup, and suggest a universal mechanism governing drop and bubble breakup at low Weber numbers.
ER -