Self-organized breakthrough morphodynamics in fluid-driven branching
Phys. Rev. Fluids 11, 023301 – Published 2 February, 2026
DOI: https://doi.org/10.1103/lps4-8j6d
Abstract
Self-organized branching instabilities in fluids arise from the interplay of rheology, interfacial forcing and boundary constraints. We investigate the morphologies that develop when a liquid is injected into a Hele-Shaw cell filled with a yield-stress fluid, with outflow constrained to a single point sink. A transition in branching morphodynamics emerges: at low injection rates, a single finger dominates breakthrough, whereas at high rates, arborized structures form and reorganize upon reaching the sink. We explain this sudden shift as a function of the fluid's switchlike local response to dynamical stresses and the role of out-of-plane confinement, and show that at the transition, breakthrough occurs with minimal injected fluid. Furthermore, the emergence of different breakthrough morphologies between the source and sink shows a trade off between speed and accuracy in these arborization patterns. Overall, our study highlights how the interplay between local material response and global constraints determines branching morphodynamics.
