Exploitation-exploration transition in the physics of fluid-driven branching

TL;DR

This study investigates how fluid-driven branching structures in a yield-stress fluid transition from direct to branched morphologies as injection rate varies, revealing a physical analogy to search strategies in living systems.

Contribution

It demonstrates a novel transition in fluid morphology driven by injection rate, linking physical instabilities to exploration-exploitation dynamics.

Findings

Abrupt morphological transition observed at a critical injection rate

Minimal fluid volume needed for breakthrough at the transition point

Trade-off identified between injection speed and pattern accuracy

Abstract

Self-organized branching structures can emerge spontaneously as interfacial instabilities in both simple and complex fluids, driven by the interplay between bulk material rheology, boundary constraints, and interfacial forcing. In our experiments, injecting dye between a source and a sink in a Hele-Shaw cell filled with a yield-stress fluid reveals an abrupt transition in morphologies as a function of injection rate. Slow injection leads to a direct path connecting the source to the sink, while fast injection leads to a rapid branching morphology that eventually converges to the sink. This shift from an exploitative (direct) to an exploratory (branched) strategy resembles search strategies in living systems; however, here it emerges in a simple physical system from a combination of global constraints (fluid conservation) and a switch-like local material response. We show that the amount of fluid needed to achieve breakthrough is minimal at the transition, and that there is a trade-off between speed and accuracy in these arborization patterns. Altogether, our study provides an embodied paradigm for fluidic computation driven by a combination of local material response (body) and global boundary conditions (environment).