2025/12/23 by Akilan Sankaran, Sankaran, Akilan, Diego Israel Chavez +1
Engineering · Physics and Astronomy · #Electrowetting and Microfluidic Technologies #FOS: Physical sciences #Innovative Microfluidic and Catalytic Techniques Innovation #Mathematical Physics (math-ph) #Micro and Nano Robotics
paper · doi:10.48550/arxiv.2512.20110
openalex publication_date 2025/12/23 · openalex created_date 2025/12/25 · openalex updated_date 2026/07/28
We investigate the ability of millimetric walking droplets to tunnel between spatially-structured cavities. By synthesizing experimental and theoretical analysis, we provide a comprehensive framework for droplet tunneling mechanics in three spatial dimensions. We define a generalized Dirichlet-to-Neumann operator that enables explicit characterization of droplet and wave-field dynamics under highly intricate variable-topography systems. This formalism enables a reduced, three-dimensional description of the pilot-wave field, facilitating high-fidelity numerical simulations of tunneling probabilities and long-time macroscopic dynamics with significantly improved accuracy over existing quasi-two-dimensional models. Moreover, we demonstrate experimental droplet tunneling in complex cavity geometries and discuss many-droplet coupling in the context of tunneling observations.