Rising bubbles draw surface patterns: A numerical study
Phys. Rev. Fluids 11, 023602 – Published 6 February, 2026
DOI: https://doi.org/10.1103/bd6d-fwmn
Abstract
Small bubbles rising in a chain can self-organize into regular patterns upon reaching a liquid's free surface. This phenomenon is investigated through direct numerical simulations. By varying the bubble release period, distinct branching patterns characterized by different numbers of arms are observed. These macroscopic patterns are found to stem from localized interactions between the bubbles, the free surface, and the surrounding liquid flow. A heuristic model is proposed that quantitatively relates the number of arms to the bubble release period and predicts the probability of observing specific arm counts. This study provides insights into broader nonlinear pattern formation and self-organization phenomena.
