Self-similar Worthington jets

JosÃ© M. Gordillo; Javier RodrÃ­guez-RodrÃ­guez; Vatsal Sanjay

fluid dynamics

Self-similar Worthington jets

arXiv:2607.08972

summary

The paper studies how tiny bubbles bursting create fast, narrow jets (Worthington jets) by focusing inertia, showing that the jet’s size follows a self‑similar scaling law and that the inertia dominates over surface tension, leading to nanometer‑scale droplets.

Abstract

When a micron-sized bubble bursts, capillary waves deform the cavity into a cone that ejects a Worthington jet. The jet is born by inertial focusing, and the local collapse follows self-similar Euler solutions set by the semiangle $I^^{2}$ . Writing $r_{j}$ and $v_{j}$ for the dimensionless jet-base radius and velocity, the local Weber number $W e_{j} = r_{j} v_{j}^{2}$ measures inertia relative to capillarity. The theory, supported by accurate numerical simulations gives $r_{j} \propto I ¨ ^{I^\pm (I^^{2})}$ with $I^\pm ≃ 0.63$ and, hence $W e_{j} ≫ 1$ , with $W e_{j} \to \infty$ as $r_{j} \to 0$ , so inertia increasingly overwhelms capillarity. In simulations, the interface collapses onto a universal shape for more than two decades in dimensionless time when lengths are scaled using our prediction for $r_{j}$ . For water, this gives incipient radii of $O (1)$ nm, predicting nanometric sea-spray aerosols.

Topics & keywords

#bubble bursting #worthington jet #self-similarity #inertial focusing #capillary waves #nanodroplet formationWeber numberEuler self-similar solutionsscaling exponent α≈0.63numerical simulationsnanometric sea‑spray aerosols