Impulse-induced liquid jets from bubbles with arbitrary contact angles

TL;DR

This study models and experimentally investigates how the contact angle of bubbles affects impulsively induced liquid jet speeds, revealing optimal geometries only when the bubble is submerged, with jet speed depending on bubble shape and submersion depth.

Contribution

The paper derives a pressure impulse model for arbitrary bubble shapes and demonstrates the influence of contact angle and submersion on jet speed through experiments.

Findings

Jet speed depends on bubble curvature and submersion depth.

Optimal bubble curvature exists only when the bubble is submerged.

Experimental results support the theoretical predictions.

Abstract

This paper investigates the relationship between the contact angle of a spherical bubble attached to a tube submerged in a container and the jet speed induced by an impulsive acceleration at its base. While it has been well established that bubble geometry strongly influences the ejection speeds of liquid jets, mathematical studies of liquid jets with arbitrary bubble shapes remain limited. In this work, we derive a pressure impulse in the small-cavity limit as a tractable integral of classical Legendre functions. It is shown that the jet speed can be divided into two components: (i) the velocity induced by the hydrostatic pressure impulse distribution created by the curvature of the bubble, and (ii) the velocity induced by the distribution of the submersion of the tube in a container. This decomposition reveals that an optimal bubble curvature emerges only when the tube is submerged: the optimality is absent for non-submerged configurations, where the jet speed increases monotonically with bubble depth. Experiments confirm this non-monotonicity and quantitatively support the predicted shift of the optimal geometry with submersion depth.