Fracture of a viscous liquid

TL;DR

This paper investigates the impact dynamics of viscous liquids on pools of the same liquid, revealing exponential curvature growth at the impact point, a critical velocity for cusp collapse, and phase entrainment phenomena.

Contribution

It provides experimental validation of theoretical models for impact-induced cusp formation and entrainment in viscous liquids, linking shape evolution to impact velocity.

Findings

Curvature at impact point increases exponentially with velocity.

Identified a characteristic velocity for cusp collapse.

Characterized the critical velocity for phase entrainment.

Abstract

When a viscous liquid hits a pool of liquid of same nature, the impact region is hollowed by the shock. Its bottom becomes extremely sharp if increasing the impact velocity, and we report that the curvature at that place increases exponentially with the flow velocity, in agreement with a theory by Jeong and Moffatt. Such a law defines a characteristic velocity for the collapse of the tip, which explains both the cusp-like shape of this region, and the instability of the cusp if increasing (slightly) the impact velocity. Then, a film of the upper phase is entrained inside the pool. We characterize the critical velocity of entrainment of this phase and compare our results with recent predictions by Eggers.