Bursting Bubble in a Viscoplastic Medium (2101.07744v4)

Abstract: When a rising bubble in a Newtonian liquid reaches the liquid-air interface, it can burst, leading to the formation of capillary waves and a jet on the surface. Here, we numerically study this phenomenon in a yield stress fluid. We show how viscoplasticity controls the fate of these capillary waves and their interaction at the bottom of the cavity. Unlike Newtonian liquids, the free surface converges to a non-flat final equilibrium shape once the driving stresses inside the pool fall below the yield stress. Details of the dynamics, including the flow's energy budgets, are discussed. The work culminates in a regime map with four main regimes with different characteristic behaviours.

• The paper reveals that yield stress significantly modifies bubble bursting dynamics by suppressing droplet formation and changing cavity collapse behavior.
• The paper details how energy is distributed into plastic dissipation, residual surface energy, and gravitational potential energy, differing from Newtonian systems.
• The paper demonstrates that capillary wave interactions with non-yielded fluid regions further complicate the bursting process, affecting industrial and geophysical applications.

Bursting Bubble in a Viscoplastic Medium

The paper of bubble dynamics, particularly the bursting of bubbles at fluid interfaces, is an intricate subject in fluid mechanics, imbued with both fundamental and applied significance. The paper "Bursting Bubble in a Viscoplastic Medium" by Vatsal Sanjay, Maziyar Jalaal, and Detlef Lohse presents a detailed investigation of this phenomenon in viscoplastic media, diverging from the extensively studied Newtonian fluid scenarios.

Core Investigation

The research undertakes a comprehensive numerical simulation approach to elucidate the dynamics of bubbles bursting within viscoplastic, or yield-stress, fluids. These fluids, which exhibit solid-like behavior until a critical stress threshold is exceeded, present unique challenges and phenomena not observed in Newtonian fluids. The authors employ advanced Direct Numerical Simulations (DNS) to explore these complex interactions, leveraging computational resources to simulate conditions that are often impractical to achieve experimentally.

Key Findings

1. Yield Stress Impact: The paper reveals that the yield stress of a viscoplastic fluid significantly alters bubble bursting dynamics. At moderate yield stresses, while a Worthington jet—characteristic of bursting bubbles—is still observed, the increased effective viscosity suppresses subsequent droplet formation. Conversely, at higher yield stresses, the bubble bursts lead to intricate equilibrium shapes as the non-yielded regions of the fluid inhibit cavity collapse.
2. Energy Dissipation Patterns: An interesting dimension of this research is the energy distribution following bubble bursting. Unlike in Newtonian systems where energy transitions to gravitational or viscous dissipation post-bursting, viscoplastic systems show energy funneled into plastic dissipation as well as maintaining residual surface energy and gravitational potential energy due to incomplete cavity collapse.
3. Capillary Wave Interactions: The paper identifies the interaction of capillary waves with yield surfaces as a noteworthy effect, further complicating the bubble bursting process in viscoplastic contexts.

Implications and Applications

The findings from this paper have multifaceted implications encompassing scientific understanding and industrial applications. In fields such as food processing—where bubble dynamics can influence texture—and bioreactors—where bubble interactions might affect cell cultures—the insights into viscoplastic fluid behavior are potentially transformative. Furthermore, this research bears relevance for geophysical processes, including magmatic and mud volcano dynamics, where similar fluid characteristics are present.

Theoretical and Future Research Directions

This paper contributes a foundational understanding of viscoplastic bubble dynamics, yet raises several avenues for future exploration. There remains an opportunity to develop refined models that capture the transitional behavior between Newtonian and yield-stress systems. Additionally, extending these simulations to three-dimensional geometries or incorporating variable ambient conditions could offer deeper insights into the broader applicability of these findings.

The intersection of complex fluid dynamics and numerical computation seen in this paper not only advances theoretical fluid mechanics but also bridges the gap toward practical applications in diverse industrial sectors.