Dynamics and frictional dissipation for treading slowly in a puddle

Area of Science:

• Fluid Dynamics
• Physics of Liquids

Background:

• Liquid column dynamics are complex, involving surface tension, potential energy, and kinetic energy.
• Numerical simulations often hinder a full understanding of the underlying physics, especially concerning pinch-off.
• Turbulence in real-world scenarios like rain makes simple theoretical analysis difficult.

Purpose of the Study:

• To elucidate the mechanism driving liquid column morphological changes.
• To derive analytic expressions for critical height and upper radius during stage transitions.
• To analyze the pinch-off process in laminar flow regimes.

Main Methods:

• Focusing on low Reynolds number cases to ensure laminar flow.
• Utilizing simple models to analyze fluid behavior.
• Deriving analytic expressions for morphological transitions and pinch-off.

Main Results:

• Identified three distinct stages in liquid column evolution: static/reversible, irreversible shrinking, and accelerated contraction.
• Derived analytic expressions for critical height and upper radius.
• Successfully predicted the quantitative behavior of column neck contraction during pinch-off, noting the absence of self-similarity.

Conclusions:

• The study provides a theoretical framework for understanding liquid column dynamics in laminar flow.
• Analytic expressions offer predictive power for morphological changes and pinch-off.
• The absence of self-similarity in pinch-off is explained within the developed model.