[Paper Review] Bursting Bubble in a Viscoplastic Medium

Vatsal Sanjay, Detlef Lohse+1 more|University of Twente Research Information|Jan 19, 2021

Fluid Dynamics and Heat Transfer59 references42 citations

TL;DR

The paper studies how yield-stress (viscoplastic) fluids alter bubble bursting at a free surface using DNS, revealing four regimes and non-flat final crater shapes due to plastic resistance. It maps energy budgets and regime transitions as functions of plastocapillary and Ohnesorge numbers.

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.

Motivation & Objective

• Investigate how viscoplastic yield stress modifies the bursting of a bubble at a free surface.
• Characterize capillary-wave dynamics and jet formation in a viscoplastic medium.
• Quantify energy transfer and dissipation during the bursting process.
• Map the regimes of behavior in a plastocapillary vs. Ohnesorge parameter space.
• Provide insights applicable to industrial processes and geophysical contexts.

Proposed method

• Direct Numerical Simulations (DNS) with a Volume of Fluid (VoF) method to track the gas-liquid interface.
• Regularized Bingham model for viscoplastic stresses with J = yield/tension ratio, and Ohnesorge number Oh to compare inertial-capillary and viscous time scales.
• Non-dimensional governing equations for the liquid phase including inertia, pressure, viscous/yield stresses, and gravity, with a gas phase solved similarly.
• Adaptive Mesh Refinement (AMR) ensuring fine resolution near the interface and capillary waves, with minimum cell size Delta = R0/512.
• Initial condition set to Bo -> 0 (Bo = 1e-3) for nearly spherical bubbles at a fluid interface; rim retraction and film rupture modeled to form an initial cavity.
• Energy budget analysis decomposing total energy into kinetic, surface, and dissipation terms (viscous and yield) with a stoppage criterion based on residual kinetic energy.

Experimental results

Research questions

• RQ1 How does the plastocapillary number J influence capillary-wave dynamics as the bubble cavity collapses?
• RQ2 Under what conditions does a Worthington jet form and/or break up into droplets in a viscoplastic medium?
• RQ3 How does yield stress alter the final crater shape and preserve residual surface energy?
• RQ4 What are the different regimes of bubble bursting in viscoplastic fluids as functions of J and Oh?
• RQ5 How is the energy budget partitioned between kinetic energy, surface energy, and dissipation for varying J and Oh?

Key findings

• Capillary waves and jetting are significantly modified by yield stress; higher J damps waves, can suppress jetting, and can halt full cavity yield.
• There are four regimes in the J–Oh regime map: jet that breaks into droplets, jet without breakup, entire cavity collapses but surface remains non-flat, and a non-yielding bottom that freezes the cavity shape.
• Final crater shapes are non-flat with residual surface energy, unlike Newtonian fluids where the surface tends to a flat state; the final crater depth and capillary-wave strength depend on J and Oh.
• Energy budgets show that increasing J shifts dissipation toward yield stresses, with more energy stored in crater surface energy when yielding is suppressed at the bottom.
• For J around 0.65 or higher, the bottom plug remains unyielded, preventing full collapse and fixing the crater height near the initial depth.
• The regime transitions occur at specific lines in the J–Oh plane, with outcomes influenced by both capillary and yield-stress effects.