🫧 Rising Bubble in Viscous Fluid

A gas bubble rises through a viscous liquid driven by buoyancy. Stokes drag, Morton number, and Eötvös number determine shape and terminal velocity.

Fluid DynamicsInteractive
Bubble rises by buoyancy · trailing vortex wake shown · P pause · R reset

How it Works

The simulation solves Newton's second law for a bubble rising under buoyancy with Stokes drag and added mass. The Eötvös number Eo = Δρ·g·(2R)²/σ determines bubble shape: spherical at low Eo, ellipsoidal at moderate Eo, and spherical-cap at high Eo. The aspect ratio a/b is computed from the Eo value and applied to deform the ellipsoidal outline.

A simplified wake is rendered as fading tracer particles that show the induced downward return flow. As viscosity decreases, the Re increases and the bubble deforms more. Multiple bubbles can be spawned; they interact through the induced velocity field approximation.

F_buoy = (4/3)πR³·Δρ·g
F_drag = 6πμR·U (Stokes, Re<<1)
U_T = 2R²·Δρ·g / (3μ)
Eo = Δρ·g·(2R)² / σ

Frequently Asked Questions

What drives a bubble to rise in a liquid?

Buoyancy drives bubble rise. Because the bubble gas density is much lower than the surrounding liquid, the net upward pressure force (Archimedes force) exceeds gravity, accelerating the bubble upward.

What is Stokes drag?

Stokes drag is the viscous drag on a sphere at low Reynolds number: F_D = 6πμR·U. It arises from the creeping-flow solution of Navier-Stokes and grows linearly with velocity and radius.

What is terminal velocity of a bubble?

Terminal velocity is reached when buoyancy exactly balances drag. For a small spherical bubble in Stokes flow: U_T = (2R²·Δρ·g) / (3μ), where Δρ is the density difference.

What is the Eötvös number (Bond number)?

The Eötvös number Eo = Δρ·g·D²/σ compares gravitational to surface-tension forces. At low Eo bubbles remain spherical; at high Eo surface tension is weak and bubbles deform significantly.

What is the Morton number?

The Morton number Mo = g·μ⁴·Δρ / (ρ_L²·σ³) characterises the fluid properties alone. Together with Eo it determines bubble shape regime in the Grace diagram.

What shapes can rising bubbles take?

Depending on Eo and Re, bubbles are spherical (small), ellipsoidal (intermediate), spherical-cap (large), or wobbling/skirted. The Grace diagram maps these regimes.

How does viscosity affect bubble rise?

Higher viscosity increases Stokes drag, slowing the bubble. It also suppresses wake instabilities that cause zigzag or spiral paths at higher Reynolds numbers.

What is a bubble wake and why does it matter?

A bubble wake is the recirculation zone behind the rising bubble. For Re above ~200 the wake becomes unstable, causing the bubble to zigzag or spiral rather than rise straight.

Does bubble size affect rise velocity?

Yes. In the Stokes regime U_T scales as R², so larger bubbles rise faster. However very large bubbles deform into caps and follow a different drag law where U_T scales as sqrt(R).

What industrial processes involve rising bubbles?

Rising bubbles are central to bubble column reactors, flotation mineral processing, CO2 sequestration, carbonated beverage quality, and boiling heat transfer in nuclear and thermal power plants.

About this simulation

Each bubble is pushed upward by a buoyancy force computed from its volume and the density gap between water and gas, opposed by Stokes drag and added-mass inertia. The code derives the Eötvös number from radius and surface tension every frame and uses it to flatten the bubble outline into an ellipse — small, low-Eo bubbles stay round while larger or lower-tension bubbles squash sideways, matching real bubble-shape regimes.

🔬 What it shows

Gas bubbles accelerating toward a terminal rise velocity, deforming from sphere to ellipsoid as their Eötvös number grows, while faded tracer dots trail behind to depict the induced return flow in the wake.

🎮 How to use

Adjust Bubble Radius R, Viscosity μ, Surface Tension σ and Gravity g with the sliders, click anywhere on the canvas to spawn extra bubbles at that point, or press P/R to pause/reset.

💡 Did you know?

In the Stokes regime a bubble's terminal velocity scales with the square of its radius, so doubling bubble size roughly quadruples its rise speed — until it grows large enough to flatten into a spherical cap and follow a different drag law.

Frequently asked questions

What happens when I click the canvas?

Clicking spawns a new bubble of the current radius R at the cursor position, letting you compare several bubbles rising and interacting with the wake at once.

Why do some bubbles look flattened instead of round?

The simulation computes an Eötvös number from radius, gravity and surface tension each frame, then uses aspectRatio() to squash the vertical scale — higher Eo (larger radius or weaker surface tension) means a flatter, more ellipsoidal bubble.

Why does increasing viscosity slow the bubble down?

Stokes drag in the code, fDrag = 6πμRv, scales directly with viscosity μ, so raising the Viscosity slider increases the opposing force and caps the bubble's terminal velocity at a lower value.

What do the small dots trailing the bubble represent?

They are wake tracer particles spawned probabilistically behind each rising bubble, drifting slowly downward to visualise the return flow that viscous fluid displaced by the bubble must fill in.

Why does the bubble stop accelerating after a while?

The code caps vertical velocity at twice the analytically computed terminal velocity vT = 2R²Δρg/(3μ), representing the point where buoyancy and drag forces balance.