🫧 Rising Bubble in a Viscous Fluid

About this simulation

A gas bubble released at the bottom of a liquid column accelerates upward under buoyancy until viscous drag balances gravity, reaching a steady terminal velocity. How fast it rises — and what shape it settles into — depends on its size, the fluid's viscosity and density, and the interplay between viscous, inertial and surface-tension forces.

How it works

• Stokes regime (small bubble / thick fluid) — viscous forces dominate, the Reynolds number stays below 1, and the bubble stays almost perfectly spherical. Terminal velocity follows Stokes' law: v = (2/9)·Δρ·g·R²/μ.
• Ellipsoidal regime (intermediate) — as the bubble grows or the fluid thins, inertial forces start to matter and the bubble wobbles into a flattened, oblate shape.
• Spherical-cap regime (large bubble / thin fluid) — when the Eötvös number (buoyancy vs. surface tension) is large, the bubble flattens into a mushroom-like cap with an indented base, rising at a size-independent speed set by v ≈ 0.711·√(g·R).
• Streaks around the bubble sketch the recirculating flow the bubble drags with it as it climbs.

Controls

• Bubble radius — sets the bubble size in millimetres (0.3–20mm).
• Fluid viscosity — sweeps from water-thin to honey-thick liquids.
• Fluid density — density of the surrounding liquid (800–1400 kg/m³).
• Show flow streaks — toggles the visualised velocity field around the bubble.
• ↺ Reset bubble — sends the bubble back to the bottom of the column. Drag to rotate, scroll to zoom.

Did you know?

The transition from spherical to spherical-cap bubbles is captured by the Grace diagram, which maps bubble shape against the Reynolds, Eötvös and Morton numbers — it is still the standard reference engineers use to predict bubble behaviour in reactors, aeration tanks and volcanic conduits.