Presets
Playback
Column and gas
Pick the liquid, then change gas flow, bubble size and cell oxygen uptake.
Layers
Model checks
The science
Bubble rise
A clean air bubble of diameter d in a liquid rises at about vt = √(2σ/(ρd) + g d/2) (Mendelson), the speed of a capillary-gravity wave of wavelength πd. For small bubbles in viscous liquids the Stokes-type limit g d2ρ/(12μ) takes over; the page blends the two as 1/v2 = 1/vM2 + 1/vS2. In a swarm the mean gas velocity is vg = C0 Ug + vt (Zuber-Findlay drift flux, C0 about 1.2: bubbles concentrate where the liquid flows up fastest).
Gas holdup and mass transfer
The gas volume fraction follows from continuity: Ug = ε v, so ε = Ug/(C0Ug + vt). The interfacial area per liquid volume is a = 6ε/d. Higbie's penetration theory gives kL = 2√(DL/(π tc)) with contact time tc = d/vt, so the oxygen concentration obeys dC/dt = kLa (C* - C) - OUR, an exponential approach to C* with time constant 1/kLa.
Honest simplifications: homogeneous bubble regime only (no churn-turbulent flow, coalescence or breakup, no liquid circulation), one bubble size, perfectly mixed liquid, constant C* (no depletion of oxygen in the gas or hydrostatic pressure effect), Higbie theory is an upper estimate (real small, surfactant-covered bubbles behave closer to rigid spheres, with kLa mostly 0.01-0.2 1/s), the drawn bubbles are representative samples of a far larger real population.
What to try
- Water preset with fast-forward: oxygen climbs along the dashed analytic curve.
- Fine bubbles preset: more area, so kLa is larger and the gauge fills sooner.
- Heavy sparging: holdup rises but less than in proportion to Ug.
- Bioreactor preset: cells consume oxygen, the curve levels off below saturation.