On the ground, warm exhaled CO2 rises away from a sleeper's face — a buoyancy-driven convection current. In orbital free-fall there is no "up", so that current does not exist: molecular diffusion is far too slow to clear the roughly 300 mL of CO2 exhaled every minute, and it collects in a stagnant pocket right around the head. Real ISS crews have reported waking with headaches when a sleep-station fan failed — flight rules now mandate airflow at every crew quarter.
This 2D redraw uses the exact same mass-balance ODE as the 3D version — same constants, same equilibrium formula, verified numerically to converge to the analytic steady state below to within floating-point error — and renders it as a flat, pannable/zoomable cross-section instead of an orbit-camera scene:
dC/dt = P/V − (k_diff + k_fan)·(C − C_ambient)
P = CO2 production rate (∝ breathing rate)
V = local pocket volume
k_diff = weak baseline mixing (diffusion + cabin leakage)
k_fan = fan_power × (ref_distance / vent_distance)²
- Breathing rate — scales CO2 production P; faster breathing (restless sleep, exertion before bed) raises the source term.
- Ventilation fan — the only real removal mechanism in microgravity; 0% reproduces the historical "fan-off headache" reports.
- Vent duct distance — airflow strength falls off with the square of distance from the duct to the sleeper's head.
- Equilibrium level — the steady-state concentration C = C_ambient + P·V⁻¹ / (k_diff + k_fan) the pocket is heading toward; watch it fall as you turn the fan up.
Risk bands loosely follow NIOSH/OSHA CO2 exposure guidance: under 1,000 ppm is unremarkable indoor air, 1,000–5,000 ppm brings drowsiness and headache risk over a sleep shift, and above 5,000 ppm is treated as an occupational exposure limit exceedance.