Gas injection into a tilted rotating cylinder

The flux of CO₂ diffusing inside a new type of bioreactors has been measured experimentally. This geoinspired bioreactor consists of a partially filled cylinder rotating around its axis tilted vertically, thus mimicking the precession motion of the Earth. The height of fluid is chosen equal to two radii in order for the first Kelvin mode to be resonant. The CO₂ diffuses through a membrane located at the bottom of the liquid. The partial pressure of CO₂ above the free surface is measured as a function of time. This temporal evolution is modeled by the presence of diffusive layers with no advection at the top and the bottom of the liquid. This basic model leads to an experimental value for the flux of CO₂ at the membrane, which is found to be proportional to the inverse square root of the Ekman number. This is in agreement with the presence of Ekman layers of thickness proportional to the square root of the Ekman number. At a given Ekman number, the flux weakly depends on the tilt angle α with a scaling as $α 1 / 4$⁠.