A pneumatic bioreactor includes a vessel containing a fluid to be mixed and at least one mixing device driven by gas pressure. A first embodiment includes a floating impeller that rises and falls in the fluid as gas bubbles carry it upward to the surface where the gas is then vented, permitting the impeller to sink in the fluid. The floating impeller may be tethered to a second impeller with a flexible member and pulley. The mixing speed is controlled with electromagnets in the vessel acting upon magnetic material in the impeller or its guides. In another embodiment, floating pistons mix the fluid, pushing it through a mixing plate with one or more apertures. In a third embodiment, the mixing device is a rotating drum with bubble-catching blades and rotating mixing plates with apertures. The top of the vessel for these mixers may include a closed top and sterile filters.

A measuring system includes a measuring chamber for receiving a sample fluid; an agitating element for agitating the sample fluid and having a variable position between first and second positions depending on a flow rate of the sample fluid; and an optical measurement arrangement with an optical measurement path for determining the position of the agitating element; wherein the measuring system determines the position of the agitating element based on a measurement signal from the optical measurement arrangement, the measurement signal being indicative of the agitating element being inside or outside of the optical measurement path.