A dialysis apparatus for machines such as artificial kidneys and heart-lung machines has a warning device activated to prevent air bubbles from entering the blood circulation system of the patient and controlled by the vertical position of a float in a float chamber where air is separated from the blood. The warning signal is triggered when the air/blood volume ratio in the chamber is increased so that the float sinks and closes off the outlet at the bottom portion of the chamber. Continued blood supply to the chamber compresses the air therein and the corresponding pressure increase is detected and used to generate a warning signal.