Abstract: A medical device and method for affecting mass transfer between blood and a fluid. In one application, this mass transfer is an oxygenation of the blood. Generally, a membrane which separates the blood and fluid is moved in a predetermined manner and in a direction which is substantially parallel to that of the primary direction of the flow to augment the mass transfer efficiency/rate. Importantly, this movement of the membrane is relative to the blood mass transfer boundary layer which steepens or increases the oxygen concentration gradient and decreases the thickness of the blood mass transfer boundary layer and thereby improves upon the mass transfer efficiency/rate of oxygen into the blood.