a) Industrial/clay: A lumen is the bore of a tube. Thus, halloysite is a tubular mineral with an approximately 30 nanometer diameter lumen that runs the length of the tube.
b) Medical: A cavity of passage in a tubular organ; e.g., the lumen of the intestine. Also, commonly applied to those clay minerals where medications are loaded into the tube bore, and the clay particle is coated with an excipient to control the timing of delivery.