A filtration device is provided for withdrawing permeate essentially continuously from a multicomponent aqueous substrate containing growing microorganisms in a reservoir. A vertical skein of fiber is scrubbed with coarse bubbles which emanate from a conversion baffle positioned under the skein. The substrate is aerated with fine bubbles in a size range small enough to transfer oxygen to the substrate efficiently. The baffle traps the fine bubbles and converts them to coarse bubbles which are effective to scrub the fibers. In the most preferred embodiment, the finished headers of the skein are derived from composite headers comprising a fixing lamina of resin in which the fibers are potted near their terminal ends, and a fugitive lamina of fugitive powdery material in which the terminal ends of the fibers are potted. The fugitive lamina is removed, preferably by dissolving the powder, e.g. finely divided common salt in water.