A frameless array unconfined in a modular shell, proves to be a surprisingly effective membrane device for withdrawing permeate from a substrate, the flux through the membranes reaching an essentially constant relatively high value because of the critical deployment of fibers of the array as a skein, arching in a buoyantly swayable generally parabolic configuration within the substrate, above at least one of the array's headers in which the terminal end portions of the fibers are potted. The length of each fiber must be greater than the direct center-to-center distance between the array's pair of headers. For use in a large reservoir, an assembly of the array and a gas distributor means has fibers preferably >0.5 meter long, which together provide a surface area >10 m2. The terminal end portions of fibers in each header are substantially free from fiber-to-fiber contact. When used in a tank from which the permeate is withdrawn at a location low enough to overcome the transmembrane pressure differential of the fibers, the permeate is withdrawn under a vacuum induced by gravity. To increase flux, a pump may be used which provides a suction less than 75 cm of Hg. When used in combination with a gas-distribution manifold disposed beneath the skein so as to flow bubbles through it, the surfaces of the fibers are surprisingly resistant to being fouled by build-up of deposits of inanimate particles or microorganisms in the substrate. Membranes with high transmembrane pressure differential may be used, if desired, and permeate removed with a vacuum pump.