Polymer fibers having a novel cross-sectional geometry are used as stationary phase materials for liquid chromatography separations. Fibers of 20 to 50 micrometer diameters have surface-channel structures extending their entire lengths. Bundles of fibers having this novel cross-sectional geometry are packed in columns. Different polymer compositions permit the "chemical tuning" of the separation process. Channeled fibers composed of polystyrene and polypropylene have been used to separate mixtures of polyaromatic hydrocarbons (PAHs), Pb-containing compounds and fatty acids. Use of channeled fibers allows a wide range of liquid flow rates with very low backing pressures. Applications in HPLC, cap-LC, prep-scale separations, analytical separations, single fiber separations, waste remediation/immobilization, extraction of selected organic molecules/ions from solution, purification of liquid streams (process waste, drinking water, pure solvents), selective extraction of cell matter and bacteria from growth media, and immobilization of cell matter and bacteria are envisioned.