A deep gradient-density filter device capable of effectively filtering a fluid containing a distribution of particles in the range of approximately 25 microns to approximately 0.2 micron at a fluid velocity of at least approximately 100 cm/hr and an initial hydraulic permeability of greater than approximately 10 cm/hr/psi. The deep gradient-density filter device includes several layers of filtration material, each having specific predetermined particle retention properties. In one product embodiment, the deep gradient-density filter device uses "loose" fibrillated cellulose fiber material as a primary filter element. In a method aspect, the deep gradient-density filter device is used for either the secondary clarification of industrial-scale volumes of cultured or fermented protein-containing biopharmaceutical fluids or the primary clarification of pilot-scale volumes.