A Mathematical Model of a Hollow-Fibre Filter

Abstract

A typical hollow-fibre water filter consists of a long hollow circular cylindrical casing inside which is packed a large number of hollow fibres each with its axis parallel to the casing axis. Water is pumped across the casing in a radially symmetric fashion, enters the region outside the fibres, and then flows into the interior of the hollow fibres leaving impurities at the fibre surface. In an ideal filter the fluid pressure outside the fibres is uniform (equal to the inlet pressure) and the fluid pressure inside the fibres is also uniform (equal to the low exit pressure). The water flow into the fibres is then uniform and inpurities are deposited uniformly throughout the filter. This ideal situation cannot be achieved exactly in practice since pressure gradients are required to drive the flow against inertia and viscous forces. Using a Mathematical Model design criteria are established under which the filter can be regarded as ideal. The Model is also used to estimate the pressure drop at a small inlet, a potential source of inefficiency.