A model of the gas flow in hollow fibres with permeable walls

A model of the isothermal flow of a viscous ideal gas in long tubes (hollow fibres) with permeable walls is constructed. Analytical relations are derived for the relative flow rate of the gas through the permeable walls of tubes made of porous and non-porous materials. It is established that, for a specified pressure drop, there is an optimum length of the tube when the gas flow rate through its walls reaches a maximum value. A formula is derived for calculating the characteristic fibre length for which the gas flow rate through the tube walls becomes predominant in the overall balance of the gas flow rate entering the input section of the fibre. A single universal dimensionless relation, describing the balance of the gas flow rates for fibres having different permeability mechanisms, is proposed.