Deadend outside-in hollow fiber membrane filter: Mathematical model

A mathematical model describing the performance of deadend outside-in hollow fiber filters developed on the basis of Darcyʹs law and the theory of depth filtration accounting for the decrease in the liquid flow rate with filter depth coordinate due to permeate withdrawal is studied. The system of governing equations is solved with the generalized Crank–Nicholson method of central finite differences and approximate methods based on averaging certain process parameters, which use simple Laplace transform solutions for particular cases. It is shown that some of the approximate methods provide an accuracy acceptable for engineering calculations, implying that they can be used in designing more efficient filters.