Whereas the structure of the flow field generated in the hollow fiber membrane modules operating as liquid-liquid or gas-liquid contactors has been studied extensively theoretically, this is not the case for the much more complex flow field generated during the filtration operation of the same type of modules. The present work is a first approach to analyze and understand the particular flow field. The mathematical problem is formulated and then geometrical and physical simplifications are introduced in order to decompose the full problem in a series of simpler sub-problems. In addition to the presentation of the general structure and the features of the problem, the focus of the present work is to derive all possible analytical solutions of the sub-problems. Several results based on analytical or simple numerical approaches are also presented. (c) 2008 Elsevier B.V. All rights reserved.