{'fraction_non_alphanumeric': 0.01235657546337158, 'fraction_numerical': 0.0, 'mean_word_length': 5.670588235294118, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
ANALYTICAL AND NUMERICAL SOLUTIONS OF THE MASS CONTINUITY EQUATION IN THE LUMEN SIDE OF A HOLLOW-FIBER MEMBRANE CONTACTOR WITH LINEAR OR NONLINEAR BOUNDARY CONDITIONS

Mass transfer in fully developed laminar flow in hollow-fiber membrane contactors is encountered in a variety of many important applications, such as supported gas and liquid membranes, reverse osmosis, pervaporation, membrane reactors, and biological processes. In this article the complexity of the partial differential equation that describes the concentration profile in the lumen with the associated linear or nonlinear boundary conditions at the fiber wall is simplified by means of analytical and numerical methods using current computational tools. A comparison between the numerical and analytical solution for the linear case reveals the inadequacy of the latter for the evaluation of the lumen Sherwood numbers in the entrance region. For a nonconstant concentration of the diffusing component in the shell side an integro-differential boundary condition at the fiber wall arises, which was approximated by the Gauss–Jacobi orthogonal collocation method.