Darcy Permeability of Hollow Fiber Bundles Used in Blood Oxygenation Devices

Many industrial and biomedical devices (e.g. blood oxygenators and artificial lungs) use bundles of hollow fiber membranes for separation processes. Analyses of flow and mass transport within the shell-side of the fiber bundles most often model the bundle for simplicity as a packed bed or porous media, using a Darcy permeability coefficient estimated from the Blake-Kozeny equation to account for viscous drag from the fibers. In this study, we developed a simple method for measuring the Darcy permeability of hollow fiber membrane bundles and evaluated how well the Blake-Kozeny (BK) equation predicted the Darcy permeability for these bundles. Fiber bundles were fabricated from commercially available Celgard® ×30-240 fiber fabric (300 microm outer diameter fibers @ 35 and 54 fibers/inch) and from a fiber fabric with 193 microm fibers (61 fibers/inch). The fiber bundles were mounted to the bottom of an acrylic tube and Darcy permeability was determined by measuring the elapsed time for a column of glycerol solution to flow through a fiber bundle. The ratio of the measured Darcy permeability to that predicted from the BK equation varied from 1.09 to 0.56. A comprehensive literature review suggested a modified BK equation with the "constant" correlated to porosity. This modification improved the predictions of the BK equation, with the ratio of measured to predicted permeability varying from 1.13 to 0.84.