Gas flow dynamics in hollow‐fiber membranes

Abstract

Biomedical and chemical separations often use hollow-fiber membranes for exchanging diffusible species between segregated gas and liquid flow streams. A classic example is the hollow fibers used in extracorporeal and intracorporeal artificial lungs (cf., High et al., 1993). In artificial lung devices, oxygen and carbon dioxide diffuse oppositely across the fiber membranes between a blood phase flowing outside the fibers, and a gas phase flowing through the fiber lumen (sweep gas). The principal determinants of exchange are the overall mass-transfer coefficient of the device, the total membrane surface area, and the differences in gas species partial pressure driving the exchange. Although most of the mass-transfer resistance resides within the membrane and blood phases (Qi and Cussler, 1985a,b), the flow dynamics of the sweep gas play a key role by dictating the partial pressure of the exchanging species within the gas phase. That is, for a given species exchange rate (0, or CO,), the fractional gas species concentration along the fiber depends on the sweep gas-flow rate through the fiber, and in turn the species partial pressure along the fiber lumen, the key intrafiber determinant of exchange, depends directly on both the fractional species concentration and the total gas pressure along the fiber. Thus, understanding the gas-flow dynamics (pressure-flow behavior) within hollow-fiber bundles becomes essential to designing oxygenators and to modeling their gas-exchange performance.The dynamics of gas flow within hollow-fiber membranes may appear superficially as an application of simple incompressible Poiseuille flow theory. The internal caliber of these fibers is generally 300 ,um or smaller, and their length to diameter ratios are typically large. For the gas-flow rates usually involved, Reynolds numbers are therefore unity or smaller, and the flow can be considered fully developed and laminar. The incompressible Poiseuille flow paradigm predicts, for example, a linear relation between pressure drop Correspondence concerning this article should be addressed to W. J. Federspiel. and resulting gas-flow rate (Gerhart et al., 1992). Although the usual indices suggesting compressible flow are small (e.g., Mach number and kinetic energy variations), the gas flow in hollow-fiber membranes cannot necessarily be considered incompressible. The small size of the fibers, coupled with their great relative length, means that flow resistance and pressured drops can be appreciable, and that variations in fluid density are potentially important.Our interest in studying the gas flow dynamics within hollow-fiber membranes arose as part of development work (Hattler et al., 1992) on an intravenous membrane oxygenator (IMO). All artificial lung devices must flow sufficient 0, sweep gas to minimize CO, accumulation in the fibers, and to avoid reducing CO, exchange as a result (cf., High et al., 1993). Extracorporeal oxygenators typically use several thousand fibers in parallel ( -4,000 to S,OOO), each of a relatively short length ( -...

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