A mathematical model has been developed to predict the coupled hydrodynamics and high-molecular-weight protein transport in mammalian-cell hollow-fiber bioreactors (HFBRs). The analysis applies to reactors with isotropic ultrafiltration membranes under startup conditions when the extracapillary space (ECS) is essentially unobstructed by cells. The model confirms the experimental finding that secondary ECS flows, engendered by the primary flow in the fiber lumens, can cause significant downstream polarization of ECS proteins al typical mammalian-cell HFBR operating conditions. It also reveals that the osmotic activity of the proteins, by curtailing transmembrane fluid fluxes, can influence strongly the outcome of the polarization process. In fact, at order-of-magnitude higher protein concentrations and/or lower recycle flow rates, the secondary flow velocities can be reduced by as much as six orders-of-magnitude throughout the ECS, thereby virtually eliminating the polarization problem. This result has important implications for improved reactor startup procedures.