Modeling the Transverse Shell-side Mass Transfer in Hollow Fiber Membrane Contactors at Low Reynolds Numbers

A method for calculating the external mass transfer in a contactor with a transverse confined flow of a viscous incompressible liquid (gas) past hollow fibers at low Reynolds numbers is proposed. The method is based on the concept of regular arrays of parallel fibers with a well-defined flowfield. As a simplest model system, a row of parallel fibers is considered, for which dependences of a drag force and an efficiency of a solute retention on the inter-fiber distance, membrane mass transfer coefficient, Peclet and Reynolds numbers are computed. The influence of the fluid inertia on the mass transport is studied. It is shown that a linear Stokes equations can be used for as higher Re numbers, as denser is the fiber array. In this case the flow field is independent on the Re number, and analytical solutions for the flowfield and fiber sorption efficiency (fiber Sherwood number) can be used.