Cross-flow mass transfer in a model hexagonal system of hollow fiber membranes

Abstract

A method for calculating external mass transfer in a contactor with transverse confined flow of a viscous incompressible liquid (gas) past a hollow fiber membrane at low Reynolds numbers has been proposed. The method is based on the concept of array of hollow fiber membranes as a hexagonal system of parallel fibers to which the Kuwabara cell model with a known flowfield is applicable. Asymmetric membranes with macroporous permeable outer supports have been considered. A solution of the problem on the external Stokes flow past a hollow fiber membrane in the cell, taking into account the hydrodynamic permeability of the support, has been found in terms of the model. To describe the flow inside and outside the support, joining of the general solutions to the Stokes and Brinkman equations has been used. The Saffman slip condition has been set on the surface of the low-permeability membrane. The dependences of the stream function, velocity components, and drag force upon the fiber packing density and support permeability and thickness have been revealed. Efficiency η of solute sorption by the fiber has been calculated for the flowfield found, assuming zero component concentration at the membrane surface (full absorption approximation). The dependences of η on the diffusion Peclet number, support permeability and thickness, and fiber packing density have been calculated. Direct 3D simulation of convective mass transfer in the contactor at low Reynolds numbers has been performed, and the cell model has been shown to be applicable to the calculation of the contactor with a predominantly two-dimensional transverse flow.