Simulation of Impurity Absorption from Laminar Flow in a System of Hollow Fiber Membranes

The external steady flow of a viscous incompressible fluid and the convective-diffusion mass transfer of a solute in an ordered system of parallel hollow fiber membranes located perpendicular to the flow have been calculated in the ranges of Reynolds numbers \(\operatorname{Re} \) = 0.01–100 and Schmidt numbers \({\text{Sc}}\) = 1–1000. The Navier–Stokes equations and the convective diffusion equation have been solved using computational fluid dynamics methods with the no-slip boundary condition and the condition of a constant solute concentration on the outer surface of the streamlined fiber. Calculations have been performed for one row of fibers and for a system consisting of four and sixteen rows of fibers. The output concentrations and impurity absorption coefficients by the fiber \(\eta \) have been calculated depending on the packing density of the fibers \(\alpha \) and numbers \(\operatorname{Re} \) and \({\text{Sc}}\). The studies have shown that the absorption coefficient \(\eta \) by the fiber in an isolated row of fibers can be used to calculate the absorption efficiency of a thick fibrous bed.