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Simulation of convective-diffusional processes in hollow fiber membrane contactors

•A model hollow-fiber contactor with a regular arrangement of fibers is considered.•An impact of the fiber packing density on the constrained flow is studied.•Best-fit regression formula for the fiber Sherwood number at Re⩽50 is derived.•A retarded increase in Sh with Re at constant Pe and packing d...

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Published in:Separation and purification technology 2016-07, Vol.167, p.63-69
Main Authors: Kirsch, V.A., Roldugin, V.I., Bildyukevich, A.V., Volkov, V.V.
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description •A model hollow-fiber contactor with a regular arrangement of fibers is considered.•An impact of the fiber packing density on the constrained flow is studied.•Best-fit regression formula for the fiber Sherwood number at Re⩽50 is derived.•A retarded increase in Sh with Re at constant Pe and packing density is demonstrated.•Contactors with radial Stokes flow are studied. A model for the simulation of the shell-side convective diffusion of a solute in the hollow-fiber contactor with a regular arrangement of fibers is advanced. The model takes into account the impact of the fiber packing density on the shell-side constrained flow and solute transport. A system of periodic rows of parallel monodisperse fibers arranged normally to the laminar flow direction is considered as a model contactor. Flow and solute concentration fields are calculated from the numerical solution of the Navier-Stokes and convective diffusion equations over a broad range of the inter-fiber distances, Reynolds (Re) and diffusion Peclet (Pe) numbers. For the calculated fiber drag force and for the fiber Sherwood number (Sh) for high and intermediate Peclet numbers Pe≫1 and at Re⩽50, the best-fit regression formulas are found. The fiber Sherwood number governs the contactor retention efficiency via E=1-exp(-4αHSh/a), where a is the fiber radius, H is the thickness of the layer of fibers, α is the packing density of fibers. For a dense fibrous medium, a retarded increase in Sh with Re at constant Pe and packing density is demonstrated. Fiber retention efficiency is shown to follow the fiber drag force, which makes it possible to estimate the solute retention efficiency of a contactor from its hydrodynamic resistance to the shell-side flow. A convective-diffusional transport of a solute in the hollow fiber contactor with a radial Stokes flow is also considered.
doi_str_mv 10.1016/j.seppur.2016.04.042
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A model for the simulation of the shell-side convective diffusion of a solute in the hollow-fiber contactor with a regular arrangement of fibers is advanced. The model takes into account the impact of the fiber packing density on the shell-side constrained flow and solute transport. A system of periodic rows of parallel monodisperse fibers arranged normally to the laminar flow direction is considered as a model contactor. Flow and solute concentration fields are calculated from the numerical solution of the Navier-Stokes and convective diffusion equations over a broad range of the inter-fiber distances, Reynolds (Re) and diffusion Peclet (Pe) numbers. For the calculated fiber drag force and for the fiber Sherwood number (Sh) for high and intermediate Peclet numbers Pe≫1 and at Re⩽50, the best-fit regression formulas are found. 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A model for the simulation of the shell-side convective diffusion of a solute in the hollow-fiber contactor with a regular arrangement of fibers is advanced. The model takes into account the impact of the fiber packing density on the shell-side constrained flow and solute transport. A system of periodic rows of parallel monodisperse fibers arranged normally to the laminar flow direction is considered as a model contactor. Flow and solute concentration fields are calculated from the numerical solution of the Navier-Stokes and convective diffusion equations over a broad range of the inter-fiber distances, Reynolds (Re) and diffusion Peclet (Pe) numbers. For the calculated fiber drag force and for the fiber Sherwood number (Sh) for high and intermediate Peclet numbers Pe≫1 and at Re⩽50, the best-fit regression formulas are found. 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source ScienceDirect Journals
subjects Computer simulation
Contactors
Convective diffusion
Diffusion
Drag force
Fiber retention efficiency
Fibers
Hollow-fiber membrane
Mathematical models
Membrane contactor
Navier-Stokes equations
Packing density
Row of fibers
title Simulation of convective-diffusional processes in hollow fiber membrane contactors
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