# Simulation of Convection–Diffusion Transport in a Laminar Flow Past a Row of Parallel Absorbing Fibers

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A.V. Topchiev Institute of Petrochemical Synthesis, Russian Academy of Sciences, Moscow 119991, Russia

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A.N. Frumkin Institute of Physical Chemistry and Electrochemistry, Russian Academy of Sciences, Moscow 119071, Russia

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Institute of Physical Organic Chemistry, National Academy of Sciences of Belarus, 220072 Minsk, Belarus

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Author to whom correspondence should be addressed.

Received: 1 November 2018 / Revised: 20 November 2018 / Accepted: 22 November 2018 / Published: 25 November 2018

(This article belongs to the Special Issue Polymer Hollow Fiber Membrane 2019)

A numerical simulation of the laminar flow field and convection–diffusion mass transfer in a regular system of parallel fully absorbing fibers for the range of Reynolds numbers up to Re = 300 is performed. An isolated row of equidistant circular fibers arranged normally to the external flow is considered as the simplest model for a hollow-fiber membrane contactor. The drag forces acting on the fibers with dependence on Re and on the ratio of the fiber diameter to the distance between the fiber axes, as well as the fiber Sherwood number versus Re and the Schmidt number, Sc, are calculated. A nonlinear regression formula is proposed for calculating the fiber drag force versus Re in a wide range of the interfiber distances. It is shown that the Natanson formula for the fiber Sherwood number as a function of the fiber drag force, Re, and Sc, which was originally derived in the limit of high Peclet numbers, is applicable for small and intermediate Reynolds numbers; intermediate and large Peclet numbers, where Pe = Re × Sc; and for sparse and moderately dense rows of fibers.