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Incorporating Darcy's law for pure solvent flow through porous tubes: Asymptotic solution and numerical simulations
Author(s) -
Tilton Nils,
Martinand Denis,
Serre Eric,
Lueptow Richard M.
Publication year - 2012
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.13823
Subject(s) - mechanics , darcy's law , flow (mathematics) , compressibility , tube (container) , coupling (piping) , newtonian fluid , porous medium , porosity , thermodynamics , physics , engineering , mechanical engineering , geotechnical engineering
Abstract A generalized solution for pressure‐driven, incompressible, Newtonian flow in a porous tubular membrane is challenging due to the coupling between the transmembrane pressure and velocity. To date, all analytical solutions require simplifications such as neglecting the coupling between the transmembrane pressure and velocity, assuming the form of the velocity fields, or expanding in powers of parameters involving the tube length. Moreover, previous solutions have not been validated with comparison to direct numerical simulation (DNS). We comprehensively revisit the problem to present a robust analytical solution incorporating Darcy's law on the membrane. We make no assumptions about the tube length or form of the velocity fields. The analytic solution is validated with detailed comparison to DNSs, including cases of axial flow exhaustion and cross flow reversal. We explore the validity of typical assumptions used in modeling porous tube flow and present a solution for porous channels in Supporting Information. © 2012 American Institute of Chemical Engineers AIChE J, 2012