Incorporating Darcy's law for pure solvent flow through porous tubes: Asymptotic solution and numerical simulations

Nils Tilton, Denis Martinand*, Eric Serre, Richard M Lueptow

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

14 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)2030-2044
Number of pages15
JournalAICHE Journal
Volume58
Issue number7
DOIs
StatePublished - Jul 1 2012

Keywords

  • Asymptotic expansion
  • Cross flow filtration
  • Darcy's law
  • Direct numerical simulation
  • Porous tube

ASJC Scopus subject areas

  • Biotechnology
  • Environmental Engineering
  • Chemical Engineering(all)

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