Pressure-driven flow across a hyperelastic porous membrane

Ryungeun Song, Howard A. Stone, Kaare H. Jensen, Jinkee Lee*

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

We report an experimental investigation of pressure-driven flow of a viscous liquid across thin polydimethylsiloxane (PDMS) membranes. Our experiments revealed a nonlinear relation between the flow rate and the applied pressure drop, in apparent disagreement with Darcy's law, which dictates a linear relationship between flow rate, or average velocity, and pressure drop. These observations suggest that the effective permeability of the membrane decreases with pressure due to deformation of the nanochannels in the PDMS polymeric network. We propose a model that incorporates the effects of pressure-induced deformation of the hyperelastic porous membrane at three distinct scales: the membrane surface area, which increases with pressure, the membrane thickness, which decreases with pressure, and the structure of the porous material, which is deformed at the nanoscale. With this model, we are able to rationalize the deviation between Darcy's law and the data. Our result represents a novel case in which macroscopic deformations can impact the microstructure and transport properties of soft materials.

Original languageEnglish
JournalJournal of Fluid Mechanics
Volume871
Pages (from-to)742-754
Number of pages13
ISSN0022-1120
DOIs
Publication statusPublished - 2019

Keywords

  • Microfluidics
  • Porous media

Cite this

Song, Ryungeun ; Stone, Howard A. ; Jensen, Kaare H. ; Lee, Jinkee. / Pressure-driven flow across a hyperelastic porous membrane. In: Journal of Fluid Mechanics. 2019 ; Vol. 871. pp. 742-754.
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Pressure-driven flow across a hyperelastic porous membrane. / Song, Ryungeun; Stone, Howard A.; Jensen, Kaare H.; Lee, Jinkee.

In: Journal of Fluid Mechanics, Vol. 871, 2019, p. 742-754.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - Pressure-driven flow across a hyperelastic porous membrane

AU - Song, Ryungeun

AU - Stone, Howard A.

AU - Jensen, Kaare H.

AU - Lee, Jinkee

PY - 2019

Y1 - 2019

N2 - We report an experimental investigation of pressure-driven flow of a viscous liquid across thin polydimethylsiloxane (PDMS) membranes. Our experiments revealed a nonlinear relation between the flow rate and the applied pressure drop, in apparent disagreement with Darcy's law, which dictates a linear relationship between flow rate, or average velocity, and pressure drop. These observations suggest that the effective permeability of the membrane decreases with pressure due to deformation of the nanochannels in the PDMS polymeric network. We propose a model that incorporates the effects of pressure-induced deformation of the hyperelastic porous membrane at three distinct scales: the membrane surface area, which increases with pressure, the membrane thickness, which decreases with pressure, and the structure of the porous material, which is deformed at the nanoscale. With this model, we are able to rationalize the deviation between Darcy's law and the data. Our result represents a novel case in which macroscopic deformations can impact the microstructure and transport properties of soft materials.

AB - We report an experimental investigation of pressure-driven flow of a viscous liquid across thin polydimethylsiloxane (PDMS) membranes. Our experiments revealed a nonlinear relation between the flow rate and the applied pressure drop, in apparent disagreement with Darcy's law, which dictates a linear relationship between flow rate, or average velocity, and pressure drop. These observations suggest that the effective permeability of the membrane decreases with pressure due to deformation of the nanochannels in the PDMS polymeric network. We propose a model that incorporates the effects of pressure-induced deformation of the hyperelastic porous membrane at three distinct scales: the membrane surface area, which increases with pressure, the membrane thickness, which decreases with pressure, and the structure of the porous material, which is deformed at the nanoscale. With this model, we are able to rationalize the deviation between Darcy's law and the data. Our result represents a novel case in which macroscopic deformations can impact the microstructure and transport properties of soft materials.

KW - Microfluidics

KW - Porous media

U2 - 10.1017/jfm.2019.298

DO - 10.1017/jfm.2019.298

M3 - Journal article

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