Journal
JOURNAL OF FLUID MECHANICS
Volume 871, Issue -, Pages 742-754Publisher
CAMBRIDGE UNIV PRESS
DOI: 10.1017/jfm.2019.298
Keywords
microfluidics; porous media
Categories
Funding
- Basic Science Research Program through the National Research Foundation of Korea (NRF) - Ministry of Science, ICT & Future Planning [2014M3C1B1033982, 2017R1A2B2006964]
- NSF [CMMI-1661672, DMR-1420541]
- VILLUM FONDEN [13166]
- National Research Foundation of Korea [2014M3C1B1033982, 2017R1A2B2006964] Funding Source: Korea Institute of Science & Technology Information (KISTI), National Science & Technology Information Service (NTIS)
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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 Q and the applied pressure drop Delta p, 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.
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