A modified Darcy’s law for viscoelastic flows of highly dilute polymer solutions through porous media
نویسندگان
چکیده
Viscoelastic flows of polymer solutions in complex geometries can generate a strong localization stress within small regions the fluid and formation birefringent strands. In porous media, these localized structures drive preferential flow paths increase global dissipation. Modeling impact such effects at Darcy or larger scales is daunting task—one reasons being lack approaches using homogenization theories to help figure out both correct form averaged transport equations relevant set effective parameters. Here we homogenize incompressible Oldroyd-B zero Reynolds number obtain scale model that captures effect polymeric stress. This consists an advection—reaction equation for average conformation tensor along with Darcy’s law contains additional forcing term associated The derivation based upon limit high dilution, regime where be transformed into sequence linear problems asymptotic developments. We validate our approach test cases corresponding channel through arrays circles. Besides providing new viscoelastic work also shows modeling media not simply matter determining apparent permeability tensor—the homogenized cannot easily reduced simple law—but rather requires development specific models capture coupling between momentum.
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ژورنال
عنوان ژورنال: Journal of Non-newtonian Fluid Mechanics
سال: 2022
ISSN: ['1873-2631', '0377-0257']
DOI: https://doi.org/10.1016/j.jnnfm.2022.104919