The slow viscous flow around doublyperiodic arrays of infinite slender cylinders
Abstract
The slow viscous flow through a doublyperiodic array of cylinders does not have an analytical solution. However, as a reduced model for the flow within fibrous porous media, this solution is important for many realworld systems. We asymptotically determine the flow around a doublyperiodic array of infinite slender cylinders, by placing doublyperiodic twodimensional singularity solutions within the cylinder and expanding the noslip condition on the cylinder's surface in powers of the cylinder radius. The asymptotic solution provides a closedform estimate for the flow and forces as a function of the radius and the dimensions of the cell. The force is compared to results from latticeBoltzmann simulations of lowReynoldsnumber flows in the same geometry, and the accuracy of the noslip condition on the surface of the cylinder, predicted by the asymptotic theory, is checked. Finally, the behaviour of the flow, flux, force and effective permeability of the cell is investigated as a function of the geometric parameters. The structure of the asymptotic permeability is consistent with other models for the flow parallel to an array of rods. These models could be used to help understand the flows within porous systems composed of fibres and systems involving periodic arrays such as deterministic lateral displacement.
 Publication:

arXiv eprints
 Pub Date:
 January 2023
 DOI:
 10.48550/arXiv.2301.12774
 arXiv:
 arXiv:2301.12774
 Bibcode:
 2023arXiv230112774K
 Keywords:

 Physics  Fluid Dynamics;
 Condensed Matter  Soft Condensed Matter