Permeability of periodic arrays of cylinders for viscoelastic flows

Abstract

In this paper we numerically investigate the motion of viscoelastic liquids passing through two-dimensional periodic arrays of cylindrical particles using the finite element method. The viscoelastic liquid is modeled by the Chilcott–Rallison version of the finitely extensible, nonlinear elastic (FENE) dumbbell model. The permeability and the viscoelastic stress distribution are studied as functions of the dimensionless relaxation time De and the dimensionless wave number kD, where k=2π/λ is the wave number, λ is the distance between the particles in the flow direction and D is the cylinder diameter. The porosity and D are held fixed. Our simulations show that for a fixed value of De the viscoelastic permeability increases with kD, but, as is the case for Newtonian fluid [Alcocer, Kumar, and Singh, Phys. Rev. E 59, 711 (1999)], this increase is not monotonic. The permeability decreases between kD≈5.0, where it is locally maximum, and kD≈7.7, where it is locally minimum. The difference between the locally maximum and minimum values of permeability increases with increasing De. When De=O(1) the locally minimum value of the permeability is ∼40% smaller than the value at the local maximum. This implies that a substantial change in permeability can be achieved by changing the distance between the particles in the flow direction while keeping De, D, and porosity fixed.

Flow of wormlike micelle solutions through a periodic array of cylinders

“…These trends also match very well with recent observations by Talwar et al [19] who studied the flow of polymer solutions through periodic arrays of cylinders as well as others [17,19,24,26,27,46,[61][62][63]. They reported a dimensionless drag in terms of the product of the friction factor and the Reynolds number fRe.…”

Elastoviscoplastic flows in porous media

“…Numerical simulations have also proved to be a valid tool to investigate viscoelastic flows in porous media, uncovering the details of the fluid deformation and stresses. Alcocer and Singh [24] studied the viscoelastic flow through an array of cylinders using the finite element method and a FENE (finitely extensible nonlinear elastic) model for the stresses. These authors have shown the influence of the cylinder distribution and Deborah number on the permeability of the medium.…”

Thickening of viscoelastic flow in a model porous medium

“…However the validity of this macroscopic approach remains largely limited to Newtonian flows. In theoretically understanding viscoelastic creeping flows in porous media, much of the progress has been made computationally [15][16][17][18][19][20][21]. Early simulations of two-dimensional (2D) viscoelastic flow past a bi-periodic square [15,16] or rectangular [17] array of cylinders observed a slightly reduced pressure drop at low Weissenberg numbers compared to that of a Newtonian fluid of matched viscosity, as seen experimentally.…”

“…Alcocer et al [19,20] investigated 2D flow of the FENE-CR model past a biperiodic array of cylinders, with a particular focus on the dependence of the effective permeability on the cell aspect ratio, for a fixed area fraction of cylinders. They demonstrated a non-monotonic dependence of permeability on aspect ratio.…”