Variational linear comparison homogenization estimates for the flow of yield stress fluids through porous media

Castañeda, Pedro Ponte

doi:10.1016/j.jnnfm.2023.105104

Cited by 2 publications

(2 citation statements)

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“…This upper bound is shown by the cyan line in the inset of figure 6 along with the proposed universal scale for comparison. Note that the upper bound proposed by Castañeda (2023) has a linear functionality with φ/(1 − φ) which further validates the universal scale derived here, although its slope is steeper -which is not surprising as it is an upper bound.…”

Section: Universal Scalesupporting

confidence: 85%

“…Circles, squares and pentagrams represent the circle, square and polygon obstacles, respectively. Inset: comparison between the upper bound of the critical pressure gradient (cyan line) derived by Castañeda (2023) and the proposed universal scale (dashed orange line). Please note that the axes of the inset are the same as the main figure.…”

Section: Universal Scalementioning

confidence: 99%

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Yielding to percolation: a universal scale

Chaparian

2024

J. Fluid Mech.

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A theoretical and computational study analysing the initiation of yield-stress fluid percolation in porous media is presented. Yield-stress fluid flows through porous media are complicated due to the nonlinear rheological behaviour of this type of fluid, rendering the conventional Darcy type approach invalid. A critical pressure gradient must be exceeded to commence the flow of a yield-stress fluid in a porous medium. As the first step in generalising the Darcy law for yield-stress fluids, a universal scale based on the variational formulation of the energy equation is derived for the critical pressure gradient which reduces to the purely geometrical feature of the porous media. The presented scaling is then validated by both exhaustive numerical simulations (using an adaptive finite element approach based on the augmented Lagrangian method), and also the previously published data. The considered porous media are constructed by randomised obstacles with various topologies; namely square, circular and alternatively polygonal obstacles which are mimicked based on Voronoi tessellation of circular cases. Moreover, computations for the bidispersed obstacle cases are performed which further demonstrate the validity of the proposed universal scaling.

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Section: Universal Scalesupporting

confidence: 85%

Section: Universal Scalementioning

confidence: 99%