On the determination of a generalized Darcy equation for yield stress fluid in porous media

Talon, Laurent

doi:10.1016/j.sctalk.2022.100042

Cited by 4 publications

(2 citation statements)

References 11 publications

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“…Howell and Atkinson (1976) showed that, in trickling filters, constant influent concentration and operating conditions can yield large fluctuations induced by sloughing events. Stewart and Scott Fogler (2002) found very large oscillations in the pressure signal due to the formation of successive stable or unstable dextran plugs of Leuconostoc mesenteroides biofilm, behaving in a way similar to a yield stress fluid, and allowing flow only through breakthrough channels -see also discussions on the flow of yield stress fluids through porous media in (Talon, 2022). Sharp et al (2005) showed that "the pore channels are dynamic, changing in sized, number and location with time" in a flat plate reactor colonized by Vibrio fischeri biofilm.…”

Section: Self-sustained Fluctuationsmentioning

confidence: 99%

Should I stay or should I go? Spatio-temporal dynamics of bacterial biofilms in confined flows

Benbelkacem,

Ramos,

El Garah

et al. 2024

Preprint

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The vast majority of bacteria live in sessile biofilms that colonize the channels, pores and crevices of confined structures. Flow in these structures carries the nutrients necessary for growth, but also generates stresses and detachment from surfaces. Conversely, bacteria tend to occupy a large part of the available space and, in so doing, increase resistance to flow and modify transport properties. Although the importance of advective transport and hydrodynamic forces on bacteria is well known, the complex feedback effects that control development in confined geome-tries are much less understood. Here, we study how couplings between flow and bacterial development control the spatio-temporal dynamics ofPseudomonas aeruginosain microchannel flows. We demonstrate that nutrient limitation drives the longitudinal distribution of biomass, while a competition between growth and flow-induced detachment controls the maximum clogging and the temporal dynamics. We find that successive cycles of sloughing and growth cause persistent fluctuations of the hydraulic resistance and prevent the system from ever reaching a true steady-state. Our results indicate that these self-sustained fluctuations are a signature effect of biofilm development in confined flows and could thus be a key component of the spreading of biofilms in infections, environmental processes and engineering applications. Consistent with the description of other bursting events, such as earthquakes or avalanches, we further show that the dynamics of sloughing can be described as a jump stochastic process with a gamma distribution of interevent times. This stochastic modeling approach opens the way towards a new quantitative approach to the characterization of the apparent randomness and irreproducibility of biofilm experiments in such systems.

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Section: Self-sustained Fluctuationsmentioning

confidence: 99%

Should I stay or should I go? Spatio-temporal dynamics of bacterial biofilms in confined flows

Benbelkacem,

Ramos,

El Garah

et al. 2024

Preprint

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“…Nevertheless, in the intricate transport mechanism of yield-stress fluids through porous media, several mutual features can be identified regardless of the scales on which the previous studies are focused. In a number of studies (Talon & Bauer 2013;Liu et al 2019;Talon 2022), four regimes are detected in terms of flow rate (Q)-applied pressure gradient ( P/L): (i) when the applied pressure gradient is less than a critical pressure gradient ( P c /L), there is no flow (Q = 0); (ii) if the applied pressure gradient slightly exceeds the critical value, the flow is extremely localised in a channel and the flow rate linearly scales with the excessive pressure gradient where other parts of the fluid are quiescent; (iii) the third regime emerges when the applied pressure gradient increases, more and more channels appear (moderate values of pressure gradient) and the flow rate scales quadratically with the excessive applied pressure gradient; (iv) finally, when the applied pressure gradient is much higher than the critical value, the flow rate again scales linearly with the excessive pressure gradient.…”

Section: Introductionmentioning

confidence: 99%

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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General hydrodynamic features of elastoviscoplastic fluid flows through randomised porous media

Parvar,

Chaparian,

Tammisola

2024

Theor. Comput. Fluid Dyn.

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A numerical study of yield-stress fluids flowing in porous media is presented. The porous media is randomly constructed by non-overlapping mono-dispersed circular obstacles. Two class of rheological models are investigated: elastoviscoplastic fluids (i.e. Saramito model) and viscoplastic fluids (i.e. Bingham model). A wide range of practical Weissenberg and Bingham numbers is studied at three different levels of porosities of the media. The emphasis is on revealing some physical transport mechanisms of yield-stress fluids in porous media when the elastic behaviour of this kind of fluids is incorporated. Thus, computations of elastoviscoplastic fluids are performed and are compared with the viscoplastic fluid flow properties. At a constant Weissenberg number, the pressure drop increases both with the Bingham number and the solid volume fraction of obstacles. However, the effect of elasticity is less trivial. At low Bingham numbers, the pressure drop of an elastoviscoplastic fluid increases compared to a viscoplastic fluid, while at high Bingham numbers we observe drag reduction by elasticity. At the yield limit (i.e. infinitely large Bingham numbers), elasticity of the fluid systematically promotes yielding: elastic stresses help the fluid to overcome the yield stress resistance at smaller pressure gradients. We observe that elastic effects increase with both Weissenberg and Bingham numbers. In both cases, elastic effects finally make the elastoviscoplastic flow unsteady, which consequently can result in chaos and turbulence. Graphical abstract

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On the determination of a generalized Darcy equation for yield stress fluid in porous media

Cited by 4 publications

References 11 publications

Should I stay or should I go? Spatio-temporal dynamics of bacterial biofilms in confined flows

Should I stay or should I go? Spatio-temporal dynamics of bacterial biofilms in confined flows

Yielding to percolation: a universal scale

General hydrodynamic features of elastoviscoplastic fluid flows through randomised porous media

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