Transport Processes in Porous Media

Coutelieris, Frank A.; Delgado, Jordi

doi:10.1007/978-3-642-27910-2

Cited by 51 publications

(46 citation statements)

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“…This value of = 10px is chosen as the most faithful representation of the actual network structure, without over-discretizing space and making numerical computation For a network of tubes with equal radii, a 0,k = a 0 , mass conservation is solved exactly by discrete values for ϕ k allowing for a standard Monte Carlo search to minimize local phase differences [3]. With a hierarchical distribution of radii, however, ϕ k are continuous and we use a Metropolis Hastings with simulated annealing technique [4,5]. The use of an augmented Lagrangian allows mass conservation to be enforced without ill-conditioning the random search [6].…”

Section: Pruning To Increase Taylor Dispersion In Physarum Polycephalummentioning

confidence: 99%

Pruning to Increase Taylor Dispersion inPhysarum polycephalumNetworks

et al. 2016

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How do the topology and geometry of a tubular network affect the spread of particles within fluid flows? We investigate patterns of effective dispersion in the hierarchical, biological transport network formed by Physarum polycephalum. We demonstrate that a change in topology -pruning in the foraging state -causes a large increase in effective dispersion throughout the network. By comparison, changes in the hierarchy of tube radii result in smaller and more localized differences. Pruned networks capitalize on Taylor dispersion to increase the dispersion capability.PACS numbers: 87.18. Vf, 87.16.Wd Transport due to fluid flowing through tubular networks is of great interest, because it has technological applications to biomimetic microfluidic devices [1][2][3], foams [4], fuel cells [5], and other filtration systems [6] and lies at the heart of extended organisms that rely on transport networks to function: animal vasculature [7,8], fungal mycelia [9], and plant tubes [10][11][12]. A big challenge regarding transport networks is to understand how network architecture changes the efficiency of particle spread throughout a network. While it is experimentally tedious to map particle transport in a network, predicting the spread of particles is also a theoretical challenge [13][14][15][16][17][18][19][20]. Attempts to understand how the network topology and geometry affect the transport of particles are scarce [17]. Alternatively, we can study the dynamic changes of tubular network architecture in living beings. Organisms spontaneously reorganize their transport networks, including tube pruning [21][22][23][24]. Examples are vessel development in zebra fish brain development [21], or growth of a large foraging fungal body [22]. Here, we study the slime mold Physarum polycephalum which emerged as an inspiring and yet puzzling model for 'intelligent' living transport networks.P. polycephalum like foraging fungi, actively adapts its network to environmental cues [25][26][27][28][29]. Networks connecting multiple food sources are a good compromise between efficiency, reliability, and cost, comparable to human transport networks [29]. Fluid cytoplasm enclosed in the tubular network exhibits nonstationary shuttle flows [30][31][32] driven by a peristaltic wave of contractions spanning the entire organism [33]. Investigations of transport in these networks are so far limited to estimates based on the minimal distance between tubes [29,34,35]. We tracked a well-reticulated individual trimmed from a larger network (Fig. 1). After several hours, the thin central tubes were abandoned in favor of a few large central tubes and globular structures at the periphery. How does this radical change of topology affect the transport capabilities of the individual? What role do hierarchical tube radii play? We present a method to efficiently map the effective dispersion of particles from any initiation site throughout any network with nonstationary but periodic fluid flows. We use this method to study the change in dispersion patterns ...

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Section: Pruning To Increase Taylor Dispersion In Physarum Polycephalummentioning

confidence: 99%

Pruning to Increase Taylor Dispersion inPhysarum polycephalumNetworks

et al. 2016

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“…Although the agreement is perfect for T = 25 • C (as expected by the "reverse engineering" process), it becomes more and more poor as temperature decreases, approaching approx. 10% difference for the low temperature of 10 • C. This inconsistency between experiment and model might be due to the internal inefficiencies of unit cell approach, which in particular overestimates the adsorption efficiency, as discussed in detail elsewhere [25]. On the contrary, modeling approach allows for a deep understanding and characterization of the processes occurs.…”

Section: Resultsmentioning

confidence: 96%

“…It should be noted that at porosities lower than 0.8, the available analytical approaches become gradually less accurate and therefore less dependable [25].…”

Section: Discussionmentioning

confidence: 99%

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A theoretical and experimental study on the P-adsorption capacity of Phoslock™

Zamparas

Gavriil

Coutelieris

et al. 2015

Applied Surface Science

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“…We will consider the case where has a uniform probability distribution and thus bounded range, and the case where takes a lognormal distribution, a common model in geophysics applications such as transport in porous media [3]. For other distributions, we assume that the diffusion coefficient .…”

Section: Uncertainty and Solution Proceduresmentioning

confidence: 99%

Linear Transport Under Uncertainty

Pettersson

Iaccarino

Nordström

2014

Polynomial Chaos Methods for Hyperbolic Partial Differential Equations

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The aim of this chapter, based on [18], is to present accurate and stable numerical schemes for the solution of a class of linear diffusive transport problems. The advection-diffusion equation subject to uncertain viscosity with known statistical description is represented by a spectral expansion in the stochastic dimension. The gPC framework and the stochastic Galerkin method are used to obtain an extended system which is analyzed to find discretization constraints on monotonicity, stiffness and stability. A comparison of stochastic Galerkin versus methods based on repeated evaluations of deterministic solutions, such as stochastic collocation, is provided but this is not our primary focus. However, we do include a few examples on relative performance and numerical properties with respect to monotonicity requirements and convergence to steady-state, to encourage the use of stochastic Galerkin methods.Special care is exercised to ensure that the stochastic Galerkin projection results in a system with a positive semidefinite diffusion matrix. The sign of the eigenvalues of a pure advection problem is not a stumbling block as long as the boundary conditions are properly adjusted to match the number of ingoing characteristics, as shown in [7]. Unlike the case of stochastic advection, the sign of the eigenvalues of the diffusion matrix of the advection-diffusion problem is crucial. A negative eigenvalue leads to the growth of the solution norm and hence numerical instability. The source of the growth is in the volume term, and no treatment of the boundary conditions can eliminate it.Advection-diffusion problems with uncertainty have been investigated by several authors. Ghanem and Dham

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Transport Processes in Porous Media

Cited by 51 publications

References 0 publications

Pruning to Increase Taylor Dispersion inPhysarum polycephalumNetworks

Pruning to Increase Taylor Dispersion inPhysarum polycephalumNetworks

A theoretical and experimental study on the P-adsorption capacity of Phoslock™

Linear Transport Under Uncertainty

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