How to calculate tortuosity easily?

Matyka, Maciej; Koza, Zbigniew

doi:10.1063/1.4711147

Cited by 72 publications

(51 citation statements)

References 21 publications

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“…4a for D A = 9.8 × 10 −10 m 2 /s and D B (m 2 /s) = 5.8 × 10 −7 = ffiffiffiffiffiffiffi tðsÞ p . The diffusivity of A in the precipitate was estimated from its molecular diffusivity in solution D A∞ = 5.3 × 10 −9 m 2 /s, the measured porosity of the precipitate ϕ = 0.52, and its tortuosity τ = 2.8, as D A = ϕD A∞ =τ; the relatively high value for the tortuosity is consistent with a precipitate composed of channels at an angle of ∼ 20°to the membrane surface (30). For the transport of B in the gel layer, we need to consider hydrodynamic effects.…”

Section: Model and Comparison With Experimentsmentioning

confidence: 99%

Wavy membranes and the growth rate of a planar chemical garden: Enhanced diffusion and bioenergetics

Ding

Batista

Steinbock

et al. 2016

Proc. Natl. Acad. Sci. U.S.A.

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To model ion transport across protocell membranes in Hadean hydrothermal vents, we consider both theoretically and experimentally the planar growth of a precipitate membrane formed at the interface between two parallel fluid streams in a 2D microfluidic reactor. The growth rate of the precipitate is found to be proportional to the square root of time, which is characteristic of diffusive transport. However, the dependence of the growth rate on the concentrations of hydroxide and metal ions is approximately linear and quadratic, respectively. We show that such a difference in ionic transport dynamics arises from the enhanced transport of metal ions across a thin gel layer present at the surface of the precipitate. The fluctuations in transverse velocity in this wavy porous gel layer allow an enhanced transport of the cation, so that the effective diffusivity is about one order of magnitude higher than that expected from molecular diffusion alone. Our theoretical predictions are in excellent agreement with our laboratory measurements of the growth of a manganese hydroxide membrane in a microfluidic channel, and this enhanced transport is thought to have been needed to account for the bioenergetics of the first single-celled organisms.

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Section: Model and Comparison With Experimentsmentioning

confidence: 99%

Wavy membranes and the growth rate of a planar chemical garden: Enhanced diffusion and bioenergetics

Ding

Batista

Steinbock

et al. 2016

Proc. Natl. Acad. Sci. U.S.A.

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“…Furthermore, for higher misalignment, it is found that pinning is clearly stronger in the case of narrower necks and smaller periods (results not shown for brevity). We also consider the tortuosity (Duda et al, 2011;Matyka & Koza, 2012). The tortuosity is a measure of the departure of fluid flow from straight pathways.…”

Section: Sinusoidal Profilesmentioning

confidence: 99%

“…The tortuosity is a measure of the departure of fluid flow from straight pathways. The calculations are made by means of the formula λ = < u > / < u x > (Duda et al, 2011;Matyka & Koza, 2012), u being the overall fluid velocity Shan & Chen, 1993;Shan & Doolen, 1995). It should be kept in mind that at the interface there are spurious currents (Wagner, 2003).…”

Section: Sinusoidal Profilesmentioning

confidence: 99%

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Lattice Boltzmann simulations on the role of channel structure for reactive capillary infiltration

Sergi

Grossi

Leidi

et al. 2015

Engineering Applications of Computational Fluid Mechanics

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It is widely recognized that the structure of porous media is of relevance for a variety of mechanical and physical phenomena. The focus of the present work is on capillarity, a pore-scale process occurring at the micron scale. We attempt to characterize the influence of pore shape for capillary infiltration by means of Lattice Boltzmann simulations in 2D with reactive boundaries leading to surface growth and ultimately to pore closure. The systems under investigation consist of single channels with different simplified morphologies: namely, periodic profiles with sinusoidal, step-shaped and zigzag walls, as well as constrictions and expansions with rectangular, convex and concave steps. This is a useful way to break the complexity of typical porous media down into basic structures. The simulations show that the minimum radius alone fails to properly characterize the infiltration dynamics. The structure of the channels emerges as the dominant property controlling the process. A factor responsible for this behavior is identified as being the occurrence of the pinning of the contact line. It turns out that the optimal configuration for the pore structure arises from the packing of large particles with round shapes. In this case, the probability of having wide and straight flow paths is higher. Faceted surfaces with sharp edges should be avoided because of the phenomenon of pinning near narrow-to-wide parts. This study is motivated by the infiltration of molten metals into carbon preforms. This is a manufacturing technique for ceramic components devised for advanced applications. Guidelines for experimental work are discussed.

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“…Another quantity that is taken into account is the tortuosity (Bear, 1972) which is defined as the ratio of the actual length of the capillary paths to the corresponding length of the sample. The formula u / u x (Duda, Koza, & Matyka, 2011;Matyka & Koza, 2012) is used for the computations, where u is the magnitude of the fluid velocity of the components u x and u y . It is worth recalling that at the interface there are spurious currents (Wagner, 2003).…”

Section: Models and Analysismentioning

confidence: 99%

Simulation of capillary infiltration into packing structures for the optimization of ceramic materials using the lattice Boltzmann method

Sergi

Grossi

Leidi

et al. 2016

Engineering Applications of Computational Fluid Mechanics

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This study uses the lattice Boltzmann method (LBM) to simulate in 2D the capillary infiltration into porous structures obtained from the packing of particles. The experimental problem motivating the work is the densification of carbon preforms by reactive melt infiltration. The aim is to determine the optimization principles for the manufacturing of high-performance ceramics. Simulations are performed for packings with varying structural properties. The results suggest that the observed slow infiltrations can be ascribed to interface dynamics. Pinning represents the primary factor retarding fluid penetration. The mechanism responsible for this phenomenon is analyzed in detail. When surface growth is allowed, it is found that the phenomenon of pinning becomes stronger. Systems trying to reproduce typical experimental conditions are also investigated. It turns out that the standard for accurate simulations is challenging. The primary obstacle to overcome for enhanced accuracy seems to be the over-occurrence of pinning. ARTICLE HISTORY

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How to calculate tortuosity easily?

Cited by 72 publications

References 21 publications

Wavy membranes and the growth rate of a planar chemical garden: Enhanced diffusion and bioenergetics

Wavy membranes and the growth rate of a planar chemical garden: Enhanced diffusion and bioenergetics

Lattice Boltzmann simulations on the role of channel structure for reactive capillary infiltration

Simulation of capillary infiltration into packing structures for the optimization of ceramic materials using the lattice Boltzmann method

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