A new partial-bounceback lattice-Boltzmann method for fluid flow through heterogeneous media

Walsh, Stuart; Burwinkle, H.; Saar, Martin O.

doi:10.1016/j.cageo.2008.05.004

Cited by 102 publications

(108 citation statements)

References 22 publications

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“…Equation (15) provides a subgrid-scale model for the membrane diffusion, and it is conveniently implemented even in arbitrarily complex geometries. Previously partialbounceback schemes have been used in the LBM context for modeling transport in porous media [15][16][17][18], thermal conduction across the boundary between two materials [19], or slip flows [20,21].…”

Section: Lattice-boltzmann Modeling Of Diffusion Across a Membranementioning

confidence: 99%

Diffusion through thin membranes: Modeling across scales

et al. 2016

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From macroscopic to microscopic scales it is demonstrated that diffusion through membranes can be modeled using specific boundary conditions across them. The membranes are here considered thin in comparison to the overall size of the system. In a macroscopic scale the membrane is introduced as a transmission boundary condition, which enables an effective modeling of systems that involve multiple scales. In a mesoscopic scale, a numerical lattice-Boltzmann scheme with a partial-bounceback condition at the membrane is proposed and analyzed. It is shown that this mesoscopic approach provides a consistent approximation of the transmission boundary condition. Furthermore, analysis of the mesoscopic scheme gives rise to an expression for the permeability of a thin membrane as a function of a mesoscopic transmission parameter. In a microscopic model, the mean waiting time for a passage of a particle through the membrane is in accordance with this permeability. Numerical results computed with the mesoscopic scheme are then compared successfully with analytical solutions derived in a macroscopic scale, and the membrane model introduced here is used to simulate diffusive transport between the cell nucleus and cytoplasm through the nuclear envelope in a realistic cell model based on fluorescence microscopy data. By comparing the simulated fluorophore transport to the experimental one, we determine the permeability of the nuclear envelope of HeLa cells to enhanced yellow fluorescent protein.

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Section: Lattice-boltzmann Modeling Of Diffusion Across a Membranementioning

confidence: 99%

Diffusion through thin membranes: Modeling across scales

et al. 2016

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“…Individual lattice nodes on one length scale are assigned generic properties of the underlying material at that node without explicitly describing the underlying material structure at the shorter length scale. Amongst such methods, the partial bounce back, effective media, algorithm proposed by Dardis and McCloskey, [9], and refined by Walsh, Burwinkle and Saar, (WBS), [10], is particularly easy to implement and computationally efficient. It has the advantage that, unlike some other schemes, it conserves mass and an analytic expression exists relating the permeability to the effective media parameter.…”

Section: Introductionmentioning

confidence: 99%

Combining effective media and multi-phase methods of Lattice Boltzmann modelling for the characterisation of liquid-vapour dynamics in multi-length scale heterogeneous structural materials

McDonald

Turner

2015

Modelling Simul. Mater. Sci. Eng.

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The combination of the lattice Boltzmann Shan-Chen pseudo-potential method for multiphase fluids (Shan & Chen, Phys. Rev. E 47, 1993, 1815 and a grey or partial bounce back lattice Boltzmann algorithm for effective media (Walsh et al, Comp. & Geosci. 35, 2009, 1186, is demonstrated for application to liquid-vapour fluid dynamics in porous media with porosity spanning a very wide range of length scales. Liquid / vapour distributions in cellular like structures with cell walls of reduced permeability are seen to follow expectation.

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“…To overcome this difficulty, we adopt LB effective media methods based on the ideas of partial bounce-back [22][23][24] to describe the C-S-H phase. Hence, each numerical node represents a permeable capillary pore, or an element of weakly-permeable nano-porous C-S-H, or an impermeable solid inclusion such as unhydrated cement.…”

Section: Introductionmentioning

confidence: 99%

“…noting that one of the methods that can be used to derive equation (13) starts by projecting the 3D lattice onto a 1D lattice (see Appendix A of [24]). The case of 0.5 σ = is a special case and may be interpreted as a checkerboard structure with 50% impermeable solids and 50% pores: the permeability of a checkerboard structure equals the permeability of a homogeneous medium for which ( ) 0.5 .…”

Section: Validation Of the Algorithmmentioning

confidence: 99%

A 3D lattice Boltzmann effective media study: understanding the role of C-S-H and water saturation on the permeability of cement paste

Zalzale

McDonald

Scrivener

2013

Modelling Simul. Mater. Sci. Eng.

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A 3D lattice Boltzmann model is developed and used to calculate the water and gas permeabilities of model cement pastes at different degrees of water saturation. In addition to permeable micron-sized capillary pores and impermeable solid inclusions, the lattice Boltzmann model comprises weakly-permeable nano-porous calcium silicate hydrate (C-S-H).The multi-scale problem is addressed by using an effective media approach based on the idea of partial bounce-back. The model cement paste microstructures are generated with the platform µic. The critical parameters, C-S-H density and capillary porosity, are taken from 1 H nuclear magnetic resonance relaxation analysis. The distribution of water and air is defined according to the Kelvin-Laplace law. It is found that when the capillary porosity is completely saturated with a fluid (either water or gas), the calculated intrinsic permeability is in good agreement with measurements of gas permeability on dried samples (10 -17 -10 -16 m 2 ).However, as the water saturation is reduced, the calculated apparent water permeability decreases and spans the full range of experimentally measured values (10 -16 -10 -22 m 2 ). It is concluded that the degree of capillary water saturation is the major cause for variation in experimental permeability measurements. It is further concluded that the role of the weaklypermeable C-S-H, omitted in earlier modelling studies, is critical for determining the permeability at low capillary saturation. Keywords

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A new partial-bounceback lattice-Boltzmann method for fluid flow through heterogeneous media

Cited by 102 publications

References 22 publications

Diffusion through thin membranes: Modeling across scales

Diffusion through thin membranes: Modeling across scales

Combining effective media and multi-phase methods of Lattice Boltzmann modelling for the characterisation of liquid-vapour dynamics in multi-length scale heterogeneous structural materials

A 3D lattice Boltzmann effective media study: understanding the role of C-S-H and water saturation on the permeability of cement paste

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