11,588 research outputs found
Lattice and Continuum Modelling of a Bioactive Porous Tissue Scaffold
A contemporary procedure to grow artificial tissue is to seed cells onto a
porous biomaterial scaffold and culture it within a perfusion bioreactor to
facilitate the transport of nutrients to growing cells. Typical models of cell
growth for tissue engineering applications make use of spatially homogeneous or
spatially continuous equations to model cell growth, flow of culture medium,
nutrient transport, and their interactions. The network structure of the
physical porous scaffold is often incorporated through parameters in these
models, either phenomenologically or through techniques like mathematical
homogenization. We derive a model on a square grid lattice to demonstrate the
importance of explicitly modelling the network structure of the porous
scaffold, and compare results from this model with those from a modified
continuum model from the literature. We capture two-way coupling between cell
growth and fluid flow by allowing cells to block pores, and by allowing the
shear stress of the fluid to affect cell growth and death. We explore a range
of parameters for both models, and demonstrate quantitative and qualitative
differences between predictions from each of these approaches, including
spatial pattern formation and local oscillations in cell density present only
in the lattice model. These differences suggest that for some parameter
regimes, corresponding to specific cell types and scaffold geometries, the
lattice model gives qualitatively different model predictions than typical
continuum models. Our results inform model selection for bioactive porous
tissue scaffolds, aiding in the development of successful tissue engineering
experiments and eventually clinically successful technologies.Comment: 38 pages, 16 figures. This version includes a much-expanded
introduction, and a new section on nonlinear diffusion in addition to polish
throughou
Dynamic development of hydrofracture
Many natural examples of complex joint and vein networks in layered sedimentary rocks are hydrofractures that form by a combination of pore fluid overpressure and tectonic stresses. In this paper, a two-dimensional hybrid hydro-mechanical formulation is proposed to model the dynamic development of natural hydrofractures. The numerical scheme combines a discrete element model (DEM) framework that represents a porous solid medium with a supplementary Darcy based pore-pressure diffusion as continuum description for the fluid. This combination yields a porosity controlled coupling between an evolving fracture network and the associated hydraulic field. The model is tested on some basic cases of hydro-driven fracturing commonly found in nature, e.g., fracturing due to local fluid overpressure in rocks subjected to hydrostatic and nonhydrostatic tectonic loadings. In our models we find that seepage forces created by hydraulic pressure gradients together with poroelastic feedback upon discrete fracturing play a significant role in subsurface rock deformation. These forces manipulate the growth and geometry of hydrofractures in addition to tectonic stresses and the mechanical properties of the porous rocks. Our results show characteristic failure patterns that reflect different tectonic and lithological conditions and are qualitatively consistent with existing analogue and numerical studies as well as field observations. The applied scheme is numerically efficient, can be applied at various scales and is computational cost effective with the least involvement of sophisticated mathematical computation of hydrodynamic flow between the solid grains
On pore-scale modeling and simulation of reactive transport in 3D geometries
Pore-scale modeling and simulation of reactive flow in porous media has a
range of diverse applications, and poses a number of research challenges. It is
known that the morphology of a porous medium has significant influence on the
local flow rate, which can have a substantial impact on the rate of chemical
reactions. While there are a large number of papers and software tools
dedicated to simulating either fluid flow in 3D computerized tomography (CT)
images or reactive flow using pore-network models, little attention to date has
been focused on the pore-scale simulation of sorptive transport in 3D CT
images, which is the specific focus of this paper. Here we first present an
algorithm for the simulation of such reactive flows directly on images, which
is implemented in a sophisticated software package. We then use this software
to present numerical results in two resolved geometries, illustrating the
importance of pore-scale simulation and the flexibility of our software
package.Comment: 15 pages, 6 figure
Pore-scale fluid flow simulation coupling lattice Boltzmann method and pore network model
The lattice Boltzmann method and pore network model are two types of the most popular pore-scale fluid flow simulation methods. As a direct numerical simulation method, lattice Boltzmann method simulates fluid flow directly in the realistic porous structures, characterized by high computational accuracy but low efficiency. On the contrary, pore network model simulates fluid flow in simplified regular pore networks of the real porous media, which is more computationally efficient, but fails to capture the detailed pore structures and flow processes. In past few years, significant efforts have been devoted to couple lattice Boltzmann method and pore network model to simulate fluid flow in porous media, aiming to combine the accuracy of lattice Boltzmann method and efficiency of pore network model. In this mini-review, the recent advances in pore-scale fluid flow simulation methods coupling lattice Boltzmann method and pore network model are summarized, in terms of single-phase flow, quasi-static two-phase drainage flow and dynamic two-phase flow in porous media, demonstrating that coupling the lattice Boltzmann method and pore network model offers a promising and effective approach for addressing the up-scaling problem of flow in porous media.Cited as: Zhao, J., Liu, Y., Qin, F., Fei, L. Pore-scale fluid flow simulation coupling lattice Boltzmann method and pore network model. Capillarity, 2023, 7(3): 41-46. https://doi.org/10.46690/capi.2023.06.0
Pore-scale Modeling of Viscous Flow and Induced Forces in Dense Sphere Packings
We propose a method for effectively upscaling incompressible viscous flow in
large random polydispersed sphere packings: the emphasis of this method is on
the determination of the forces applied on the solid particles by the fluid.
Pore bodies and their connections are defined locally through a regular
Delaunay triangulation of the packings. Viscous flow equations are upscaled at
the pore level, and approximated with a finite volume numerical scheme. We
compare numerical simulations of the proposed method to detailed finite element
(FEM) simulations of the Stokes equations for assemblies of 8 to 200 spheres. A
good agreement is found both in terms of forces exerted on the solid particles
and effective permeability coefficients
Explicit incorporation of discrete fractures into pore network models
Research Funding China Scholarship Council. Grant Number: 201708060457Peer reviewedPublisher PD
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