15,718 research outputs found
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
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
Particle Density Estimation with Grid-Projected Adaptive Kernels
The reconstruction of smooth density fields from scattered data points is a
procedure that has multiple applications in a variety of disciplines, including
Lagrangian (particle-based) models of solute transport in fluids. In random
walk particle tracking (RWPT) simulations, particle density is directly linked
to solute concentrations, which is normally the main variable of interest, not
just for visualization and post-processing of the results, but also for the
computation of non-linear processes, such as chemical reactions. Previous works
have shown the superiority of kernel density estimation (KDE) over other
methods such as binning, in terms of its ability to accurately estimate the
"true" particle density relying on a limited amount of information. Here, we
develop a grid-projected KDE methodology to determine particle densities by
applying kernel smoothing on a pilot binning; this may be seen as a "hybrid"
approach between binning and KDE. The kernel bandwidth is optimized locally.
Through simple implementation examples, we elucidate several appealing aspects
of the proposed approach, including its computational efficiency and the
possibility to account for typical boundary conditions, which would otherwise
be cumbersome in conventional KDE
Biofilms in porous media: development of macroscopic transport equations via volume averaging with closure for local mass equilibrium conditions
In this work, we upscale a pore-scale description of mass transport in a porous medium containing biofilm to develop the relevant Darcy-scale equations. We begin with the pore-scale descriptions of mass transport, interphase mass transfer, and biologically-mediated reactions; these processes are then upscaled using the method of volume averaging to obtain the macroscale mass balance equations. We focus on the case of local mass equilibrium conditions where the averaged concentrations in the fluid and biological phases can be assumed to be proportional and for which a one-equation macroscopic model may be developed. We predict the effective dispersion tensor by a closure scheme that is solved for the cases of both simple and complex unit cells. The domain of validity of the approach is clearly identified, both theoretically and numerically, and unitless groupings indicating the domain of validity are reported
Enhanced reaction kinetics and reactive mixing scale dynamics in mixing fronts under shear flow for arbitrary Damk\"ohler numbers
Mixing fronts, where fluids of different chemical compositions mix with each
other, are typically subjected to velocity gradients, ranging from the pore
scale to the catchment scale due to permeability variations and flow line
geometries. A common trait of these processes is that the mixing interface is
strained by shear. Depending on the P\'eclet number , which represents the
ratio of the characteristic diffusion time to the characteristic advection
time, and the Damk\"ohler number , which represents the ratio of the
characteristic diffusion time to the characteristic reaction time, the local
reaction rates can be strongly impacted by the dynamics of the mixing
interface. This impact has been characterized mostly either in kinetics-limited
or in mixing-limited conditions, that is, for either very low or very high
. Here the coupling of shear flow and chemical reactivity is investigated
for arbitrary Damk\"ohler numbers, for a bimolecular reaction and an initial
interface with separated reactants. Approximate analytical expressions for the
global production rate and reactive mixing scale are derived based on a
reactive lamella approach that allows for a general coupling between stretching
enhanced mixing and chemical reactions. While for , reaction kinetics
and stretching effects are decoupled, a scenario which we name "weak
stretching", for , we uncover a "strong stretching" scenario where new
scaling laws emerge from the interplay between reaction kinetics, diffusion,
and stretching. The analytical results are validated against numerical
simulations. These findings shed light on the effect of flow heterogeneity on
the enhancement of chemical reaction and the creation of spatially localized
hotspots of reactivity for a broad range of systems ranging from kinetic
limited to mixing limited situations
Multiscale reaction-diffusion algorithms: PDE-assisted Brownian dynamics
Two algorithms that combine Brownian dynamics (BD) simulations with
mean-field partial differential equations (PDEs) are presented. This
PDE-assisted Brownian dynamics (PBD) methodology provides exact particle
tracking data in parts of the domain, whilst making use of a mean-field
reaction-diffusion PDE description elsewhere. The first PBD algorithm couples
BD simulations with PDEs by randomly creating new particles close to the
interface which partitions the domain and by reincorporating particles into the
continuum PDE-description when they cross the interface. The second PBD
algorithm introduces an overlap region, where both descriptions exist in
parallel. It is shown that to accurately compute variances using the PBD
simulation requires the overlap region. Advantages of both PBD approaches are
discussed and illustrative numerical examples are presented.Comment: submitted to SIAM Journal on Applied Mathematic
The initial stages of cave formation: Beyond the one-dimensional paradigm
The solutional origin of limestone caves was recognized over a century ago,
but the short penetration length of an undersaturated solution made it seem
impossible for long conduits to develop. This is contradicted by field
observations, where extended conduits, sometimes several kilometers long, are
found in karst environments. However, a sharp drop in the dissolution rate of
CaCO_3 near saturation provides a mechanism for much deeper penetration of
reactant. The notion of a "kinetic trigger" - a sudden change in rate constant
over a narrow concentration range - has become a widely accepted paradigm in
speleogenesis modeling. However, it is based on one-dimensional models for the
fluid and solute transport inside the fracture, assuming that the dissolution
front is planar in the direction perpendicular to the flow. Here we show that
this assumption is incorrect; a planar dissolution front in an entirely uniform
fracture is unstable to infinitesimal perturbations and inevitably breaks up
into highly localized regions of dissolution. This provides an alternative
mechanism for cave formation, even in the absence of a kinetic trigger. Our
results suggest that there is an inherent wavelength to the erosion pattern in
dissolving fractures, which depends on the reaction rate and flow rate, but is
independent of the initial roughness. In contrast to one-dimensional models,
two-dimensional simulations indicate that there is only a weak dependence of
the breakthrough time on kinetic order; localization of the flow tends to keep
the undersaturation in the dissolution front above the threshold for non-linear
kinetics.Comment: to be published in Earth and Planetary Science Letter
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