Biomedical Engineering Reference
In-Depth Information
7.5.7 Numerical Implementation of the Hybrid Algorithm ............... 280
7.5.8 Coupling of the Pore-Scale and Darcy-Scale Simulations .......... 280
7.5.9 Multiresolution Implementation of the Hybrid Algorithm ......... 281
7.5.10 Time Integration .................................................... 282
7.5.11 Numerical Example ................................................. 282
7.5.12 Pore-Scale SPH Simulations ........................................ 282
7.5.13 Hybrid Simulations ................................................. 284
7.6
Summary .................................................................... 285
7.7
References ................................................................... 286
7.1 Introduction
Solute transport coupled with biomass growth and/or mineral precipita-
tion/dissolution is a complex and challenging nonlinear problem. Important
applications in biomedical systems include tumor growth (Zheng et al. 2005);
infection of prosthetic devices (Bandyk et al. 1991) and stents (Speer et al.
1988); dental plaque (Thomas and Nakaishi 2006); physiologic mineraliza-
tion (Hartgerink et al. 2001) and demineralization (Holliday et al. 1997) in
vertebrate bones (including cartilage), teeth, and otoconia; and ectopic cal-
cification that occurs when mineral precipitates pathologically in soft tissues
(Azari et al. 2008). In geological systems, microorganisms play an important
role in the formation of iron mineral deposits in acid mine drainage (Kara-
manev 1991), in the precipitation of carbonates in hot springs (Riding 2000),
in the growth of stromatolites (Reid 2000), and in weathering leading to the
release of nutrients to the environment (Leyval and Berthelin 1991). Microor-
ganisms also play an important role in corrosion (Beech and Gaylarde 1999),
waste water treatment (Wagner et al. 1996), and blockage of water pipes
(Brigmon et al. 1997) and heat exchangers. In the subsurface, microorgan-
isms may significantly reduce permeability (Rittmann 1993), catalyze redox
reactions relevant to contaminant remediation (Lensing et al. 1994), decom-
pose organic contaminants (Zhang et al. 1995), and improve oil recovery (Van
Hamme et al. 2003). Owing to the importance of these applications, there is
a strong incentive to develop predictive numerical models.
The modeling and simulation of coupled biogeochemical processes in
porous materials on the continuum (Darcy) scale relies heavily on phenomeno-
logical descriptions that complicate error analysis and reduce the predictive
ability of the models. Phenomenology is required to describe the relation-
ship between the macroscopic properties of porous media (e.g., permeability,
dispersion coecient, and effective surface area), the growth of precipitated
minerals and/or biomass and the interactions between different solid and fluid
phases. Pore-scale reactive transport models are based on fundamental con-
servation laws, such as the conservation of mass, momentum, and energy, and
they have a much higher predictive ability (Knutson et al. 2005; Tartakovsky
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