Biomedical Engineering Reference
In-Depth Information
0.6
0.5
0.4
Pore-scale
Multi-scale
0.3
0.E+00
1.E+04
2.E+04
3.E+04
4.E+04
5.E+04
Time
FIGURE 7.10
The change in porosity of the portion of a porous medium located between
x
= 8 and
x
= 24 computed with the pore-scale (the solid line) and hybrid
pore-scale/Darcy-scale (the broken line) simulations. (Tartakovsky, A.M.,
Tartakovsky, D.M., Scheibe, T.D., and Meakin, P.,
SIAM J. Sci. Comput.
, 30,
6, 2008b. Copyright 2008 American Geophysical Union. Reproduced/modified
by permission of American Geophysical Union.)
7.6 Summary
In this chapter we reviewed two Lagrangian particle methods, DPD and SPH,
and their application to modeling biofilm growth and mineral precipitation in
porous media. Both biofilm growth and mineral precipitation play a critical
role in a wide range of biological systems. The simulation results presented
here show that mineral precipitation and biofilm growth lead to changes in
pore-geometry and pore flow, and affect the continuum (effective) proper-
ties of porous media such as porosity, permeability, dispersion coecient, and
effective reaction rates. Existing continuum (Darcy scale) models use phe-
nomenological relationships to describe changes in the effective properties due
to mineral precipitation and dissolution. This significantly reduces the predic-
tive power of Darcy-scale models. To increase the predictive ability of numer-
ical models, a number of pore-scale models were developed in recent years.
The two models, described here, operate on two different scales. On smaller
scales, where the effects of random thermal fluctuations on biogeochemical pro-
cesses are important, DPD models provide a good alternative to MD models.
The DPD approach to biofilm simulation consistently incorporates thermally
driven fluctuations into models of biomass growth, while significantly extend-
ing the range of typical MD simulations. This allows the effects of fluid flow on
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