Lagrangian Particle Methods for Biological Systems - Porous Media: Applications in Biological Systems and Biotechnology - page 271

30

25

AB

20 2.00E-02

1.83E-02

1.67E-02

1.50E-02

1.33E-02

15

1.17E-02

1.00E-02

8.33E-03
6.67E-03
5.00E-03

10

5

0 0

5 10 15

X

FIGURE 7.6
Distribution of the biomass produced by Model 2. Gray particles denote soil
grains, black particles represent fluid particle with nonzero biomass concentra-
tion, and the quasicontinuous gray scale indicates the concentration product
AB in the fluid particles with zero biomass concentration (Tartakovsky et al.
2009). (Tartakovsky, A.M., Scheibe, T.D., and Meakin, P., J. Por. Med. , 12,
5, 2009. Copyright 2009 Bagell House. Modified from Bagell House.)

missing in cellular automata models, the most common approach to simulating
biofilm. In Model 2, biomass was modeled as a viscous fluid phase with a vis-
cosity ten times greater than the viscosity of the fluid containing no biomass.
Depending on the nature of the biomass, it is possible to treat the biomass as
a non-Newtonian or visco-elastic material that will increase predictive ability
of simulations.

7.4 An SPH Model for Mineral Precipitation
SPH models were developed to simulate mineral precipitation in porous and
fractured media (Tartakovsky et al. 2007a,b, 2008a). The SPH discretization of
the advection-diffusion-reaction equation with heterogeneous (dissolution or
precipitation) reaction kinetics of the form k ( C C eq ) β , where C is the solute

concentration at the liquid-solid interface, C eq is the solute concentration at

−