4.5. GROWTH BY AGGREGATION
11 9
The value of Dabs can be estimated from a log-log plot. The exponent Dabs can
be interpreted as a measure of the uniformity of the nutrient distribution. In
Table 4.2 the average absorption ain the boundary nodes, and the values of
Dabs> are listed for the various Pe numbers. Furthermore, for each cluster the
average x, y, z coordinate (the center of gravity) was measured.
4.5.4 Growth by Aggregation in a Bidirectional (Alternating) Flow
In the simulation model discussed in the previous section some important
simplifications have been made. One simplification is that it is assumed
that the growth form develops under mono-directional flow conditions. As
a consequence an asymmetric form develops, as shown in Fig. 4.24, where
the aggregates tend to grow in the upstream direction. This trend becomes
stronger for higher Pe numbers. In reality, the flow direction will basically
reverse twice a day due to the tidal movements. In this section a growth
process in a bidirectional flow is studied by using an aggregation model in
which the flow direction is reversed after each growth step. The nutrient
distribution is computed in a similar way to that discussed in the previous
section.
The basic construction of the aggregate in (alternating) bidirectional
flow is shown in Fig. 4.25. The cluster is initialized with a "seed" positioned
at the bottom plane of the lattice. The bottom plane, "the substrate", is
positioned in the xz-plane at y = 1, while the seed is one lattice site, located
at the position txrnaxf z, 2, zmax f zi. In both the cluster and substrate sites
solid boundary conditions are applied. The flow in the lattice is directed,
alternating between two phases, where the flow is directed from the left to
the right and the right to the left in Fig. 4.25. Init ially the flow is directed
from the left to the right. The flow velocity in the free fluid nodes is kept to
a constant value uby adjusting the driving force F of the system. The flow
velocity in the system is kept at a low value; all simulations are done in the
laminar flow regime. As in Sect. 4.5.3, the flow pattern about the obstacle
(substrate and cluster) is determined by a number oflattice Boltzmann steps
(XlI1l1X, ymax, ZlI1l1X)
~=-r-- source plane
Fig. 4.25. Basic construction of the
aggregate in a bidirectional flow
~::--- substra te plane
initial "seed" of the aggrega te
at txmaxh;ZlI1l1xh)
x
(1,1,1 )
flow d ir ction
11 9
The value of Dabs can be estimated from a log-log plot. The exponent Dabs can
be interpreted as a measure of the uniformity of the nutrient distribution. In
Table 4.2 the average absorption ain the boundary nodes, and the values of
Dabs> are listed for the various Pe numbers. Furthermore, for each cluster the
average x, y, z coordinate (the center of gravity) was measured.
4.5.4 Growth by Aggregation in a Bidirectional (Alternating) Flow
In the simulation model discussed in the previous section some important
simplifications have been made. One simplification is that it is assumed
that the growth form develops under mono-directional flow conditions. As
a consequence an asymmetric form develops, as shown in Fig. 4.24, where
the aggregates tend to grow in the upstream direction. This trend becomes
stronger for higher Pe numbers. In reality, the flow direction will basically
reverse twice a day due to the tidal movements. In this section a growth
process in a bidirectional flow is studied by using an aggregation model in
which the flow direction is reversed after each growth step. The nutrient
distribution is computed in a similar way to that discussed in the previous
section.
The basic construction of the aggregate in (alternating) bidirectional
flow is shown in Fig. 4.25. The cluster is initialized with a "seed" positioned
at the bottom plane of the lattice. The bottom plane, "the substrate", is
positioned in the xz-plane at y = 1, while the seed is one lattice site, located
at the position txrnaxf z, 2, zmax f zi. In both the cluster and substrate sites
solid boundary conditions are applied. The flow in the lattice is directed,
alternating between two phases, where the flow is directed from the left to
the right and the right to the left in Fig. 4.25. Init ially the flow is directed
from the left to the right. The flow velocity in the free fluid nodes is kept to
a constant value uby adjusting the driving force F of the system. The flow
velocity in the system is kept at a low value; all simulations are done in the
laminar flow regime. As in Sect. 4.5.3, the flow pattern about the obstacle
(substrate and cluster) is determined by a number oflattice Boltzmann steps
(XlI1l1X, ymax, ZlI1l1X)
~=-r-- source plane
Fig. 4.25. Basic construction of the
aggregate in a bidirectional flow
~::--- substra te plane
initial "seed" of the aggrega te
at txmaxh;ZlI1l1xh)
x
(1,1,1 )
flow d ir ction