Biomedical Engineering Reference
In-Depth Information
Figure 6.1
Schematic approach to micromanipulation of biologic targets.
simplicity, we consider a 2D element, but the reasoning is the same for a 3D volume.
The change in the mass of species in the volume is equal to the convective flux bal-
ance plus the diffusion flux balance (Figure 6.3).
Thus, we can write
¶
J
¶
c
¶
c
¶
c
¶
J
y
x
D D +
x y u
D D +
x y
v
D D +
x y
D D +
x y
D D =
x
0
(6.1)
t
x
y
x
y
¶
¶
¶
¶
¶
Figure 6.2
Different behaviors for transport of targets: (a) diffusion plays an important role
(Pe <<1); (b) targets follow streamlines; (c) inertial effects force targets to abandon the flow stream-
lines when curved (Pe >>1); and (d) large and heavy targets sediment.
