Biomedical Engineering Reference
In-Depth Information
Figure 9.11
Trajectories of paramagnetic microparticles in the vicinity of the rod if the carrier fluid
is at rest.
force decreases very rapidly from the rod surface, and particles located far from the
rod will not move significantly.
9.5.4 Trajectories (Carrier Fluid Convection)
Suppose now that the carrier fluid is slowly moving around the rod. In this case, the
flow is laminar and can be calculated either by solving the Navier-Stokes equations
(Figure 9.12), either by using Lamb's equation [14]
é
1
ù
æ
ö
u
= -
C
ln(Re) 0.5 1
-
-
sin
θ
ê
ç
÷
ú
è
2
ø
Re
ë
û
(9.27)
é
ù
æ
1
ö
u
= -
C
ln(Re) 0.5 1
+
-
cos
θ
ê
ç
÷
ú
θ
è
2
ø
Re
ë
û
Figure 9.12
Velocity field of a laminar flow around a 2-mm diameter fiber. Velocity at infinity is
1 mm/s.
