Biomedical Engineering Reference
In-Depth Information
molecules are ionized and driven by a coulombic force due to the electric fi eld. The
coulombic force, F , is given by
F
qE
(14)
where q is the charge on the molecule and E is the strength of the electric fi eld. The
velocity, v , of charged molecules fi rst accelerates towards one of the electrodes, and
then slows down to reach a terminal one, at which the coulombic force is balanced by
a drag force, the Stokes force,
F
6
πη
r h v
(15)
where
η
is the viscosity of the fl uid. The terminate v is calculated as
v
µ
E
(16)
where
µ
is the mobility of the molecules, given by
ε
θ
]
µ
q /6
πη
r
(17)
Diffusion occurs when there is a concentration gradient of one kind of molecule
within a fl uid. In terms of random walk model, the average distance, x , after an elapsed
time, t , between molecule collisions in a diffusion movement is characterized by the
Einstein-Smoluchowski relation,
(2 Dt ) 1/2
x
(18)
where D is the diffusion coeffi cient. This allows us to estimate the time t cross for taking
a molecule to cross half the microchannel width W of the main channel of a T-junction,
W 2 / 8 D
t cross
(19)
More theoretical analysis of a diffusion process can be conducted by Fick's law as
j
D (
c/
x )
(20)
where j is the diffusion molecule fl ux and equal to cv . c is the molecule concentration.
In analysis of a mass transport process, the Peclet number, P e , the ratio of the direct
fl ow to the diffusion, is used and given as
P e
vd/D
(21)
where d is a characteristic length of the microfl uidic system. The Peclet number can
be calculated in terms of Eq. (21), which is important in the design of a microfl uidic
system for control diffusion, such as for a chemical separation system or a mixer effect
of a microreactor.
11.5.2 Components in lab-on-chip systems
Among the most important fl uid handling components in an LOC are pumps and valves.
There are two main methods by which fl uid actuation through microchannels can be
achieved: pressure driven and electroosmotic fl ow. In pressure driven fl ow, the fl uid is
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