Biomedical Engineering Reference
In-Depth Information
Figure 10.20
Macroscopic velocities as a function of
t
off
(diffusion step) for two different sizes
of latex beads. In this particular case, setting
t
off
= 3s leads to a factor of 10 between the velocities.
The macroscopic mean velocity
V
of a particle at a given
t
off
is quantitatively de-
scribed by the simple model exposed above (no adjustable parameter). Figure 10.20
plots the velocities of two different latex beads as a function of
t
off
. These curves
exhibit a maximum whose position at a given
t
off
is very dependent on the size of the
particles This is thus an extremely promising although quite slow technique.
Shifted Ratchets
The previous idea (Brownian ratchet) relies on diffusion. It implies small velocities,
a disadvantage that can be corrected if we use two potentials similar to the one de-
scribed in the preceding part (Figure 10.19(a)). Here, these potentials are
shifted
by
a fraction of their common period and addressed successively [66].
When the commutation time is too small, the particle cannot escape the cor-
responding trap and the macroscopic velocity is zero but, when both times are long
enough, the particle has enough time to move by one total period per time cycle.
This velocity
V
opt
is the optimal velocity. We can rephrase this statement in terms
of mobilities instead of residence times: For identical residence times, particles will
have either a zero velocity or an optimal velocity according to their mobilities. In
other words, this device is a
ilter
according to the mobility of the particles. More-
over, the mobility threshold of this filter can be chosen by tuning the two residence
times. On a separation point of view, this filterlike situation is obviously a great
improvement compared to conventional techniques as the velocity of some of the
considered particles is exactly zero and even subtle differences in mobilities should
be usable for a separation.
Such characteristics can be obtained with the use of 2-D electrodes sputtered
on glass (see the “Christmas tree” geometry in Figure 10.21). To get successively
two of these potentials, two of these plates are stacked with their gold sides facing
