1 Introduction to Laser Micro-to-Nano Manufacturing
9
Fig. 1.4 Manipulation difference in a macroworld and a nanoworld
where τ is the transient time. The flux mode can be identified by the Reynold number
R e , R e = ρvL/η. If v ~ L, then
R e ∼ L
2
For a particle travels a distance L by diffusion in a diffusion time τ d = αD, where
α is a geometrical constant and D is the diffusion constant. One can obtain,
τ d ∼ L
2
For liquid passes through a needle with a diameter of α, if the needle length is L
and the flow rate is Q, the pressure drop through the needle will be
P =
8μl Q
πα 4 ∼ L
−3
According this scaling law, for a 30 μm in diameter and 3 cm long needle with a
flow rate of 1 microliter per min the pumping pressure is 1.5 atm, but for a 0.3 μm
in diameter needle the pumping pressure has to be more than 1.5 × 10
6 atm!
Scaling Law of Electromagnetics The nanomanufacturing and the operation of
nanodevices are frequently involve the electromagnetic properties. Table 1.2 displays
the scaling laws of the popular electromagnetic variables.
When the voltage remains constant and L varies, the electrical field E el obviously
changes E el ~ L
−1 . The magnetic field intensity in a solenoid with n turns of wire,
of the length L, is defined as B = nμI/L, then B ~ L. The magnetic energy stored in
the solenoid is
9
Fig. 1.4 Manipulation difference in a macroworld and a nanoworld
where τ is the transient time. The flux mode can be identified by the Reynold number
R e , R e = ρvL/η. If v ~ L, then
R e ∼ L
2
For a particle travels a distance L by diffusion in a diffusion time τ d = αD, where
α is a geometrical constant and D is the diffusion constant. One can obtain,
τ d ∼ L
2
For liquid passes through a needle with a diameter of α, if the needle length is L
and the flow rate is Q, the pressure drop through the needle will be
P =
8μl Q
πα 4 ∼ L
−3
According this scaling law, for a 30 μm in diameter and 3 cm long needle with a
flow rate of 1 microliter per min the pumping pressure is 1.5 atm, but for a 0.3 μm
in diameter needle the pumping pressure has to be more than 1.5 × 10
6 atm!
Scaling Law of Electromagnetics The nanomanufacturing and the operation of
nanodevices are frequently involve the electromagnetic properties. Table 1.2 displays
the scaling laws of the popular electromagnetic variables.
When the voltage remains constant and L varies, the electrical field E el obviously
changes E el ~ L
−1 . The magnetic field intensity in a solenoid with n turns of wire,
of the length L, is defined as B = nμI/L, then B ~ L. The magnetic energy stored in
the solenoid is