Page 137 - Optofluidics Fundamentals, Devices, and Applications

116 Cha pte r S i x

Here, ρ is the density of the fluid, r is the radius of rotation, and ω
is the angular velocity. In this equation, a and b are constant for a
given fluidic system. Above the threshold frequency, the centrifugal
force exceeds the capillary force, causing the suspension to burst out
from the channels. The threshold of the burst angular velocity ω
c
decreases with increasing hydraulic diameter. In the case of the evap-
oration-induced crystallization, as the solvent medium evaporates,
the colloidal particles crystallize, first from the noncontact mode, by
electrostatic repulsion. Upon further evaporation of the solvent, the
capillary force leads the particles to pack into the contact mode. At
this moment, cracks are formed as a result of the volume shrinkage
over the whole colloidal-crystal region. Instead of the capillary force,
centrifugal sedimentation can stack the colloidal particles into a close-
packed state. The centrifugal sedimentation helps to prevent crack
formation, even over a scale of several hundred micrometers. During
centrifugation, the centrifugal force packs and contacts the colloidal
particles before the evaporation of the solvent medium. This medium
is fully evaporated after crystallization of the colloids.
The Stokes equation enables us to approximate the sedimentation
velocity of colloidal particles by balancing the centrifugal driving
force P = (π/6)d (ρ − ρ)C and the friction force F = fv. Here, d is the
3
c p
particle diameter, ρ is the particle density, f = 3πμd is the friction coef-
p
ficient for a spherical particle, and C = (2π RPM)2r/60 is the centrifu-
2
gal acceleration (where r is the distance between the colloids and the
axis of rotation):
2
v = d (ρ p − ) ρ (6-2)
C 18μ
Equation (6-2) includes several assumptions, namely, no interparticle
interactions, a sufficiently large particle size relative to the solvent
molecules, and no disturbances due to convection. From this equation,
we notice that the sedimentation speed of the colloids can be enhanced
by increasing the particle size, the rotation speed of the disc, the
distance from the rotation axis, and the density contrast. Therefore, if
the colloidal particles can be dispersed in a low-density medium, it is
possible to reduce the processing time. This is particularly important
for polymeric particles, which have the small density contrast from
the aqueous medium. However, to disperse the particles into a low-
density medium, such as ethanol, their surfaces must be modified to
provide a high suspension stability; for example, we can disperse PS
particles in ethanol through the physical adsorption of polyvinylpy-
rollidone (PVP) onto the PS beads and prepare crystals composed of
the PS particles in a much shorter time than that required with an
aqueous suspension. Since different kinds of particles are sequen-
tially injected into the microchannel, on the other hand, it is possible
to produce hybrid colloidal crystals composed of several blocks.