(198e) Numerical Simulation of Flow Manipulation of Charged Metal Nano-Particle by Negative Di-Electrophoresis

Metal
nano-particles have found application in diverse fields such as catalysis,
biomedical, electronics and environment. Palladium nano-particles are used for
in vitro and sensor design applications as well as for spin coating,
self-assembly and monolayer formation. Silver nano-particles have also been
used for in vitro application, antimicrobial as well as antifungal
applications, and sensor design. Water soluble gold nano-particles can be used
for spin coating, self-assembly and monolayer formation. Nano-particles
composed of gold offer, in addition to their enhanced absorption and
scattering, good biocompatibility, facile synthesis and conjugation to a
variety of biomolecular ligands, antibodies, making them suitable for use in
biochemical sensing and detection, medical diagnostics, and therapeutic
applications. Gold nanoparticle labeled with specific antibodies
are used to stain tissues, cells etc that are then imaged using TEM. The
optical, electrical and magnetic properties of the nano-particles are size and
shape dependent. Hence, size and shape separation of the nano-particles is of
importance and need of the day. A large number of papers are available on
synthesis of nano-particles and attempts are being made to control the size at
the time of synthesis. However, during bulk synthesis it is difficult to get
monosized particles and very often product obtained is polydispersed. Hence, it
becomes necessary to separate the particles according to size, post synthesis.
Thus study on flow manipulation of nanoparticles is important. Although work on
flow manipulation of micro particle has been reported, not much work has been
reported on continuous flow manipulation of nano-particles particularly in
microchannels.

In recent
years, dielectrophoresis is gaining importance as an important technique for
manipulation of micro and nano sized particles. In a non-uniform electric field
a polarizable particle experiences a force that can cause it to move to regions
of high or low electric field, depending on the particle polarizability compared
with the suspending medium. The direction and magnitude of the dielectric force
depends on the characteristics of the applied electric field as well as the
dielectric properties of the medium as well as the particle. Some papers on
modelling the trajectory of microparticles in a microchannel, in the presence
of dielectrophoretic forces have been reported for different geometries. With decrease in size the dielectrophoretic force
decreases whereas the Brownian motion increases. Hence it was believed that it
would not be feasible to manipulate nanosize particle as it would require high
potential gradient for the dielectrophoretic motion to overcome the Brownian
motion. However, with the advancement of microfabrication, it is possible to
create high voltage gradient with micron size gap and voltage of several volts
(Kersaudy-Kerhoas et. al, 2008). When microelectrode arrays are used, the
volume in which this heat is generated is very small, and typical power
dissipation is in the range of 1?10 mW. Thermal equilibrium is reached within 1
ms of application of the electric field (Ramos et al., 1998), and they have
shown that for low conductivity media the steady-state temperature rise is
small. A number of numerical and experimental studies on dielectrophoresis trapping
of submicron size particles using planner electrode array have been reported in
literature. The study is limited to biological cells, latex and polystyrene
beads. However, studies on continuous manipulation of flow of metal
nanoparticles taking into account hydrodynamic force have not been reported
yet.

In the
present study a 2-D model was developed and simulated to predict the flow
behaviour of citrate stabilized gold nano particles of size 30 nm and 60 nm in
a microfluidic device using an AC power supply. Whenever a charged surface is
placed in contact with a fluid, the free charges in the solution will
experience a Coulombic force due to the charges on the surface. Dissolved ions
bearing the same sign as the surface (coions) will be repelled from the surface
and the ions of the opposite sign (counterions) will be attracted forming an
electrical double layer around the particle. When an electric field is applied,
the charges in the double layer will try to move towards the appropriate
electrode by Coulombic interaction. However, the same charges will also be
attracted by the particle surface. Thus there will be a slight net displacement
of the ionic charge towards the electrode. Since the charged particle and
countercharged double layer move in opposite directions under the influence of
the electric field, the centers of the charges will be displaced from the
center of the particle resulting in the double layer/particle combination
becoming polarized. This polarization process occurs in both the Stern and
diffuse layers but in a different way. In the Stern layer, the charge is fixed
on the surface and can move only on the surface, whereas in the diffuse layer
the charges, the ionic cloud is mobile.

The extent of
polarization depends on the applied field frequency, the Debye screening
length, the zeta potential, permittivity and conductivity of the particle and
the electrolyte medium. The net particle conductivity is the sum of bulk
conductivity of the particle and that of the double layer. In order to neglect
the Brownian motion, high potential gradient was used and to minimize the
electrophoretic motion, high frequency has been used. This also minimizes the
formation of an EDL on the surface of the electrode. Thus the dominating forces
are the dielectrophoretic and hydrodynamic forces. The dielectrophoretic force
is a function of the real part of the Clausius-Mossotti factor (Re[K(f)]). The
Clausius-Mossotti factor is a function of complex permittivity and conductivity
of the medium and the particle. The complex permittivity of the particle and
the medium is frequency dependent. The protoplast model is used to estimate the
effective complex permittivity of the particle. The Re[K(f)] determines whether
the particle is more or less polarizable then the medium. If it is positive,
then the particle is more polarizable than the medium and the particle moves to
the region of highest electric field strength whereas if it is negative the
particle is less polarizable than the medium it moves to the lowest field strength.
When it is zero, the particle does not experience any dielectrophoretic force. In
the present study, the frequency used was such that the particles experience a
negative dielectrophoresis, so that they do not stick to the electrodes.

The model
equations consists of the momentum balance equation for the fluid phase, taking
into account inertial, pressure, viscous and drag force; Laplace equation, for
predicting the potential distribution; momentum balance equation for the solid
particles, taking into account  dielectrophoretic, drag, pressure and collision
force. The inlet to the microchannel consists of two arms. The slurry with
solid particles are fed through one arm in line with the microchannel and only
liquid is fed through the other arm which is at an angle so that the solid
particles are focused in the region of high electric field as they enter the
main body of the microchannel. The voltage, length and positioning of the
electrodes were chosen so that the particles were allowed to flow in the desired
direction. The electrodes were placed on the side walls of the channel and
along the entire height of the channel, so that an electrical field gradient was
generated along the width of the channel. The non-uniform magnetic field forces
the particle to move along the width of the channel whereas the hydrodynamic
force will move the particles in the forward direction. The velocity of the
slurry and the liquid as well as the potential at the electrodes were adjusted
so as to the get the desired flow profile of the particles.

References:

Kersaudy-Kerhoas,
M., R. Dhariwal and M.P.Y. Desmulliez,  Recent advances in microparticle
continuous separation, IET Nanobiotechnology, 2(1), 2008,1?13.

Ramos, A., H. Morgan, N. G.
Green, and A. Castellanos. AC electrokinetics: a review of forces in
microelectrode structures. J. Phys. D Appl. Phys. 31, 1998. 2338 ?2353