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