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261368 Investigation of the Motion of Small Particles in Microfluidic Flows

The motion of micro- and nano-particles in microfluidic flows is important in several practical cases, such as in MEMS applications and in the transport of fine particles in the pore space of porous media. The goal of this work is to calculate the trajectory of individual particles in microflows by combining the Lattice Boltzmann method (LBM) with a Lagrangian particle tracking algorithm. The former method provides the velocity profile within the flow field and the latter utilizes this velocity to determine the velocity and the position of particles via force balance equations [1].

Initially, particles are released into a micro-slit with no slip boundary condition. When moving in the flow, the particles experience forces that include gravity, drag, buoyancy, and lift. Depending on the size of the particles, Brownian motion is also important. The paper will present cases where each specified force becomes dominant at low Reynolds number flow and with different particle shapes (both spherical and non-spherical particles). The diameter of particles investigated is in the range of nanometers to micrometers, and the size of the microchannel is between 5 and 10 micrometers. In the particle tracking algorithm, the particles travel in each time step due to convection, diffusion (Brownian motion) and due to the effect of total force. Convective displacement can be calculated by using the velocity obtained from LBM. Displacement due to Brownian motion is calculated by the application of random jumps that follow a normal distribution with a zero mean and a standard deviation that depends on the Schmidt number of the particle, according to Einstein’s theory for stochastic motion of particles. In this manner, particles with Schmidt number ranging from 100 to 10,000 are investigated. Lastly, displacement of particles because of resultant force is determined by Newton’s law of motion. Additionally, the interaction between the particles and the wall can be accounted by defining a Morse-like potential in regions very close to the wall [2]. In this manner, the deposition rate of the particles can be calculated, and the relative effects of the hydrodynamics forces, the Brownian motion and the particle-surface interactions can be quantified. As expected, the effect of the Brownian motion dominates the particle trajectories for nanoscale particles, while hydrodynamic forces play an increasingly important role when the particle shape becomes cylindrical with high aspect ratio.

**ACKNOWLEDGEMENTS**

The financial support of the Advanced Energy Consortium (AEC BEG08-022) and the computational support of XSEDE (CTS090017) are acknowledged.

**REFERENCES**

- Voronov, R.S., VanGordon, S., Sikavitsas, V.I., and D.V. Papavassiliou, “Efficient Lagrangian scalar tracking method for reactive local mass transport simulation through porous media,”
*Int. J. for Numerical Methods in Fluids,***67**, 501-517, 2011 - Kolmakov G., Ravanur, R., Tangirala, R., Emrick, T., Russell, T.R., Crossby A.J., and A.C. Balazs, “Using nanoparticle-filled capsules for site-specific healing of damaged substrates: Creating a repair and go system,”
*ACS Nano,***4**(2), 1115-1122, 2010.

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