(108f) Modeling of Particle Transport at Low Reynold's Number in Complex Channels Using a Dynamic Boundary-Integral Method

We have developed the first theoretical model and numerical simulation method for the 'pinched-flow fractionation' (PFF) phenomenon in a microfluidic device. Pinched-flow fractionation has been demonstrated as an efficient, practical way to achieve accurate particle sizing and separation using fluid focusing and spreading in a microchannel (Yamada et al., 2004, Anal. Chem. 76:5465-5471). The device consists of two input channels that meet to form a plane-parallel pinch area, followed by an expansion area and outlet. One of the input channels contains a dilute mixture of polydisperse particles made neutrally buoyant in the stream by a buffer solution, while the second input channel contains only a buffer solution. The higher volumetric flow rate from the inlet channel without particles causes the particles to be pushed close to one wall in the pinch area of the device. The particles then effectively separate by the spreading streamlines in the expansion area according to their sizes, as the particle centers can come no closer than one radius from the device wall in the pinch area. A theoretical description of this phenomenon based on calculation of particle trajectories has not been attempted thus far, to our knowledge.

We have developed a novel and suitable 3D boundary-integral method for low-Reynolds- number dynamical simulations of a single spherical particle in such a microchannel, assuming small volume fraction in the inlet to neglect particle-particle interactions. Complexity of channel geometry, where, outside of the pinch area, the overall device size is much larger than the particle size, provides a challenge for a numerical solution. Additionally, the need to resolve lubrication effects between the particle and channel walls when in close proximity presents a computational challenge. To provide a feasible solution, we first calculate the fluid flow in the entire channel without a particle, from the solution of a 2D boundary-integral problem with prescribed inlet and outlet Poiseuille flow profiles having specified flow rates at low Reynolds numbers. The 3D particle is then embedded in a computational cell, roughly 10-20 times larger than the particle size, but still much smaller than the overall device dimension. The cell, dynamically constructed at each time step, is an intersection of a large cube around the particle and the channel domain. Thus, we refer to this approach as a ?dynamic boundary-integral method', as the computational domain changes while the particle moves through the device. The problem is formulated as a 'completed-double-layer' boundary-integral equation for the surface potential, with the fluid velocity on the cell boundary taken from the 2D solution, and solved iteratively at each time step. High particle surface triangulations (up to 15,640 elements) and high-resolution adaptive mesh on the cell boundary allow us to accurately capture particle-wall lubrication for small separations between the particle and channel wall (~1% of particle radius).

This method is systematically used to study the effects of particle radius, the ratio of flow rates, and the channel geometry on particle trajectories and the efficiency of size segregation. Since the centers of the larger particles travel further from the nearby wall in the pinch region due to steric limitations, their trajectories upon leaving the pinch region to the outlet area also further from the device wall. Moreover, the trajectories of the larger particles deviate from the streamlines by a greater amount than that observed for smaller particles. Our calculations may be used to assess when the dynamic boundary-integral method provides a more accurate representation of particle trajectories than approximating them as fluid streamlines. Our approach is quite general for microchannel geometries consisting for an arbitrary number of rectangular panels, and it is not limited by a spherical particle shape. In the future, the model may be adapted to follow the motion of deformable drops through complex complex microfluidic devices.