Analytical model of microfluidic transport of non-magnetic particles in ferrofluids under the influence of a permanent magnet

Abstract

This study describes an analytical model and experimental verifications of transport of non-magnetic spherical microparticles in ferrofluids in a microfluidic system that consists of a microchannel and a permanent magnet. The permanent magnet produces a spatially nonuniform magnetic field that gives rise to a magnetic buoyancy force on particles within ferrofluid-filled microchannel. We obtained trajectories of particles in the microchannel by (1) calculating magnetic buoyancy force through the use of an analytical expression of magnetic field distributions and a nonlinear magnetization model of ferrofluids, (2) deriving governing equations of motion for particles through the use of analytical expressions of dominant magnetic buoyancy and hydrodynamic viscous drag forces, (3) solving equations of motion for particles in laminar flow conditions. We studied effects of particle size and flow rate in the microchannel on the trajectories of particles. The analysis indicated that particles were increasingly deflected in the direction that was perpendicular to the flow when size of particles increased, or when flow rate in the microchannel decreased. We also studied ''wall effect'' on the trajectories of particles in the microchannel when surfaces of particles were in contact with channel wall. Experimentally obtained trajectories of particles were used to confirm the validity of our analytical results. We believe this study forms the theoretical foundation for size-based particle (both synthetic and biological) separation in ferrofluids in a microfluidic device. The simplicity and versatility of our analytical model make it useful for quick optimizations of future separation devices as the model takes into account important design parameters including particle size, property of ferrofluids, magnetic field distribution, dimension of microchannel, and fluid flow rate.

Focusing microparticles in a microfluidic channel with ferrofluids

“…We have previously developed a 2D analytical model for transports of non-magnetic particles within ferrofluids in a microfluidic system (Zhu et al 2011). In this study, we extend our analytical model to enable fast and accurate predications of microparticle trajectories in all three dimensions.…”

Continuous sheath-free magnetic separation of particles in a U-shaped microchannel

“…This is a consequence of positive magnetophoresis, which is astonishing because polystyrene particles have been previously found to behave diamagnetic in ferrofluids by multiple research groups, [32][33][34][35][36][37] including ours. 30,38,39 Such a counterintuition phenomenon becomes much more obvious in Figure 3(b), where the particle mixture migrates in a focused stream adjacent to the channel sidewall nearer to the magnet as a result of the positive magnetophoretic deflection.…”

Continuous-flow ferrohydrodynamic sorting of particles and cells in microfluidic devices

“…Previously, we reported both two-dimensional (2D) and three-dimensional (3D) analytical models for microfluidic transports of microparticles in ferrofluids (Zhu et al 2011a;Zhu et al 2011b). In this work, we applied the 3D analytical model to predict cells' sorting in permanent magnet based device.…”

“…In addition, we calculated volume of a single rod-shape Escherichia coli cell with short axis of 0.5 -1 μm and long axis of 2 -4 μm to be 2.1 -16.7 μm 3 (Kaya and Koser 2009), and volume of a single sphere-shape Saccharomyces cerevisiae cell with diameter of 7 -9 μm to be 180 -382 μm 3 (Jorgensen et al 2002). (Zhu et al 2011b). Visibility was a less of a problem when diluted ferrofluids (~1% v/v) and thin microchannel were used in our device.…”

“…The same device was also applied to continuous-flow frequency-adjustable particles separation (Kose and Koser 2012). Our group developed high-efficiency and high-throughput continuous-flow particle separation and focusing devices using commercial ferrofluids and hand-held permanent magnets (Zhu et al 2010;Zhu et al 2011b;Zhu et al 2011a). Permanent magnet based devices are low-cost and easy to operate; their operations do not generate heat.…”