Inertial migrations of cylindrical particles in rectangular microchannels: Variations of equilibrium positions and equivalent diameters

Abstract

Inertial migration has emerged as an efficient tool for manipulating both biological and engineered particles that commonly exist with non-spherical shapes in microfluidic devices. There have been numerous studies on the inertial migration of spherical particles, whereas the non-spherical particles are still largely unexplored. Here, we conduct three-dimensional direct numerical simulations to study the inertial migration of rigid cylindrical particles in rectangular microchannels with different width/height ratios under the channel Reynolds numbers (Re) varying from 50 to 400. Cylindrical particles with different length/diameter ratios and blockage ratios are also concerned. Distributions of surface force with the change of rotation angle show that surface stresses acting on the particle end near the wall are the major contributors to the particle rotation. We obtain lift forces experienced by cylindrical particles at different lateral positions on cross sections of two types of microchannels at various Re. It is found that there are always four stable equilibrium positions on the cross section of a square channel, while the stable positions are two or four in a rectangular channel, depending on Re. By comparing the equilibrium positions of cylindrical particles and spherical particles, we demonstrate that the equivalent diameter of cylindrical particles monotonously increases with Re. Our work indicates the influence of a non-spherical shape on the inertial migration and can be useful for the precise manipulation of non-spherical particles.

Inertial focusing with sub-micron resolution for separation of bacteria

“…† Our results with Escherichia coli (∼1 μm long) were in agreement with previous studies, where elongated particles have been reported to focus as spherical particles with an equivalent diameter approximately similar to the largest dimension. 37,38 Salmonella typhimurium (∼1-1.5 μm long) was thus expected to behave as larger particles than Escherichia coli since they were observed to be a bit longer. However, they behaved as particles slightly smaller than the equivalent for Escherichia coli; Fig.…”

Transport of Non-Spherical Particles in Square Microchannel Flows: A Review

“…For cylindrical particles flowing in a square channel as well, Su et al [ 45 ] demonstrated numerically that there are always four stable equilibrium positions for Re varying from 50 to 200. The two-stage process (cross-streamline and cross-lateral migrations) was also shown for these cylindrical particles.…”

“…Unlike spherical particles [ 16 , 60 ], non-spherical ones oscillate while being transported in a microchannel flow. Hur et al [ 55 ], Masaeli et al [ 49 ], and Su et al [ 45 ] observed that an elongated particle ( λ > 1) will keep oscillating regardless of its position in the channel (still migrating or focused on an equilibrium position) ( Figure 11 ). This might be due to the fact that a prolate particle prefers to tumble (see Section 2.1.3 ) and that, while adopting this type of rotation, the angular velocity, the sweeping area, and the distance from the wall continuously change, leading to periodical variations of the wall-induced lift force and thus a periodic motion of the particle toward and away from the wall [ 45 ].…”

“…Hur et al [ 55 ], Masaeli et al [ 49 ], and Su et al [ 45 ] observed that an elongated particle ( λ > 1) will keep oscillating regardless of its position in the channel (still migrating or focused on an equilibrium position) ( Figure 11 ). This might be due to the fact that a prolate particle prefers to tumble (see Section 2.1.3 ) and that, while adopting this type of rotation, the angular velocity, the sweeping area, and the distance from the wall continuously change, leading to periodical variations of the wall-induced lift force and thus a periodic motion of the particle toward and away from the wall [ 45 ]. In the same way, Nizkaya et al [ 17 ] showed that an oblate particle oscillates while kayaking, since the kayaking motion is a combination of tumbling and log-rolling but stopped oscillating once it is focused on its equilibrium position.…”

Inertial migration of aerosol particles in three-dimensional microfluidic channels

“…However, the aforementioned designs mainly depend on experience. The particle's detailed motion in microchannels remains unclear, though a large body of research has been devoted to particles’ motions suspended in liquid ( Lu et al, 2017b , Su et al, 2018 , Zhang et al, 2016 ) instead of air. In a straight liquid microchannel, initial randomly distributed neutrally buoyant particles will finally migrate to several symmetric equilibrium positions due to the inertial effect ( Liu et al, 2015 , Martel and Toner, 2014 , Zhang et al, 2016 ).…”