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Abstract
In this paper, the hydrodynamic mechanism of moving particles in laminar micro-channel flows was numerically investigated. A hydrodynamic criterion was proposed to determine whether particles in channel flows can form a focusing pattern or not. A simple formula was derived to demonstrate how the focusing position varies with Reynolds number and particle size. Based on this proposed criterion, a possible hydrodynamic mechanism was discussed as to why the particles would not be focused if their sizes were too small or the channel Reynolds number was too low. The Re-λ curve (Re, λ respectively represents the channel-based Reynolds number and the particle’s diameter scaled by the channel) was obtained using the data fitting with a least square method so as to obtain a parameter range of the focusing pattern. In addition, the importance of the particle rotation to the numerical modeling for the focusing of particles was discussed in view of the hydrodynamics. This research is expected to deepen the understanding of the particle transport phenomena in bounded flow, either in micro or macro fluidic scope.
Highlights
When particles are dispersed in a laminar channel flow, they can form an annulus with a certain radius after some migration distance under proper circumstances [1]
Since the transverse force comes from the inertia of the channel flow, it is usually regarded as the inertial lift force and the aggregative motion of the particles is called the inertial focusing of particles [2,3]
It was summarized that the inertial lift force FL on a spherical particle of diameter a in a channel of dimension H could be scaled as FL ∝ ρV2 a4/H2, where ρ denotes the density of fluid and V is the average velocity of the channel flow [2,3,4]
Summary
When particles are dispersed in a laminar channel flow, they can form an annulus with a certain radius after some migration distance under proper circumstances [1]. It was summarized that the inertial lift force FL on a spherical particle of diameter a in a channel of dimension H could be scaled as FL ∝ ρV2 a4/H2, where ρ denotes the density of fluid and V is the average velocity of the channel flow [2,3,4] This expression for the inertial lift force was derived on the basis of such an assumption that the size of every particle should be far smaller than that of the channel (a
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