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Inertial migration of single particle in a square microchannel over wide ranges of Re and particle sizes

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Abstract

Inertial migration of particles has been widely used in inertial microfluidic systems to passively manipulate cells/particles. However, the migration behaviors and the underlying mechanisms, especially in a square microchannel, are still not very clear. In this paper, the immersed boundary-lattice Boltzmann method (IB-LBM) was introduced and validated to explore the migration characteristics and the underlying mechanisms of an inertial focusing single particle in a square microchannel. The grid-independence analysis was made first to highlight that the grid number across the thin liquid film (between a particle and its neighboring channel wall) was of significant importance in accurately capturing the migrating particle’s dynamics. Then, the inertial migration of a single particle was numerically investigated over wide ranges of Reynolds number (Re, from 10 to 500) and particle sizes (diameter-to-height ratio a/H, from 0.16 to 0.5). It was interesting to find that as Re increased, the channel face equilibrium (CFE) position moved outward to channel walls at first, and then inflected inwards to the channel center at high Re (Re > 200). To account for the physical mechanisms behind this behavior, the secondary flow induced by the inertial focusing single particle was further investigated. It was found that as Re increased, two vortices appeared around the particle and grew gradually, which pushed the particle away from the channel wall at high Re. Finally, a correlation was proposed based on the numerical data to predict the critical length Lc (defined to describe the size of fluid domain that was strongly influenced by the particle) according to the particle size a/H and Re.

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Abbreviations

a :

Particle diameter (m)

A :

Area of the cross-section (m2)

c :

Lattice speed (m/s)

c i :

Discrete lattice velocity in direction i (m/s)

c s :

Sound speed of the model (m/s)

D h :

Hydraulic diameter of the channel cross-section (m)

f :

Body force (N/m3)

f i :

Density distribution function in direction i (kg/m3)

f i eq :

Equilibrium density distribution function in direction i (kg/m3)

F i :

Discrete body force in direction i (kg/(m3·s))

F :

Surface force (N/m2)

g :

Acceleration due to gravity (m/s2)

H :

Height of the channel (m)

I :

Moment of inertia (kg·m2)

L :

Length of the channel (m)

m :

Mass (kg)

p :

Pressure (Pa)

Re :

Reynolds number

s :

Lagrangian coordinate

S :

Perimeter of the cross-section (m)

t :

Time (s)

u, U :

Velocity (m/s)

U a :

Average velocity (m/s)

V :

Volume (m3)

W :

Width of the channel (m)

x, X :

Eulerian coordinate

δ t :

Time step (s)

δ x, δ y :

Lattice space (m)

µ :

Dynamic viscosity (Pa·s)

ν :

Kinematic viscosity (m2/s)

ρ :

Density (kg/m3)

τ :

Dimensionless relaxation time

ω i :

Weight coefficient in direction i

Ω:

Angular velocity (rad/s)

f :

Fluid

i :

Direction i in a lattice

n :

Value at the nth time step

p :

Particle

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Acknowledgements

This work was supported by the National Natural Science Foundation of China through Grant nos. 51536005, 51706136 & 51820105009.

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  1. Key Laboratory for Power Machinery and Engineering of Ministry of Education, School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China

    Chen Yuan, Zhenhai Pan & Huiying Wu

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  1. Chen Yuan
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  2. Zhenhai Pan
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Correspondence to Huiying Wu.

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Yuan, C., Pan, Z. & Wu, H. Inertial migration of single particle in a square microchannel over wide ranges of Re and particle sizes. Microfluid Nanofluid 22, 102 (2018). https://doi.org/10.1007/s10404-018-2120-y

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