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A rapid magnetic particle driven micromixer

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Abstract

Performances of a magnetic particle driven micromixer are predicted numerically. This micromixer takes advantages of mixing enhancements induced by alternating actuation of magnetic particles suspended in the fluid. Effects of magnetic actuation force, switching frequency and channel’s lateral dimension have been investigated. Numerical results show that the magnetic particle actuation at an appropriate frequency causes effective mixing and the optimum switching frequency depends on the channel’s lateral dimension and the applied magnetic force. The maximum efficiency is obtained at a relatively high operating frequency for large magnetic actuation forces and narrow microchannels. If the magnetic particles are actuated with a much higher or lower frequency than the optimum switching frequency, they tend to add limited agitation to the fluid flow and do not enhance the mixing significantly. The optimum switching frequency obtained from the present numerical prediction is in good agreement with the theoretical analysis. The proposed mixing scheme not only provides an excellent mixing, even in simple microchannel, but also can be easily applied to lab-on-a-chip applications with a pair of external electromagnets.

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Abbreviations

A :

cross-section area of the microchannel (m2)

A p :

cross-section area of the particle (m2)

B :

magnetic flux density (Tesla)

C :

dimensionless concentration

C D :

drag coefficient

D :

diffusion coefficient (m2/s)

F :

force (N)

f :

switching frequency (Hz)

f cr :

critical switching frequency (Hz)

H :

channel height (m)

H e :

magnetic field strength (A/m)

H M :

electromagnet thickness (m)

I :

current (A)

L :

streamwise dimension or length (m)

m :

particle mass (kg)

M :

magnetization of the particle (A/m)

P :

pressure (N/m2)

Pe :

peclet number (Re Sc)

r :

particle radius (m)

Re :

Reynolds number (UWρ f /η)

Sc :

Schmidt number (η/ρ f D)

St :

Strouhal number (Wf/U)

S :

distance between two parallel electromagnets (m)

t :

time (s)

T :

period, 1/f (s)

U :

relative velocity between the fluid and particle along y direction (m/s)

V :

volume (m3)

\(\vec{V}\) :

fluid’s velocity vector

\(\vec{v}\) :

particles’ velocity vector

W :

lateral dimension or width (m)

x :

streamwise coordinate of the microchannel

y :

lateral coordinate of the microchannel

z :

coordinate in the direction normal to the x–y plane

η:

dynamic viscosity of the fluid (kg/m s)

ρ:

density (kg/m3)

χ:

magnetic susceptibility of the particle

η e :

mixing efficiency (%)

μ:

permeability (N/A2)

d:

drag

f:

fluid

m:

magnetic

M:

electromagnet

o:

prior mixing stage or medium

p:

particle

r:

relative

s:

magnetization saturation

∞:

complete mixing state

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Acknowledgments

This work was partially supported by NSF grant# 0708540 and a University of Akron Faculty Research Summer Fellowship. The authors thank Dr. Tsukerman in the Department of Electrical and Computer Engineering of the University of Akron for the helpful discussion on the magnetic force calculation.

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Authors and Affiliations

  1. Department of Mechanical Engineering, The University of Akron, Akron, OH, 44325-3903, USA

    Yiou Wang, Jiang Zhe & Benjamin T. F. Chung

  2. School of Mechanical and Materials Engineering, Washington State University, Pullman, WA, 99164-2920, USA

    Prashanta Dutta

Authors
  1. Yiou Wang
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  2. Jiang Zhe
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  3. Benjamin T. F. Chung
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  4. Prashanta Dutta
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Correspondence to Jiang Zhe.

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Wang, Y., Zhe, J., Chung, B.T.F. et al. A rapid magnetic particle driven micromixer. Microfluid Nanofluid 4, 375–389 (2008). https://doi.org/10.1007/s10404-007-0188-x

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  • DOI: https://doi.org/10.1007/s10404-007-0188-x

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