Biomedical Microdevices

, Volume 12, Issue 1, pp 23–34

Experimental and numerical characterization of magnetophoretic separation for MEMS-based biosensor applications

Authors

  • Nipu Modak
    • Department of Mechanical EngineeringJadavpur University
  • Dinabandhu Kejriwal
    • Department of Power EngineeringJadavpur University
  • Krishanu Nandy
    • Department of Power EngineeringJadavpur University
  • Amitava Datta
    • Department of Power EngineeringJadavpur University
    • Department of Power EngineeringJadavpur University
Article

DOI: 10.1007/s10544-009-9354-0

Cite this article as:
Modak, N., Kejriwal, D., Nandy, K. et al. Biomed Microdevices (2010) 12: 23. doi:10.1007/s10544-009-9354-0

Abstract

Magnetophoretic isolation of biochemical and organic entities in a microfluidic environment is a popular tool for a wide range of bioMEMS applications, including biosensors. An experimental and numerical analysis of magnetophoretic capture of magnetic microspheres in a microfluidic channel under the influence of an external field is investigated. For a given microfluidic geometry, the operating conditions for marginal capture is found to be interrelated in such a manner that a unique critical capture parameter \( \Pi _{{{\text{crit}}}} = {{\left( {I_{{{\text{crit}}}} {\text{a}}} \right)}^{2} } \mathord{\left/ {\vphantom {{{\left( {I_{{{\text{crit}}}} {\text{a}}} \right)}^{2} } {{\text{Q}}\eta }}} \right. \kern-\nulldelimiterspace} {{\text{Q}}\eta } \), that is proportional to the ratio of the magnetic force to viscous force, can be identified. Influences of the flow rate, magnetic field and other parameters on the particle trajectories in the microfluidic channel are investigated both numerically and through bright-field imaging under a microscope. Like the event of critical capture, particle trajectories are also found to be guided by a similar parameter, π. Magnetophoretic capture efficiency of the device is also evaluated as a function of a nondimensional number \( \Pi ^{*} = {\chi {\text{P}}^{2} {\text{a}}^{2} } \mathord{\left/ {\vphantom {{\chi {\text{P}}^{2} {\text{a}}^{2} } {{\left( {{\text{U}}_{0} \eta {\text{h}}^{5} } \right)}}}} \right. \kern-\nulldelimiterspace} {{\left( {{\text{U}}_{0} \eta {\text{h}}^{5} } \right)}} \), when both numerical and experimental results are found to agree reasonably well. Results of this investigation can be applied for the selection of the operating parameters and for prediction of device performance of practical microfluidic separators.

Keywords

BioMEMSMagnetic microspheresMicrofluidicMagnetophoretic separation

Nomenclature

a

Particle radius (m)

CE

Capture efficiency (dimensionless)

https://static-content.springer.com/image/art%3A10.1007%2Fs10544-009-9354-0/MediaObjects/10544_2009_9354_Figa_HTML.gif

Unit vectors along r and \( \phi \)

Fd

Drag force by the fluid on a particle (N)

Fm

Magnetic force on a particle (N)

h

Height of the straight channel, and the straight section of T-channel (m)

H

Magnetic field (A/m)

Kwall, Kwall, Kwall

Wall drag multipliers

L

Channel length (m)

lw

Distance of a particle from the wall

p

Pressure (Pa)

P

Dipole strength (per unit depth of a dipole line) (A-m)

Pix

Pixel value (Arbitrary unit)

Q

Flow rate (ml/h)

r

Position vector (m)

Re

Reynolds number (dimensionless)

dtL

Time step for integration for Lagrangian tracking (s)

t

Time (s)

U

Slip velocity between particle and fluid (m/s)

Umax

Maximum flow velocity (m/s)

V

Velocity of fluid (m/s)

Vp

Velocity of particle (m/s)

(x, y)

Coordinate references

(xmag,ymag)

Coordinates of the virtual origin of the dipole line (m)

Symbols

χ

Effective magnetic susceptibility of magnetic microspheres

χi

Intrinsic magnetic susceptibility of magnetic microspheres

η

Viscosity of fluid (N-s/m2)

λ

Particle number density (m−3)

μ0

permeability of vacuum (=1.257 × 10−6 N/A2)

\( \phi \)

Angular position

Π

\( {{\left( {{\text{I}}^{2} {\text{P}}^{2} } \right)}} \mathord{\left/ {\vphantom {{{\left( {{\text{I}}^{2} {\text{P}}^{2} } \right)}} {{\left( {\eta {\text{Q}}} \right)}{\left( {{\text{m}}^{5} } \right)}}}} \right. \kern-\nulldelimiterspace} {{\left( {\eta {\text{Q}}} \right)}{\left( {{\text{m}}^{5} } \right)}} \)

Π*

\( {{\left( {a^{2} \chi _{{{\text{eff}}}} {\text{P}}^{2} } \right)}} \mathord{\left/ {\vphantom {{{\left( {a^{2} \chi _{{{\text{eff}}}} {\text{P}}^{2} } \right)}} {{\left( {\eta {\text{U}}_{{{\text{av}}}} {\text{h}}^{5} } \right)}}}} \right. \kern-\nulldelimiterspace} {{\left( {\eta {\text{U}}_{{{\text{av}}}} {\text{h}}^{5} } \right)}} \)

ρ

Density of fluid (kg/m3)

\( \underline{\underline \tau } \)

Stress tensor (N/m2)

ξ

a/lw

Subscript

cr

Corresponding to critical or marginal capture

Copyright information

© Springer Science+Business Media, LLC 2009