Biomedical Microdevices

, Volume 12, Issue 1, pp 23–34

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

  • Nipu Modak
  • Dinabandhu Kejriwal
  • Krishanu Nandy
  • Amitava Datta
  • Ranjan Ganguly


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.


BioMEMS Magnetic microspheres Microfluidic Magnetophoretic separation 



Particle radius (m)


Capture efficiency (dimensionless)

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Unit vectors along r and \( \phi \)


Drag force by the fluid on a particle (N)


Magnetic force on a particle (N)


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


Magnetic field (A/m)

Kwall, Kwall, Kwall

Wall drag multipliers


Channel length (m)


Distance of a particle from the wall


Pressure (Pa)


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


Pixel value (Arbitrary unit)


Flow rate (ml/h)


Position vector (m)


Reynolds number (dimensionless)


Time step for integration for Lagrangian tracking (s)


Time (s)


Slip velocity between particle and fluid (m/s)


Maximum flow velocity (m/s)


Velocity of fluid (m/s)


Velocity of particle (m/s)

(x, y)

Coordinate references


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



Effective magnetic susceptibility of magnetic microspheres


Intrinsic magnetic susceptibility of magnetic microspheres


Viscosity of fluid (N-s/m2)


Particle number density (m−3)


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

\( \phi \)

Angular position


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


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


Density of fluid (kg/m3)

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

Stress tensor (N/m2)





Corresponding to critical or marginal capture


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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Nipu Modak
    • 1
  • Dinabandhu Kejriwal
    • 2
  • Krishanu Nandy
    • 2
  • Amitava Datta
    • 2
  • Ranjan Ganguly
    • 2
  1. 1.Department of Mechanical EngineeringJadavpur UniversityKolkataIndia
  2. 2.Department of Power EngineeringJadavpur UniversityKolkataIndia

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