Microfluidics and Nanofluidics

, Volume 12, Issue 1–4, pp 565–580 | Cite as

Effects of particle–fluid coupling on particle transport and capture in a magnetophoretic microsystem

  • Saud A. Khashan
  • Edward P. Furlani
Research Paper


A numerical analysis is presented of the effects of particle–fluid coupling on the transport and capture of magnetic particles in a microfluidic system under the influence of an applied magnetic field. Particle motion is predicted using a computational fluid dynamic CFD-based Lagrangian–Eulerian approach that takes into account dominant particle forces as well as two-way particle–fluid coupling. Two dimensionless groups are introduced that characterize particle capture, one that scales the magnetic and hydrodynamic forces on the particle and another that scales the distance to the magnetic field source. An analysis is preformed to parameterize capture efficiency with respect to the dimensionless numbers for both one-way and two-way particle–fluid coupling. For one-way coupling, in which the flow field is uncoupled from particle motion, correlations are developed that provide insight into system performance towards optimization. The difference in capture efficiency for one-way versus two-way coupling is analyzed and quantified. The analysis demonstrates that one-way coupling, in the dilute limit, provides a conservative estimate of capture efficiency in that it overpredicts the magnetic force needed to ensure particle capture as compared with a more rigorous fully coupled analysis. In two-way coupling there is a cooperative effect between the magnetic force and a particle-induced fluidic force that enhances capture efficiency. Thus, while one-way coupling is useful for rapid parametric screening of particle capture performance, more accurate predictions require two-way particle–fluid coupling. This is especially true when considering higher capture efficiencies and/or higher particle concentrations.


Magnetic separation Particle–fluid coupling Magnetophoresis Magnetophoretic microsystem Magnetic particle transport Magnetic field Directed particle transport 

List of symbols


Defined in Eq. 7


Particle radius (m)

a (axay)

Particle acceleration field (m/s2)


Magnitude of the magnetic field induction (T)


Magnetic field induction (T)


Particle mobility defined as (6πηa)−1


Capture efficiency (dimensionless)


Brownian critical particle radius (m)


Distance between the two dipole conductors (m)


Particle diameter (m)

\( \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{e}_{r} ,\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{e}_{\phi } \)

Unit vector along r and ϕ


Magnetic force field (N)


Counter drag force density (N/m3)


Drag force (N)


External force (N)


Gravitational acceleration (m/s2)


Magnitude of the applied external magnetic field (A/m)


Applied external magnetic field (A/m)


Channel height (m)


Current (A)

\( \hat{i},\hat{j} \)

Unit vectors along x and y


Boltzmann constant


Channel length (m)


Saturation magnetization (A/m)


Particle mass (kg)

\( \dot{m}_{\text{stream}} \)

Stream mass flow rate of a single injection (kg/s)


Number of injection streams

\( \dot{n}_{\text{parcel}} \)

Number of particles in a parcel per second


Line dipole strength (A-m)


Pressure (Pa)


Radial polar coordinates (m)


Normalized slip (=|u − u p|/u i)


Temperature (K)


Time (s)


Inlet mean velocity (m/s)


Fluid velocity vector (m/s)


Particle velocity vector (m/s)


Computational cell volume (m3)


Particle volume (m3)


Continuum spatial coordinates (m)

xp (xpyp)

Particle instantaneous position (m)


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


Vertical distance between the dipole and the lower plate (m)


=μ 0 χa 2/9ηu i (m3/A2)


=(0.5μ 0 χV p p 2)/(6πηau i h 5) (dimensionless)


Fluid volume-averaged susceptibility (dimensionless)


Particle volume-averaged susceptibility (dimensionless)


=y c/h (dimensionless)


Fluid molecular viscosity (N s/m2)


Free-space magnetic permeability (=1.257 × 10−6 N/A2)


Angular position


Injection particle loading by volume (%)


Fluid density (kg/m3)


Particle density (kg/m3)


Particle response time (s)



S.A. Khashan acknowledges the financial support received from the Research Affairs at the UAE University under contract number. 01-05-7-12/10.


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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Mechanical Engineering DepartmentUnited Arab Emirates UniversityAl AinUAE
  2. 2.Department of Chemical and Biological EngineeringUniversity at Buffalo, SUNYNew YorkUSA
  3. 3.Department of Electrical EngineeringUniversity at Buffalo, SUNYNew YorkUSA

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