Cell separation in a microfluidic channel using magnetic microspheres

Research Paper

DOI: 10.1007/s10404-008-0343-z

Cite this article as:
Modak, N., Datta, A. & Ganguly, R. Microfluid Nanofluid (2009) 6: 647. doi:10.1007/s10404-008-0343-z

Abstract

Magnetophoretic isolation of biological cells in a microfluidic environment has strong relevance in biomedicine and biotechnology. A numerical analysis of magnetophoretic cell separation using magnetic microspheres in a straight and a T-shaped microfluidic channel under the influence of a line dipole is presented. The effect of coupled particle–fluid interactions on the fluid flow and particle trajectories are investigated under different particle loading and dipole strengths. Microchannel flow and particle trajectories are simulated for different values of dipole strength and position, particle diameter and magnetic susceptibility, fluid viscosity and flow velocity in both the microchannel configurations. Residence times of the captured particles within the channel are also computed. The capture efficiency is found to be a function of two nondimensional parameters, α and β. The first parameter denotes the ratio of magnetic to viscous forces, while the second one represents the ratio of channel height to the distance of the dipole from the channel wall. Two additional nondimensional parameters γ (representing the inverse of normalized offset distance of the dipole from the line of symmetry) and σ (representing the inverse of normalized width of the outlet limbs) are found to influence the capture efficiency in the T-channel. Results of this investigation can be applied for the selection of a wide range of operating and design parameters for practical microfluidic cell separators.

Keywords

Magnetic microspheres Microfluidics Cell separation CFD 

List of symbols

a

particle radius (m)

CE

capture efficiency (dimensionless)

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

unit vectors along r and ϕ

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)

h1

length of the limbs of T-channel (m)

h2

width of the limbs of T-channel (m)

H

magnetic field (A/m)

\( \underline{\underline{\text{I}}} \)

unit tensor

kn

number of particle cluster entering the channel every dtL time interval

\( K_{\text{wall}} ,\, K_{\text{wall}}^{\parallel } ,\, K_{\text{wall}}^{ \bot } \)

wall drag multipliers

L

channel length (m)

Npart

particle flux into the channel (m−2s−1)

NC

number of particles per cluster

p

pressure (Pa)

P

dipole strength (A-m)

r

position vector (m)

Re

Reynolds number (dimensionless)

dtL

time step for integration for Lagrangian tracking (s)

t

time (s)

Uav

average 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 line dipole (m)

α

π/h5 (nondimensional group variable)

β

h/|xmag − L| for T-channel h/|ymag| for straight channel, (dimensionless)

χeff

effective magnetic susceptibility of magnetic microspheres

χi

Intrinsic magnetic susceptibility of magnetic microspheres

γ

h/|h1 + h/2 – ymag| (dimensionless)

η

viscosity of fluid (Pa-s)

λ

particle number density (m−3)

μ0

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

ϕ

angular position

π

\( {{\left( {a^{2} \chi_{\text{eff}} P^{2} } \right)} \mathord{\left/ {\vphantom {{\left( {a^{2} \chi_{\text{eff}} P^{2} } \right)} {\left( {\eta {\text{U}}_{\text{av}} } \right)}}} \right. \kern-\nulldelimiterspace} {\left( {\eta {\text{U}}_{\text{av}} } \right)}} \) (m5)

ρ

density of fluid (kg/m3)

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

stress tensor (N/m2)

ξ

ratio of particle diameter to its distance from the wall

σ

h/h2 (dimensionless)

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Mechanical Engineering DepartmentJadavpur UniversityKolkataIndia
  2. 2.Power Engineering DepartmentJadavpur UniversityKolkataIndia

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