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, a and b. 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 c (representing the inverse of normalized offset distance of the dipole from the line of symmetry) and r (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.
List of symbolsa particle radius (m) CE capture efficiency (dimensionless) e _ r ; e _ / unit vectors along r and / F d drag force by the fluid on a particle (N) F m magnetic force on a particle (N) h height of the straight channel, and the straight section of T-channel (m) h 1 length of the limbs of T-channel (m) h 2 width of the limbs of T-channel (m) H magnetic field (A/m) I unit tensor k n number of particle cluster entering the channel every dt L time interval K wall ; K k wall ; K ? wall wall drag multipliers L channel length (m) N part particle flux into the channel (m -2 s -1 ) N C number of particles per cluster p pressure (Pa) P dipole strength (A-m) r position vector (m) Re Reynolds number (dimensionless) dt L time step for integration for Lagrangian tracking (s) t time (s) U av average flow velocity (m/s) V velocity of fluid (m/s) V p velocity of particle (m/s) x, y coordinate references x mag , y mag coordinates of the virtual origin of the line dipole (m) a p /h 5 (nondimensional group variable)
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