Numerical simulation of magnetic separation of particles in a rectangular microchannel

Sorting of paramagnetically labelled cells or particles in microsystems is an important application for biological and biomedical use. Typically the magnetic separation process consists of magnetic trapping of particles on the channel surface followed by flushing the trapped particles out of the separator system. However, in our micromachined magnetic cell sorter, two buffer streams center a sample containing flow stream. Cells of interest are drawn into the acceptor buffer stream by magnetic deflection and separated from negative cells by splitting the flow channel in 2 outlets. The lack of information on the behaviour of magnetically labelled cells or particles in microfluidic structures has prevented us from improving the design of our sorter chip. Thus far, improvements were based on trial and error.
In this project we are developing a numerical model for the motion of magnetically labelled cells exposed to a magnetic force. The objective of our model is to investigate the relations between magnetic gradient, magnetic properties of the cell, volume flow rate and the channel dimensions. Our model assumes that cells can be regarded as small spheres and therefore uses the equation of Maxey and Riley to describe cell motion. The equation of motion with inclusion of magnetic force is solved using the Runge-Kutta method. Results will be presented in the form of cell trajectories, deflection as function of volume flow rate and magnetic susceptibility of the cell.
These results will allow a rational approach to the optimisation of the design of micromachined magnetic cell sorter.