The effect of adjusting exposure time was explored, and it was found that
short exposures result in less particle capture at early stages and aggregation by
stronger magnets at later stages. This important discovery that proper temporal
programming can prevent aggregation makes the MAGSEP concept feasible. In
addition, the magnets used in the above experiment had pole fluxes ranging
over two orders of magnitude, and the weak magnets were shown to attract
large beads while, in separate experiments, the strong magnets were shown to
attract weak particles such as magnetotactic bacteria (data not shown).
2.1.3
Theory and Mathematical Models
The range of magnetic field required for cell separation is obviously decided by
the magnetic and mechanical properties of the cells. A review of the mathematical formulae that are relevant to cell extraction and their illustration by
selected examples was presented well by Zborowski [43].
The magnetic field is a space domain where an electrical charge ‘e’ moving
with velocity ‘v e ’ experiences a magnetic force ‘F m ’, given by
F m = IlB
(1)
where ‘I’ is the current intensity, l is length of element, and B is the magnetic
field intensity (kg A –1 s –2 or Tesla, T ) given as
B = m o H
(2)
where m o is magnetic permeability of free space and H is the magnetic field
strength (A m –1 ). The presence of matter in the magnetic field modifies the field
fluxes at given constant field strengths. The magnetic properties of matter are
defined by induced polarization M to account for the variation in magnetic flux.
For isotropic media
M = c m H
(3)
where c m is magnetic susceptibility. In the uniform magnetic field the magnetic particle undergoes rotation until Maxwell stress tensor becomes zero and
then remains stationary with respect to the medium. In the non-uniform field,
differences in the Maxwell stresses result in a net force F m acting on the
magnetic particle given as
F m = V p (M ◊ —) B
(4)
where V p is the volume of the particle. In the simplest one-dimensional case,
using Eq. (3), it can be written as
dB
F m = V p c m H 41
(5)
dz
In homogenous media, magnetic field B is parallel and proportional to the
magnetic field strength H. Magnetic force lines are defined as curves which are
Multistage Magnetic and Electrophoretic Extraction of Cells, Particles and Macromolecules
153
short exposures result in less particle capture at early stages and aggregation by
stronger magnets at later stages. This important discovery that proper temporal
programming can prevent aggregation makes the MAGSEP concept feasible. In
addition, the magnets used in the above experiment had pole fluxes ranging
over two orders of magnitude, and the weak magnets were shown to attract
large beads while, in separate experiments, the strong magnets were shown to
attract weak particles such as magnetotactic bacteria (data not shown).
2.1.3
Theory and Mathematical Models
The range of magnetic field required for cell separation is obviously decided by
the magnetic and mechanical properties of the cells. A review of the mathematical formulae that are relevant to cell extraction and their illustration by
selected examples was presented well by Zborowski [43].
The magnetic field is a space domain where an electrical charge ‘e’ moving
with velocity ‘v e ’ experiences a magnetic force ‘F m ’, given by
F m = IlB
(1)
where ‘I’ is the current intensity, l is length of element, and B is the magnetic
field intensity (kg A –1 s –2 or Tesla, T ) given as
B = m o H
(2)
where m o is magnetic permeability of free space and H is the magnetic field
strength (A m –1 ). The presence of matter in the magnetic field modifies the field
fluxes at given constant field strengths. The magnetic properties of matter are
defined by induced polarization M to account for the variation in magnetic flux.
For isotropic media
M = c m H
(3)
where c m is magnetic susceptibility. In the uniform magnetic field the magnetic particle undergoes rotation until Maxwell stress tensor becomes zero and
then remains stationary with respect to the medium. In the non-uniform field,
differences in the Maxwell stresses result in a net force F m acting on the
magnetic particle given as
F m = V p (M ◊ —) B
(4)
where V p is the volume of the particle. In the simplest one-dimensional case,
using Eq. (3), it can be written as
dB
F m = V p c m H 41
(5)
dz
In homogenous media, magnetic field B is parallel and proportional to the
magnetic field strength H. Magnetic force lines are defined as curves which are
Multistage Magnetic and Electrophoretic Extraction of Cells, Particles and Macromolecules
153