the radial cross section, or
∂B
41 = 0
(14)
∂r
By taking the dot product of the magnetic field and the gradient of the magnetic field, the following differential relationship is determined:
∂B z
∂B z
B · —B = B z · 51 + B r · 51
(15)
∂r
∂z
This relationship, combined with the above assumptions to simplify the
magnetic force equation, yields the scalar magnetic force relationship similar
to that given in Eq. (9). If all variable parameters for the MAGSEP experiment in this equation (B and particle size a p ) are set, then the susceptibility difference, Dc m is the controlling variable governing the magnetic
force. Based on this calculation, the separation of the cells as it relates to the
susceptibility difference can be governed by controlling the magnetic field B,
the vertical height of separation Dz, and the time interval required for separation, Dt.
The volumetric susceptibility difference Dc m can be measured by sampling a
distribution of particle positions (which is a function of their velocities). If the
particles are placed in a thin flat layer across the bottom of a cavity and covered
with a solution to a depth Dz, the particles can then be aligned below a shallow
upper cavity with an activated magnet. The magnetic field of the upper magnet
can then attract particles for a time Dt, and when a sufficient amount of
particles have migrated into the shallow upper cavity, the cavities can be halfstepped to separate the particles as shown in Fig. 3. The volumetric susceptibility can then be calculated by the following relationship:
9u p h/a 2
p + 2g (DÇ)
Dc m = 000
(16)
dB
B · 41
dz
where v p is the velocity, and can be assumed to be equal to Dz/Dt. The number
of particles transferred represents a distribution of the total particles and is
also a representation of the number of particles within a volumetric susceptibility range. If enough separation in these stages takes place, then this
volumetric susceptibility range can be assumed to be an absolute volumetric
susceptibility. Further modeling of magnetic extraction in MAGSEP is in
progress.
Continuous flow magnetic cell sorting using soluble immunomagnetic label
and the corresponding theory was presented by Zborowski et al. [44].
156
K.S.M.S. Raghavarao et al.
∂B
41 = 0
(14)
∂r
By taking the dot product of the magnetic field and the gradient of the magnetic field, the following differential relationship is determined:
∂B z
∂B z
B · —B = B z · 51 + B r · 51
(15)
∂r
∂z
This relationship, combined with the above assumptions to simplify the
magnetic force equation, yields the scalar magnetic force relationship similar
to that given in Eq. (9). If all variable parameters for the MAGSEP experiment in this equation (B and particle size a p ) are set, then the susceptibility difference, Dc m is the controlling variable governing the magnetic
force. Based on this calculation, the separation of the cells as it relates to the
susceptibility difference can be governed by controlling the magnetic field B,
the vertical height of separation Dz, and the time interval required for separation, Dt.
The volumetric susceptibility difference Dc m can be measured by sampling a
distribution of particle positions (which is a function of their velocities). If the
particles are placed in a thin flat layer across the bottom of a cavity and covered
with a solution to a depth Dz, the particles can then be aligned below a shallow
upper cavity with an activated magnet. The magnetic field of the upper magnet
can then attract particles for a time Dt, and when a sufficient amount of
particles have migrated into the shallow upper cavity, the cavities can be halfstepped to separate the particles as shown in Fig. 3. The volumetric susceptibility can then be calculated by the following relationship:
9u p h/a 2
p + 2g (DÇ)
Dc m = 000
(16)
dB
B · 41
dz
where v p is the velocity, and can be assumed to be equal to Dz/Dt. The number
of particles transferred represents a distribution of the total particles and is
also a representation of the number of particles within a volumetric susceptibility range. If enough separation in these stages takes place, then this
volumetric susceptibility range can be assumed to be an absolute volumetric
susceptibility. Further modeling of magnetic extraction in MAGSEP is in
progress.
Continuous flow magnetic cell sorting using soluble immunomagnetic label
and the corresponding theory was presented by Zborowski et al. [44].
156
K.S.M.S. Raghavarao et al.