so that a bioparticle of mobility m E moves a distance y in an electric field of intensity E applied for a time of t. It is obvious that if E is increased t can be
decreased to achieve the same distance of migration and vice-versa, under
otherwise similar conditions.
The bioparticles are randomly distributed in space over the volume of the
bottom chamber. However, the time required for any individual particle to
move into the top chamber increases as its distance from the top surface of the
bottom chamber increases, under a given set of experimental conditions of E
and t. That is, the ratio of these heights gives the relative number of bioparticles
that migrate to the top chamber at any given set of E and t. To calculate the
absolute number of particles transferred to the top chamber, the ratio of the
distance to the top of the chamber to the total height h, has to be multiplied by
the concentration of the particles (i.e., number of particles per unit volume),
since the ratio of the heights is nothing but the ratio of the volumes of the
chamber corresponding to the location considered.
Therefore, when an electric field is applied to capture the particles with
mobility m E located at distance y from the top surface of bottom chamber, the
number of bioparticles that would migrate during a single step is
m = (y/h) [N] = (m E E t/h) [N]
(23)
where N = (C) (pr c
2 h) and C is the cell concentration (cells ml –1 ) and pr c
2 h is the
volume of the chamber and since y = m E Et [from Eq. (22)]. This movement of
particles has already been depicted in Fig. 14
2.2.3.2
Mixed Cells/Particles
The bottom chamber contains two types of particles having electrophoretic
mobilities m 1E and m 2E . The change in the number of type-1 particles in a stage
n during step r will be equal to the number of bioparticles that migrated to the
top chamber during step r. So the general equation can be written for this
situation by material balance as
– [x 1 N] n, r + [x 1 N] n, r –1 = (m 1 ) n, r
(24)
where (m 1 ) n, r is number of type-1 particles with mobility m E1 that migrated
from stage n during step r to the top chamber; N is the total number of bioparticles present in any of the n bottom chambers, at t = 0; N 1 is the number of
bioparticles with mobility m 1E ; N 2 is the number of bioparticles with mobility
m 2E ; N = N 1 + N 2 and x 1 = N 1 /[N 1 + N 2 ] = N 1 /N. Now using Eq. (22), Eq. (24) can
be written as
– [x 1 N] n, r + [x 1 N] n, r –1 = (m 1E Et/h) [N 1 ] n, r –1
(25)
where [N 1 ] n, r –1 = number of bioparticles with mobility m 1E in stage n at step
(r – 1), i.e., (C 1 ) (pr c
2 h) where C 1 is the concentration of type-1 cells.
Alternatively the number of type 1 particles remaining will, since N 1 = x 1 (N),
Multistage Magnetic and Electrophoretic Extraction of Cells, Particles and Macromolecules
167
decreased to achieve the same distance of migration and vice-versa, under
otherwise similar conditions.
The bioparticles are randomly distributed in space over the volume of the
bottom chamber. However, the time required for any individual particle to
move into the top chamber increases as its distance from the top surface of the
bottom chamber increases, under a given set of experimental conditions of E
and t. That is, the ratio of these heights gives the relative number of bioparticles
that migrate to the top chamber at any given set of E and t. To calculate the
absolute number of particles transferred to the top chamber, the ratio of the
distance to the top of the chamber to the total height h, has to be multiplied by
the concentration of the particles (i.e., number of particles per unit volume),
since the ratio of the heights is nothing but the ratio of the volumes of the
chamber corresponding to the location considered.
Therefore, when an electric field is applied to capture the particles with
mobility m E located at distance y from the top surface of bottom chamber, the
number of bioparticles that would migrate during a single step is
m = (y/h) [N] = (m E E t/h) [N]
(23)
where N = (C) (pr c
2 h) and C is the cell concentration (cells ml –1 ) and pr c
2 h is the
volume of the chamber and since y = m E Et [from Eq. (22)]. This movement of
particles has already been depicted in Fig. 14
2.2.3.2
Mixed Cells/Particles
The bottom chamber contains two types of particles having electrophoretic
mobilities m 1E and m 2E . The change in the number of type-1 particles in a stage
n during step r will be equal to the number of bioparticles that migrated to the
top chamber during step r. So the general equation can be written for this
situation by material balance as
– [x 1 N] n, r + [x 1 N] n, r –1 = (m 1 ) n, r
(24)
where (m 1 ) n, r is number of type-1 particles with mobility m E1 that migrated
from stage n during step r to the top chamber; N is the total number of bioparticles present in any of the n bottom chambers, at t = 0; N 1 is the number of
bioparticles with mobility m 1E ; N 2 is the number of bioparticles with mobility
m 2E ; N = N 1 + N 2 and x 1 = N 1 /[N 1 + N 2 ] = N 1 /N. Now using Eq. (22), Eq. (24) can
be written as
– [x 1 N] n, r + [x 1 N] n, r –1 = (m 1E Et/h) [N 1 ] n, r –1
(25)
where [N 1 ] n, r –1 = number of bioparticles with mobility m 1E in stage n at step
(r – 1), i.e., (C 1 ) (pr c
2 h) where C 1 is the concentration of type-1 cells.
Alternatively the number of type 1 particles remaining will, since N 1 = x 1 (N),
Multistage Magnetic and Electrophoretic Extraction of Cells, Particles and Macromolecules
167