ARTICLE
Wall Effects in Continuous Microfluidic
Magneto-Affinity Cell Separation
Liqun Wu,1 Yong Zhang,2 Moorthi Palaniapan,1 Partha Roy2
1Department of Electrical and Computer Engineering, National University of Singapore,
Singapore
2Division of Bioengineering, Block E1, No. 05-22, 9 Engineering Drive 2,
National University of Singapore, Singapore 117576, Singapore; telephone: 65-6516-1624;
fax: (65) 68723069; e-mail: biepr@nus.edu.sg
Received 14 July 2009; revision received 25 November 2009; accepted 17 December 2009
Published online 20 January 2010 in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/bit.22665
ABSTRACT: Continuous microfluidic magneto-affinity cell
separator combines unique microscale flow phenomenon
with advantageous nanobead properties, to isolate cells with
high specificity. Owing to the comparable size of the cell–
bead complexes and the microchannels, the walls of the
microchannel exert a strong influence on the separation of
cells by this method. We present a theoretical and experi-
mental study that provides a quantitative description of
hydrodynamic wall interactions and wall rolling velocity
of cells. A transient convectionmodel describes the transport
of cells in two-phasemicrofluidic flow under the influence of
an external magnetic field. Transport of cells along the
microchannel walls is also considered via an additional
equation. Results show the variation of cell flux in the fluid
phases and the wall as a function of a dimensionless para-
meter arising in the equations. Our results suggest that
conditions may be optimized to maximize cell separation
while minimizing contact with the wall surfaces. Experi-
mentally measured cell rolling velocities on the wall indicate
the presence of other near-wall forces in addition to fluid
shear forces. Separation of a human colon carcinoma cell
line from a mixture of red blood cells, with folic acid
conjugated 1mm and 200 nm beads, is reported.
Biotechnol. Bioeng. 2010;106: 68–75.
! 2010 Wiley Periodicals, Inc.
KEYWORDS: cell separation; microfluidic; wall effect;
magneto-affinity
Introduction
Typical animal and plant tissues are comprised of a mixture
of different cell types. Isolation of a specific cell type
has important applications in the clinic, in basic research
and industry. Sorting cells with magnetic fields has
been shown to be highly effective. With the exception
of a few, intrinsically magnetic cell types, for example,
red blood and white blood cells, most cells require
labeling with magnetic nanobeads. This is beneficial for
separation since it allows highly specific targeting of cell
surface receptors. Magnetic affinity cell sorting (MACS;
Miltenyi Biotec GmbH, Gladbach, Germany; Miltenyi et al.,
1990) is the current gold standard in cell separation. The
basic principle of MACS is that the desired cells are
labeled with ligand-coated superparamagnetic beads.
Subsequently, the labeled and non-labeled cells are separated
with a high-gradient magnetic field induced on a column
matrix. Although MACS has important advantages like
high throughput, it is inherently a batchwise process where
cells may be damaged by extended contact with the solid
phase.
Continuous and highly specific cell sorting becomes
feasible by the application of microfluidics technology.
Researchers (Han and Frazier, 2004, 2005, 2006) have
demonstrated the separation of red and white blood cells,
due to their native magnetic properties, by placing a
ferromagnetic wire in a microchannel. Others (Inglis et al.,
2004) have applied magnetic stripes to direct the movement
of magnetically labeled cells. However, the most promising
method arises from the application of unique microfluidic
flow phenomena that results in multiphase flow of perfectly
miscible aqueous fluids pumped into multiple inlets. A
number of researchers have demonstrated microfluidic
magneto-affinity cell sorting using two (Blankenstein, 1997;
Nan Xia et al., 2006; Yung et al., 2009), three (Hyun-Seok
et al., 2007), or more inlets (Pamme and Wilhelmb, 2006).
Owing to the comparable dimensions of the cells and
microchannel, design of such microseparators requires
careful consideration of the cells interactions with the
microchannel surfaces, that is, hydrodynamic and physical
parameters such as rolling velocity.
Correspondence to: P. Roy
Contract grant sponsor: NUS FRC
Contract grant number: R-263-000-326-112
68 Biotechnology and Bioengineering, Vol. 106, No. 1, May 1, 2010 ! 2010 Wiley Periodicals, Inc.

Models of microfluidic magneto-affinity separation are
limited in the current literature. Past theoretical models may
be divided into two types: capture of magnetic particles only
(Chronis et al., 2001; Fukui et al., 2004; Hoffmann and
Franzreb, 2004; Warnke, 2003), and capture of cells (Han
and Frazier, 2005, 2006; Kim et al., 2007; Nan Xia et al.,
2006). All previous theoretical studies incorporate basic
magnetic and hydrodynamic forces. However, in microscale
continuous flow systems, additional hydrodynamic inter-
actions, such as interparticle and particle–wall interactions
must be considered, due to their significant influence on
cell motion and distribution. Mikkelsen et al. (2005) have
presented a theoretical comparison of magnetic and hydro-
dynamic interactions between microbeads in a microfluidic
channel. They considered a single inlet fluid flow system
with far-field hydrodynamic interactions of the microbeads
with one wall.
In this study, we present a detailed theoretical model
and accompanying experimental data for a continuous
microfluidic magneto-affinity cell separator. The transient
convection of cells in two-phase microfluidic flow under an
externally applied magnetic field is described by our model.
Moreover, the cell velocities are calculated from detailed
hydrodynamic interactions of the cell with two enclosing
plane parallel walls of the microchannel. Additionally,
the model incorporates transport of the cells along the
microchannel walls. Experiments are reported with a colon
carcinoma cell line and quantify important parameters such
as the wall rolling velocity of cells, separation yield, and
viability achieved.
Theory
Model Formulation
As shown in Figure 1, the main microchannel has two inlets:
a feed channel and a separation channel. The incoming cell–
nanobead complexes are entrained in the feed channel fluid
phase, while the fluid phase in the separation channel is cell
free. A transverse magnetic field is applied as shown (Fig. 1),
and the cells with attached nanobeads move toward the
separation channel under the action of the magnetic field
force. Cells experiencing a strong magnetic force will reach
the other wall and get transported along the wall. A mass
balance equation involving the dimensionless number
density of cellsNc(t, x, z) in the microchannel is expressed as:
@Nc
@t
þ uxðzÞ
@Nc
@x
þ a
@uzðzÞNc
@z
¼ 0 (1)
where a ¼ uz cL=yavgW , uxðzÞ ¼ u0xðzÞ=yavg, and
uzðzÞ ¼ u0zðzÞ=uz c are the dimensionless cell velocities in
x and z directions; yavg is the average fluid flow velocity; uz_c
is the z-directed cell velocity without hydrodynamic wall
effect; z is made dimensionless with W which is the width is
the width of the microchannel; and x is made dimensionless
with L which is the length is the length of the microchannel
(Table I). The dimensional cell number density in the
channel has the unit of number per unit volume unit volume
and is made dimensionless with the inlet cell density. Due to
the large size, the diffusion coefficient of cells is very small.
Thus, cell transport is convection dominated with a large
translational Pe´clet number. This allows us to simplify the
governing equation by leaving out the diffusion terms. It is
assumed that over the timescale of the magnetic separation,
there is no significant change in the cell–nanobead
complexes due to binding/unbinding of the nanobeads to
the cell surface receptors. The mass conservation equation
for cell transport along the wall is given by
@Nw
@t
þ uw
@Nw
@x
¼ auz z ¼ 1%
Rc
W
! "
Nc t; x; z ¼ 1%
Rc
W
! "
(2)
Figure 1. a: Model-based schematic of cell–nanobead transport in microchan-
nel. b: A three-dimensional depiction of the main and inlet/outlet microchannels, as
well as the magnet location. [Color figure can be seen in the online version of this
article, available at www.interscience.wiley.com.]
Table I. Parameter values employed in the model results given in
Figure 6.
Ba 0.0988 T
rBa 123.2 T/m
La 2 cm
Wa 208mm
Ha 76mm
uz_c
b 0.01169 cm/s
uw
a As per experimental data in Figure 5
aMeasured values.
aEstimated.
Wu et al.: Wall Effects in Magneto-Affinity Cell Separation 69
Biotechnology and Bioengineering

where uw ¼ u0w=yavg is the dimensionless rolling velocity on
the wall,Nw(t, x) is the dimensionless cell number density on
the wall surface (made dimensionless with the inlet cell
density and W) and dimensional density has the unit of
number per unit area, and Rc is the radius of the cell.
Equations (1) and (2) are subject to the following initial and
boundary conditions:
Ncðt ¼ 0; x; zÞ ¼ 0
Nc t; x ¼ 0; RcW & z &
1
2
# $
¼ 1
Nc t; x ¼ 0; 12 < z & 1%
Rc
W
# $
¼ 0
Nc t; x; z ¼ RcW
# $
¼ 0
Nwðt ¼ 0; xÞ ¼ 0
Nwðt; x ¼ 0Þ ¼ 0
(3)
Magnetic Force
In a weak magnetic field, the magnetization of super-
paramagnetic particles remains unsaturated. A strong
magnetic field is needed to saturate the magnetization of
the particles (Zborowski, 1997). We have employed the
following magnetic force equations for unsaturated nano-
beads (Jackson 1998; Zborowski, 1997):
Fm ¼
Vm
m0
9ðxm % xaqÞ
ð3þ xmÞð3þ xaqÞ
BrB (4)
where B is the external magnetic field (magnetic flux
density), 5B is the gradient of magnetic field, Vm is the
volume of the superparamagnetic core of nanobeads, xm
and xaq are the volume magnetic susceptibility of the
beads and medium, respectively, and m0 is the magnetic
permeability of air or vacuum. A correction to Equation (4)
has been proposed recently by our group (Wu et al., 2009)
and may be incorporated into the model to describe core–
shell-type superparamagnetic beads. The magnetic force on
a cell that is bound to Nm nanobeads is simply given by
Fc¼NmFm.
Estimation of Velocities (ux, uz)
The velocity of the cell–nanobead complex has two
components: ux in the direction of fluid flow and uz
parallel to the magnetic field. These velocities may be
computed by setting the sum of all forces (and torques, if
rotation is considered, see discussion below) in each
direction to zero. Here, we consider the hydrodynamic
interaction of the cells with the two bounding walls of the
microchannel. In the limit that Rc/W! 0, the velocities may
be computed without the consideration of wall effects. The
cell is convected along with the flow and ux may be assumed
to be identical with the fluid flow profile. When the
cell size is comparable with the width of microchannel
(Rc/W> 0.01), the cell velocity is strongly influenced by
hydrodynamic wall interactions. The velocities (ux, uz) of
cells will differ from the fluid velocity due to increased
hydrodynamic drag arising from the presence of the walls. In
addition, the drag force is no longer constant, but will
increase as the cells approach the wall. Hence, both ux and uz
are functions of z and will be maximum at the center of the
channel and minimum at the walls.
The drag force perpendicular to the wall is expressed with
a correction coefficient l(<0): Fdrag ¼ 6phRcu0zðzÞl, where
l<%1 with wall effect and l¼%1 in unbounded fluid (Wu
et al., 2007). Hence, u0zðzÞ ¼ ðNmVm=6pRchm0ð%lÞÞ
ð9ðxm % xaqÞ=ð3þ xmÞð3þ xaqÞÞBrB. Since uz c ¼ ðNm
Vm=6pRchm0Þð9ðxm % xaqÞ=ð3þ xmÞð3þ xaqÞÞBrB, then
uzðzÞ ¼
%1
l
(5)
Previous work (Ganatos et al., 1980a) has tabulated the
values of l (range 1:1ðRc=WÞ & z & 1% 1:1ðRc=WÞ) for a
rigid sphere moving perpendicular to two-plane parallel
walls. For the range ððRc þ dÞ=WÞ & z & 1:1ðRc=WÞ and
1% 1:1ðRc=WÞ & z & 1% ððRc þ dÞ=WÞ, we utilize the
lubrication theory result to calculate l (Kim and Karrila,
1991): l ¼ %ð1="Þ þ C1 % ð1=21Þ" ln ð1="Þ þ Oð"Þ, where
" ¼ ðz% Rc=WÞ=ðRc=WÞ and C1 is obtained from data
(Ganatos et al., 1980a) given at z ¼ 1:1Rc=W .
For the parallel motion of a sphere between two-plane
parallel channel walls, the drag force is given by (Ganatos
et al., 1980b) Ft ¼ 6phRcu0xðzÞF
t
x and the force due to
Poiseuille flow is given by Fp ¼ 6phRcycFpx , where F
t
x and
Fpx are the non-dimensional force of Ft and Fp, respectively,
h is the fluid viscosity, and yc is the centre line flow velocity.
Hence, the cell velocity in x direction is: u0xðzÞ ¼
ycFpx=ð%F
t
xÞ. Since yc ¼ 1:5yavg, then
uxðzÞ ¼
1:5Fpx
ð%FtxÞ
(6)
The values of Ftx and F
p
x in the range of
1:1ðRc=WÞ & z & 1% 1:1ðRc=WÞ are obtained from the
previous study (Ganatos et al., 1980b). For the range
ððRc þ dÞ=WÞ & z & 1:1ðRc=WÞ and 1% 1:1ðRc=WÞ & z
& 1% ððRc þ dÞ=WÞ, we again employ the lubrication
theory result to calculate Ftx (Kim and Karrila 1991):
Ftx ¼ %ð8=15Þ ln ð1="Þ þ C2 % ð64=375Þ" lnð1="Þ þ Oð"Þ,
where C2 is obtained from the data given before (Ganatos
et al., 1980b) and Fpx from linear extrapolation of that data
(Ganatos et al., 1980b).
Separation Ratio
Cell fluxes at steady state are computed as the integral of
the velocity and number density over the respective z
coordinates of each phase. The average cell fluxes in the
channel and on the wall are given by:
hFi ¼
R
uxðzÞNcðt; x; zÞ dzR
dz
(7a)
70 Biotechnology and Bioengineering, Vol. 106, No. 1, May 1, 2010

hFwi ¼ uwNwðt; xÞ (7b)
So the cell flux ratio in the feed channel outlet is
FRfeed ¼ hFfeed%outi=hFtotali and the cell flux ratio in the
separation channel and on the wall outlet are
FRsep ¼ hFsep%outi=hFtotali and FRwall ¼ hFw%outi=hFtotali,
respectively, where hFtotali ¼ hFfeed%outiþ hFsep%outiþ
hFw%outi. Moreover, FRfeed þ FRsep þ FRwall ¼ 1 should
be satisfied at steady state. From our experiments, we have
found that owing to cell deposition in the inlet tubing,
the flux ratio is better expressed in terms of the actual cell
count at the outlet. Cell deposition within the micro-
channels is quite low and differences in inlet and outlet
counts are small.
Numerical Simulation
The corner transport upwind method (LeVeque, 2004), a
finite volume method, was used to solve Equation (1). The
spatial domain was divided into grid cells and the estimated
values are modified in each time step by the flux through the
edges of the grid cells. Equation (2) was solved with the
finite difference method (Strikwerda, 1989). Forward
difference was used in time domain and fourth-order
derivatives were used in the x domain. Numerical solutions
were verified with analytical solution for the constant
velocity (ux and uz) case. All computations were carried out
on an Intel(R) Core(TM)2 Duo PC Dell, Round Rock, TX,
running at 2.33 GHz with 3.25 GB of RAM.
Experimental Materials and Methods
Materials
SU-8 50 negative photoresist was bought from Microchem
Corp. Newton, MA(USA). Poly(dimethylsiloxane) (PDMS)
was purchased from Dow Corning (Sylgard 184, Midland,
MI). Folic acid, N-(3-dimethylaminopropyl)-N0-ethylcar-
bodiimide hydrochloride (EDC), N-hydroxysuccinimide
(NHS), triethylamine, dimethyl sulfoxide (DMSO), and
Dulbecco’s modified eagle medium (DMEM) were obtained
from Sigma–Aldrich, St. Louis, MO. Hyclone fetal bovine
serum (FBS) and penicillin–streptomycin were purchased
from Thermo Scientific Waltham, MA, Trypsin–EDTA was
obtained from Biowest Nuaille, (France). Phosphate-
buffered saline (PBS) was from 1st BASE (Singapore).
Human colon carcinoma cells (HT-29) were purchased
from American Type Culture Collection (ATCC, Manassas,
VA). Horse whole blood was obtained from Innovative
Research Inc. Novi, MI. Goat polyclonal antibody, anti-
carcinoembryonic antigen (CEA), was purchased from
Arista Biologicals, Inc. Allentown, PA. NHS-Fluorescein was
purchased from Thermo Fisher Scientific, Inc., Pierce
Rockford, IL. One micrometer (Lot No.: 0509/07) and
200 nm (Lot No.: 2907/08) magnetic beads were purchased
from Chemicell GmbH (Berlin, Germany).
Cell Culture
HT-29 cells (the human colonic adenocarcinoma cells with
diameter of about 15mm) were used in the experiment.
Folate receptors (FR, a-isoform), which are overexpressed
by HT-29 cells (Nonancourt-Didion et al., 2001), can bind
folic acid with high affinity (dissociation constant'0.1 nM)
(Sudimack and Lee, 2000). HT-29 cells were cultured at
378C with 5% CO2 in air, in DMEM medium supplemented
with 10% FBS, and 100 units/mL penicillin–streptomycin.
For subculture, the cells were washed with PBS and
incubated with 0.05% trypsin–EDTA solution for 8min
at 378C to detach the cells. Then, the complete medium was
added to inhibit the effect of trypsin. The cells were washed
by centrifuging and resuspended in complete medium for
reseeding in new culture flasks. HT-29 cells with passage
number between 22 and 25 were used in the experiments.
Red blood cells (RBCs) were isolated from whole horse
blood by centrifugation, stored in PBS at 48C, and used
within a week.
Folic Acid Conjugation to Magnetic Beads
One micrometer (stock¼ 9( 1010/mL) and 200 nm
(stock¼ 1.1( 1013/mL) silica-coated magnetic beads with
amine groups on the surface were used in our experiments.
A fraction of the stock solution (100mL) of beads in de-
ionized (DI) water was added to a mixture of folic acid
(1mL, 20mM) in DMSO, EDC (5mL, 100mM) in DI
water, and NHS (5mL, 15mM) in DI water. Triethylamine
was used as the solubilizing agent for folic acid. The mixture
was incubated on a shaker overnight and washed four
times by centrifuging in PBS. The presence of folic acid
on beads was detected by measuring the absorbance of
product at 288 nm by UV spectrophotometer (Shimadzu
corporation Kyoto, Japan; Wu, 2009). We have quantified
the specific and non-specific binding parameters for 1 mm
beads attaching to HT-29 cells (Wu, 2009) and found
specific binding to dominate in surface-attached cells.
Microchannel Fabrication
The main microchannel and inlet/outlet arms were
fabricated by photolithography and micromolding tech-
nique and had dimensions of 20(L)( 0.208(W)(
0.076(H)mm3 and 10( 0.108( 0.076mm3, respectively.
Themaster was produced by SU-8 50, a negative photoresist.
The photoresist was spin-coated on a silicon wafer and
then pre-baked at 658C for 6min and at 958C for 20min.
The wafer was then exposed to UV light (l¼ 365 nm)
through a transparency mask, then baked at 658C for 1min
and at 958C for 5min, and finally developed by SU-8
developer to remove the unexposed parts of SU-8.
Profiling showed a 76 mm high SU-8 mold. PDMS was
poured onto the master mold and baked in an oven (658C)
for 1 h and then peeled off. Inlet and outlet holes were
Wu et al.: Wall Effects in Magneto-Affinity Cell Separation 71
Biotechnology and Bioengineering

punched to access the microchannels. The PDMS micro-
channel was reversibly sealed against another piece of PDMS
with an adapter.
Cell Separation Experiments
Polyetheretherketone (PEEK) tubingwas used to connect the
microchannel inlets to a syringe pump (KDS Scientific,
Holliston, MA). NdFeB35 permanent magnet (34(
4.8( 1mm3 and Br¼ 12,000G; NEOFLUX
1 Goudsmit
Magnetics Waalre, the Netherlands) was placed at a distance
of 1mm from the microchannel. Folic acid-conjugated
beads were added into the mixture of HT-29 cells (viability
>94%, '1( 105/mL) and horse RBCs in PBS ('1( 106/
mL), and the mixture was incubated on a rotisserie
hybridization rotator (Thermo Scientific LabQuake
Waltham, MA) for 60min (Wu, 2009). The ratios of 1
mm and 200 nm beads to HT-29 cells were 200 and 5,000,
respectively. The cell and bead mixture was injected into the
upper inlet, while PBS buffer was perfused into the lower
inlet simultaneously. For different flow rates, after attain-
ment of steady state, the eluent were collected at the two
outlets in batches of 8 mL volume. Two microliters of 0.4%
trypan blue was added to each eluent batch for the
cell viability test. The number of HT-29 and RBC including
the dead cells were counted on the hemocytometer and
then the yield (estimated separately for each cell type is
FRsepþ FRwall) and the viability of separated HT-29 cells
were estimated. We have also carried out HT-29-specific
antibody (fluorescence-labeled polyclonal anti-CEA) bind-
ing assay to verify the accuracy of our size-based (HT-29
cells are clearly bigger than RBCs) counting method on the
hemocytometer (Wu, 2009).
Cell Rolling Velocity Measurement
The microchannel system was placed under a microscope
with an attached video camera. Videos of cells flowing in the
channel were taken at different pump flow rates. The videos
were divided into frames in Adobe Premiere (Adobe Systems
Incorporated San Jose, CA). From frame-by-frame analysis,
the distance of a specified cell rolling on the wall could be
measured. The time between frames was known, so the cell
rolling velocity for different pump flow rates could be
estimated. On the side walls of the microchannel, the
movement of cells along the wall height (y axis) is not
measurable. However, the errors arising from this are
expected to be small because the channel height is much
smaller than the lengths over which the cells are tracked.
Careful inspection of videomicroscopy images confirm that
the rolling cells are either in contact or very near (<0.5 Rc) to
the wall. Thus, wall contact is not guaranteed, but the positive
deviation from expected shear flow velocities are true as
shown in Figure 5.
Results and Discussion
Our microfluidic magneto-affinity cell separator has two
fluid inlets and outlets, resulting in a two-phase flow of
aqueous fluids as shown schematically in Figure 1. The cell
mixture containing magnetically labeled and unlabelled cells
is perfused continuously into one inlet (feed channel),
while the other inlet carries an aqueous buffer (separation
channel). The permanent magnet placed adjacent to
the microchannel attracts cell–nanobead complexes into
the separation channel for continuous separation, while
unlabelled cells remain confined to the feed phase and exit
the feed outlet.
The mathematical model presented above considers cell
transport with flow along the length of the microchannel or
x-axis, and transverse to flow along the width or z-axis and
along the microchannel wall. The fluid velocity profile is
assumed to be parabolic. This is strictly true if the two-phase
viscosities are closely matched and the aspect ratio (height/
width) of the channel is large (>10). A dilute suspension of
cells flowing in a high aspect ratio channel will experience
hydrodynamic interactions primarily, with the two-plane
parallel bounding walls at z¼ 0 and z¼ 1. Figure 2a illustrates
the change of cell velocity ux as the cell size increases with
respect to the wall spacing or W/2Rc decreases. As stated
above (Theory Section), the velocity is estimated from
translationalmotion (yielding forces) of the cells. This implies
that rotational motion (yielding torques) has been neglected
because of the small contribution as verified by our
calculations (results not shown) and discussed by others
(Nitsche and Roy, 1996).
Hydrodynamic interactions with two walls have a much
stronger influence on the z-directed velocity (uz) of the cells
as shown in Figure 2b. It is observed that forW/2Rc¼ 10, the
velocity is reduced by a minimum of 20% from that when
wall effects are ignored. This reduction in velocity has a
strong effect on the cells that are transported along the wall
as discussed below. It is worthwhile to note that lubrication
theory reveals a singularity upon wall contact, implying that
cells will not accumulate on the wall. This is physically
unrealistic since wall accumulation is well-documented
experimentally (Ahn et al., 1996; Wu 2009). We have
corrected for this by truncating the lubrication theory drag
force at a specified distance d¼W/10,000 from the wall. A
sufficiently small d is chosen to minimize the variation of cell
flux on the wall. Hydrodynamic interactions between cells
are ignored due to dilute cell numbers; that is, experimental
values are fixed to be <1 order of magnitude below
theoretical estimates at which drag changes bymore than 5%
of Stokes drag.
The main non-dimensional parameter arising from
Equations (1) and (2) is a. The parameter a increases
when, inter alia, magnetic force increases, hydrodynamic
drag decreases, channel length increases, fluid flow velocity
decreases, and channel width decreases. Figure 3 shows the
change of flux ratio (FR) in the feed and separation channels
and the wall as a function of parameter a, for W/2Rc¼ 10
72 Biotechnology and Bioengineering, Vol. 106, No. 1, May 1, 2010

and 5. The greatest changes in FR are observed to occur over
a narrow range of parameter a, that is, between roughly 0.2
and 2. The interesting consequence of this is seen in the uz
velocity required to achieve a separation, since L/W) 1 is
typical for microchannels, it follows that uz_c/yavg* 1 or
that a very small z-directed velocity will suffice. Two
additional observations are worth noting from Figure 3.
First, the wall flux does not become appreciable until
the feed channel flux reduces nearly to zero. There exist
distinct values of a ('0.71 for W/2Rc¼ 10) for which the
flux is confined entirely to the separation channel, that
is, FRsep+ 1, while FRfeed and FRwall+ 0. Secondly, as the cell
size increases, the value of a required to attain the same
degree of separation increases. This is because of an increase
in hydrodynamic drag due to wall effect on larger cells.
Figure 4 illustrates the hydrodynamic wall effect for W/
2Rc¼ 10. The neglect of hydrodynamic interactions with the
wall results in substantial overestimation of the cell flux in
the separation channel and the wall. This follows from the
higher uz velocity that arises when wall effects are ignored.
The results presented in Figures 3 and 4 were obtained by
fixing the wall rolling velocity on the basis of fluidic shear
forces only. This means that u0w is the fluid shear velocity
acting on the center of the rolling cells (¼6yavgRc/W).
However, the rolling velocity is also affected by magnetic
forces on the attached beads and other near-wall effects.
We have measured the rolling velocity and compared
it with the theoretical value as shown in Figure 5a and b.
Figure 3. FRfeed (black), FRsep (red), and FRwall (green) as a function of parameter
a, with wall effects for W/2Rc¼ 10 (solid line) and W/2Rc¼ 5 (dashed line). Cell
velocities ux and uz as in Figure 2. [Color figure can be seen in the online version of this
article, available at www.interscience.wiley.com.]
Figure 4. FRfeed (black), FRsep (red), and FRwall (green) as a function of parameter
a when W/2Rc¼ 10. The solid line denotes the wall effect and the dashed line
represents the case of no-wall effect (l¼%1). Cell velocities ux and uz as in Figure 2.
[Color figure can be seen in the online version of this article, available at www.
interscience.wiley.com.]
Figure 2. Cell velocities (a) ux (Eq. 6) and (b) uz (Eq. 5) as a function of z due to
cell-wall hydrodynamic interactions. Black line: W/2Rc¼1 (no-wall effect); red line:
W/2Rc¼ 10; green line: W/2Rc¼ 5; blue line: W/2Rc¼ 3; pink line: W/2Rc¼ 2. [Color
figure can be seen in the online version of this article, available at www.interscience.
wiley.com.]
Wu et al.: Wall Effects in Magneto-Affinity Cell Separation 73
Biotechnology and Bioengineering

Two important observations, which are common to
Figures 5a and b, may be made here. First, at fluid flow
velocities above 0.2 cm/s, the measured rolling velocity is
higher than the theoretical value and the difference increases
with fluid velocity. The higher than expected rolling
velocities are indicative of additional near-wall forces at
higher fluid velocities. Secondly, at low fluid velocity
(<0.2 cm/s), the measured rolling velocity goes to zero faster
than the theoretical velocity. The second observation may be
expected to arise from magnetic forces on the beads, but
other effects such as wall ‘‘stickiness’’ are also possible.
Figures 6a and b presents the results of our separation
experiments involving a mixture of HT-29 and RBCs. The
ratios of HT-29:RBC were 0.1, 0.06 (1mm beads) and
0.17, 0.1 (200 nm beads) based on outlet cell counts. At
residence times (L/yavg) between 2 and 4 s, the 1-mm beads
isolate about 70% of the HT-29 cells, while the 200-nm
beads isolate about 85% of the cells. It is important to note
that viability of the cells was higher (>80%) when contact
time with tubing and other surfaces was reduced. The RBCs
appearing in the separation mixture is <5%. This is most
likely due to the intrinsic magnetic property of RBCs or non-
specific binding of beads. When the residence time is
decreased below 2 s (increased fluid velocity >1 cm/s), the
cell separation ratio is observed to decrease as predicted by
theory (see Fig. 6a and b). Exact quantitative comparison
with theory is not feasible due to the dimensions of our
experimental system where all four walls exert a hydro-
dynamic effect. However, we present a theoretical curve in
Figure 6a and b to provide a qualitative comparison. The
qualitative agreement appears to be good since increased
hydrodynamic wall effects will reduce the separation flux
ratio in the channel and wall.
Figure 5. Cell rolling velocity u0w as a function of average flow velocity yavg: (a)
1mm and (b) 200 nm beads. Red dots are experimental data, and black line is the
theoretical result as given by u0w ¼ ð6Rc=W Þyavg . [Color figure can be seen in the
online version of this article, available at www.interscience.wiley.com.]
Figure 6. Cell separation ratio as a function of average flow velocity yavg. 1mm
(a) and 200 nm (b) beads applied to a mixture of HT-29 and RBCs. Red dots are
experimental separation ratio of HT-29 cells while blue dots are experimental
separation ratio of RBCs. Black line is the model result with wall effects when W/
2Rc¼ 10 and uz_c¼ 0.01169 cm/s. Other parameter values are listed in Table I. [Color
figure can be seen in the online version of this article, available at www.interscience.
wiley.com.]
74 Biotechnology and Bioengineering, Vol. 106, No. 1, May 1, 2010

Conclusion
Affinity targeting of cell surface receptors offers a highly
specific method for separating cells. When the separation is
carried out in microfluidic channels with magnetic beads,
the walls of the channel exert hydrodynamic and other
interaction forces that need to be understood and
incorporated into design calculations. We have illustrated
the effects of hydrodynamic interactions with two bounding
plane parallel walls of the microchannel. It is interesting to
note that conditions may be tuned to minimize contact
with wall surfaces and thereby reduce the possibility of cell
damage. This may be achievable even though any real
separation will involve a range of values of the parameter a.
Experimental data provide evidence of the existence of other
near-wall forces that increase cell rolling velocity beyond
that predicted by fluid shear forces alone. We have
demonstrated a high degree of separation of human colon
carcinoma cells from RBCs. Further improvements
are possible in this separator design that will lead to a
high throughput compact device with many important
applications.
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