6th Micro and Nano Flows Conference
Atlanta,USA, 9-12 September 2018

Particle and Red Blood Cell Concentration Distributions
in Narrow Microchannel Flows with Wall Effects
Kazuya TATSUMI*, Shinnosuke NOGUCHI, Akira TATSUMI, Reiko KURIYAMA, Kazuyoshi NAKABE* Corresponding author: Tel.: +81-75-383-3606; Fax: +81-75-383-3608; Email: tatsumi@me.kyoto-u.ac.jp
Department of Mechanical Engineering and Science, Kyoto University Kyoto, Japan

Keywords: Microchannel Flows, Red Blood Cells, Particles, Collision model, Wall Effects, Number Density
1. Introduction

2. Experimental Methods and Conditions
Figure 1 (a) shows the schematic of the microchannel. Particles andRBCs mixed fluids were supplied to the straight channel inlet by thepressure controlled-type flow pump. The straight channel region
split into three channels by two partitions with edge shaped leadingends. This configuration produced a uniform number density
distribution at the inlet of the center channel in which themeasurement was conducted. The width and height of this area were28m and 27m, respectively. Images of the particles and RBCs
were measured by a microscope and high-speed video camera. The
images were analyzed by ImageJ to obtain the number density
distributions. Figs. 1 (b) and (c) show the examples of the images.
Micro polystyrene particles 5m and 8m in diameters(Microparticles GmbH, PS-R-5.0, PS-R-8.1) were used for particles.
Red blood cells were collected from healthy volunteers. We
rigidized the RBCs by suspending the collected concentrated RBCs
in 0.025% glutaraldehyde mixed phosphate buffered saline solution.
We removed the effects of tank treading motions of the red blood
cells in order to focus on the effects of rotational motions, andcollisions between the cells and wall.
The microchannel and particles were washed by 10wt% bovine
serum albumin (BSA: Sigma-Aldrich, A2153-50G) water solution
to coat the surface and prevent the adhesion and aggregation. The
particles and RBC were respectively mixed with 10wt% BSA
solution and 0.1wt% sodium lauryl sulfate (Nacalai tesque) solution.
Hematocrit (Hct) of the particle and RBC solutions were varied in
the range of 9.2~16.6%. The flow rate was 0.6L/min. Reynolds
number based on the channel height and particle diameter (8m) inthis cases were 0.23 and 5.910-4, respectively.

Reservoir
500m0150mCover glass

1500m

6mm

170m

x28m
27m
28m

yFlow

138m

Diffusion and motions of particle and blood cell in blood flow andparticle-concentrated flows are essential phenomena in the fields ofmedicine, biology and microfluidic systems in terms ofunderstanding the mass and momentum transfer rates at bloodvessels walls, and developing drug delivery systems and lab-on-achip devices. The concentration distribution and mass flux of thesolute and other objects are influenced by the motion and number
density distribution (concentration) of the particle and blood cell in
the flow. Therefore, many studies have been made in this field [1].
However, particles and blood cell concentration distributions andmass transfer for highly concentrated flows in channels withcharacteristic length of several cell, in which the wall effects are
significant, is not known well. In this study, we measured the particle
and red blood cell concentration in microchannel flow and applied
analytical models considering the particle-particle collision, fluid
dynamic force and wall effects.

PDMS(a) Microchannel and measurement area(b) Images of particles(c) Images of RBC

Figure 1. Schematic of the microchannel and recorded images of
8 m particles and red blood cells (the flow is from the left to theright).
3. Results and Discussion
3.1 Particle concentration distribution
Figure 2 shows the number density (concentration)  distributions in
the channel spanwise direction for 5m and 8m particles. The
distributions show the results obtained at the streamwise locations of
̅ is the spanwise average value of In
x=0, 3,000 and 6,000m. ∅the case of Hct=11.7% for 8m particles shown in Fig. 2 (a), auniform profile is observed in the channel center region (y/w0) at
̅ in this region increases in the downstream and
x=0m. ∅/∅converges to a distribution showing maximum peaks at the channelcenter and channel walls. This trend is also observed in Fig. 2 (b) forthe case of Hct=16.6%. In the case of 5m diameter particles, similar
distribution and characteristics are also obtained while a third peak
additionally appears in the middle of the two peaks at y/w0.25.
To understand the factors producing these distributions, onedimensional computation solving the particle concentrationconservation equation shown in Eq. (1) and employing the model
considering the particle-particle collision, fluid dynamic force andwall effects was conducted. The first term in Eq. (1) is the convection
term for the streamwise direction. vc and vf in the second term are thevelocity (flux) attributed to the particle-particle collisions [1, 2] andfluid dynamic force exerted on the particles.
𝑢p𝜕𝜙𝜕𝑥+𝜕𝜕𝑦((𝑣c + 𝑣f )𝜙) = 0(1)vc is based on the collision rate and displacement of the particle oncethe collision occurs and is obtained by Eq. (2).

6th Micro and Nano Flows Conference
Atlanta,USA, 9-12 September 2018
55x=0mx=3,000m
x=6,000m

33x=0mx=3,000m
x=6,000m

4
32

211

Red blood cells (Hct = 10%)
Particle (d = 8 m, Hct = 11.7%)
Particle (d = 5 m, Hct = 9.2%)

2/

410-0.50-0.25

0.00

0.25

00.50 -0.50-0.25y/w

50.25

0.50

y/w

(a) d=8m Hct=11.7%
MeasurementModel00.0(b) d=8m Hct=16.6%
x = 0 mx = 3000 mx = 6000 m
model

4

3

3

2

2

1

1

0.1

0.2

0.3

0.4

0.5y/w

54

0.00(a) Comparison with particle distributions
4
without R and vw
with R

3

with R and vw

-0.25

0.00

y/w

0.25

00.50 -0.50(c) d=8m Hct=11.7%

-0.25

0.00

0.25

/experiment

0-0.500.50

y/w(d) d=5m Hct=9.2%

21

Figure 2. Particle number density (concentration) distributionsin the channel spanwise direction.

00.0

0.1

0.2

0.3

0.4

0.5

y/w𝑣c (𝑦) =𝑑𝐾 ∫−𝑑 𝑙(𝑦, 𝑠) ∙ 𝜙(𝑦 + 𝑠) ∙ |𝑢(𝑦 + 𝑠) − 𝑢(𝑦)| ∙ 2√𝑑2 − 𝑠 2 𝑑𝑠(b) Comparison with model(2)

l is the displacement of particles when colliding with neighboring
particles. y is the spanwise location of the particle of interest and s isthe distance from the center of this particle. The collision rate is
proportional to  and the velocity difference with the colliding
particles.
Lift force exerted on the particle was referred to the analytical results[3] and was applied to the Stokes equation to derive the resulting
particle velocity vf. Further, we considered the wall effect byconsidering the distance between the particle and wall in the
integration region of Eq. (2) and displacement l.
Fig. 2 (c) shows the computational results. The model correctly
presents the maximum peaks at the channel center and near wallregions. Furthermore, the distribution agrees reasonably well withthe measurement. The increase of  observed at the channel center
was attributed to the parabolic velocity profile of the Poiseuille flowin which the shear rate decreases toward the channel center. On theother hand, the modification of the asymmetric distribution of thecollision rate on both sides of the particles due to the wall effectproduces the peaks at the wall.
In the case of 5m diameter particle, the model presents the third
peak at the same position with reasonable accuracy. This third peak
was attributed to the high concentration of particles flowing along
the channel wall. As the particles are packed at the wall surface, thesecond layer of particles is formed with distance of one particle
diameter from the wall.
3.2 Red blood cell concentration distribution
Concentration  distribution of the RBCs is shown in Fig. 3 for thehalf-side of the channel. Compared to the 8m diameter particle
distribution, the maximum peak observed at the channel sidewall
decreases and a third peak appears at the location of approximately
y/w=0.3. The rotating motion of the RBC is believed to be the main
factor for these characteristics. The “tumbling” motion of RBC
increases the collision rate between the RBCs and with the wallcompared with the RBC in steady state. Larger displacement andspanwise velocity for the RBC is produced in this case especially inFigure 3. RBC number density distributions in the spanwise
direction (Hct=10%).
the near wall region.
We applied this effect to the model by modifying the collision rateand adding another spanwise velocity (flux) vR to the second term ofEq. (1). Collision rate was modified by a weighting factor R which
was based on the distance s. vR was defined as 𝑣𝑅 = 𝐾𝑅 𝑙𝑅 γ̇ wherelR and γ̇ are the displacement due to collision in the RBC case andthe flow shear rate, respectively.
The computational result is shown in Fig. 3 (b). The third peak is
produced by the model and the distribution matches well with themeasurement particularly when R and vw are both applied to themodel. The peak observed in the near wall region slightly decreases
compared with the particle case. Further modification, threrefore, isstill required for the parameters in the model to produce larger wall
effects. Nevertheless, we can obtain the fundamental characteristicsof the  distribution and may derive the conclusion that the smaller
effective length of the RBC and the collision of the RBC with thewall due to the RBC rotation decreases the concentration at wall andproduces a third peak in the concentration distribution.
4. Conclusions
We measured and calculated the particle and RBC concentration
distributions for flow in channel with narrow width and showed thatthe particle size, Hct, and the shape and motion of the RBC affectthe distributions. The wall effect was significant and the wall
function model we showed agreed reasonably well with themeasurement. Further study on varying the conditions, considering
the deformation and tank treading motion of the RBC, and applying
the volumetric concentration to the model is required as future work.
References[1] X. Grandchamp et al., Physical Review Letters, (2013) Vol. 110, 108101.
[2] D. Leighton and A. Acrivos, J. Fluid Mech, (1987) Vol. 181, pp. 415-439.
[3] R. J. Phillips, R. C. Armstrong, R. A. Brown, A. L. Graham and J. R.
Abbott, Physics of Fluids, (1991) Vol. 4, pp. 30-40.
[4] B. P. Ho and L. G. Leal, J. Fluid Mech, (1974) Vol. 65, pp. 365-400.