The influences of tracking nano-particles on micro/nano flow
visualization
Zhan-Hua Silber-Li, Xu Zheng, Xu-Wei Wang
State Key Laboratory of Nonlinear Mechanics (LNM), Institute of Mechanics,
Chinese Academy of Sciences, Beijing 100190, China
Corresponding author Zhan-Hua Silber-Li, lili@imech.ac.cn
Abstract
Two experiments presented in this talk show the influences of tracer particles sizes and numbers
on measurements of micro scale flows. One is about the velocity profile measurement near the wall of
a micro-channel by Micro-PTV. Based on the experiments with 200nm and 50nm particles, we
noticed that the particle sizes, concentration distributions and focal plane thickness in shear flow field
results in a large velocity near wall (0.25m<z<1.5m). In another experiment about Brownian
motion of 200nm particles, we found that, the number of particles used for statistic analyses should
be verified related with the dispersity of particle’s diameters.
Keywords: nano-particles, MicroPIV/PTV, Brownian motion, concentration
1. Introduction
MicroPIV/PTV was developed by Santiago et al. [1] (1998) and Meinhart et al. [2] (1999) 10 years
ago. Recently, some experiments found large measured velocities near the solid boundary.
Devasenathipathy et al.[3] (2003) measured the velocity profile at the central plane upon glass substrate
in a rectangular microchannel. They found the measured velocity was approximately 10% larger than
the theoretical value near wall. Joseph and Tabeling [4] (2005) measured the velocity directly at a
hydrophilic wall in a microchannel using 200 nm particles. But they found that the measured velocities
for z<1m were noticeably larger than the expected theoretical no-slip values for a hydrophilic glass
wall. Zheng and Silber-Li [5] (2008) also measured velocity profiles in 14 horizontal planes of a
rectangular microchannel. The measured velocities in the main flow region were in good agreement
with the theoretical no-slip velocity profile, however, the measured velocities for 0.5<z<1m were
approximately 18% larger than the theoretical no-slip velocity profile. Therefore, the detail velocity
measurements with different sizes tracers are performed at 0.25m<z<1.5m from wall.
Another part of this talk concerns the Brownian motion of nano-particles with MPT (multi-particle
tracking) [6]. Firstly, it's difficult to record particles with long trajectories because nano-particles often
move out of the thin focal plane. To obtain a reliable measurement, an evaluation of the lowest
trajectory length is required. Secondly, the diameters of nano-particles are usually not uniform. The
standard variance of 200nm particles is 5%, while that of 50nm particles can reach to 15%. It is
necessary to know how many particles should be tracked to measure the mean square displacement
correctly.
2. Experimental apparatus and methods
(1) Measurement of velocity profiles
The experiments were carried out on a microPIV/PTV system at the LNM, Institute of Mechanics,
CAS [5]. It consisted of a fluorescent inverted microscope (Olympus IX71) with a 100× oil immersed
objective (numerical aperture NA=1.35), a 1004×1002 pixel 14 bit EMCCD (Andor DV885) and a
nano-scale vertical adjustment instrument with a piezo-transducer (Physik Instrument LVPZT E665).
A mercury lamp was used as the light source.
10th Asian Symposium on Visualization, KLCE, INDIA, 2009.
1
50 nm and 200 nm fluorescent polystyrene particles (Duke Scientific Corporation) were used
as tracers in the experiments. The exciting/emitted waves were 530nm/600610nm. The volume
concentrations of the fluorescent particles were 310-5 510-5.
In the velocity profile measurement, the PDMS-glass hybrid microchannels (19.10.1 m in
height, 56.00.2 m in width and 28.000.02 mm in length) were used.
A PTV method was employed. The exposure time t varied from 5ms to 25ms. At least 200
images were recorded at each measurement position. A threshold of the grey-scale value was chosen
to filter out the out-of-plane particles. This threshold value was set as 80% of the maximum grey-scale
value in the images. More than 2000 vectors were obtained from 200250 frames at each horizontal
position.
(2) Brownian motion measurement of particles
For the measurement of Brownian motion, a droplet of solution was put onto a coverslip. The
droplet volume was about 50µL. The focal plane was adjusted to 10µm away from the top surface of
the coverslip. The image series were acquired at 50 different positions in the same horizontal plane. At
each position, 200 frames of image were acquired with an exposure time of 10ms.
In MPT method, the diffusion coefficient is evaluated following Einstein equation,
r 2  4 Dt
(1)
where r is the mean square displacement during interval time Δt. Then the diffusion coefficient of
the same particle j for K steps of trajectory is calculated based on equation (1)
2
Dj =
1 K
1 K
2

r

(xi2 + yi2 )
 i K 4t 
K 4t i=1
i=1
(2)
On the other hand, the average diffusion coefficient obtained from N particles is
Dexp =
1 N
 Dj
N j=1
(3)
3. Experimental results
3.1 Measurement of velocity profiles
(1)Velocity measurement near wall
The horizontal velocity measurements (in x-y planes) using 200nm particles were performed at five
positions (z+=1.25, 2.5, 3.75, 5.0 and 7.5), under three different driven pressures (p=0.8kPa, 1.6kPa
and 2.4kPa). The Reynolds numbers Re=0.04–0.13 based on the hydrodynamic diameter of the
channel. The non-dimensionalized vertical velocity u+=u/Umax measured at y=0 for each value of z+ are
selected to plot the velocity profiles near the wall (Fig. 1a), where Umax is the theoretical maximum
velocity in the channel. The experimental velocity data are compared with the 3D theoretical no-slip
velocity profiles:
4h 2 p
u x ( y, z )  3
 L
y
cosh( n )
1
z
h
[1 
]sin( n )

3
w
n
h
n 1,3,5...
cosh( n
)
2h
(4)

where h is the height of the channel, L is the length of the channel. The average relative deviation
between experimental data and the theoretical values is defined as:
u
)
1 n (u
(5)
   exp,n theo,n
n n 1
utheo ,n
n is the number of data in a profile. At the highest distance from the wall z+ =7.5,  1.7%. However,
for the closest location z+ =1.25,  93.1%.
10th Asian Symposium on Visualization, KLCE, INDIA, 2009.
2
Fig. 1. A comparison of the dimensionless measured data (crosses with error bars), the predicted
velocity (dash line) and the theoretical velocity profile (solid line) in x-o-z plane using 200nm (a) and
50nm particles (b). The measured data were obtained under driven pressures 0.8, 1.6 and 2.4kPa.
For the 50nm particles, the measurement conditions were the same as for the 200nm particles.
The distances from the wall were z+=5, 10, 15, 20 and 30. The relative deviation  =-0.7% at z+=30,
but at z+=5,  =45.8% (Fig 1b). It means that the measured velocity value decreases when smaller
particles used. It is clear that while measurements for z+>10 agree well with theory, but the values of
the measured velocities at z+<10 are significantly larger than the theoretical values.
(2) The particle concentration distributions
In the experiments, we also observed that the particle concentrations are not uniform near wall.
The particle concentration distribution could be obtained by counting the number of particles at each z
location (Fig 2). Approximately 3000 particles were counted from a series of 250 images at each plane.
A dimensionless form of the particle concentration distribution can be expressed by [7]:

c  ( z  )  n( z )

n0
 a1 (e a2 z  1)
(6)
where c+ is the dimensionless particle concentration, n(z+) is the particle number count at position z+,
n0 is the uniform concentration in the main flow region, a1 and a2 are constants determined by fitting.
For 200nm particles, the fitting curve with 95% confidence is (Fig. 2a):

c ( z  )  1.13(e0.3874 z 1)
(7)
For 50 nm particles, the fitting result is (Fig 2b):

c ( z  )  1.03(e0.3071z 1)
(8)
Fig. 2. The dimensionless concentration distributions c+(z) and the fitting curves along the vertical
direction for 200nm particles (a) and 50 nm particles (b).
(3) Predicted velocity profile
Here, we will analyze the reason of velocity deviation near wall. The “effective focus plane
thickness” z is evaluated to be approximately 400nm. The measured velocity u( z ) at a focus plane
0
z=z0 is actually a spatial average over the effective focus plane thickness z. Taking account of the
particle concentration distribution, a predicted average velocity u '( z0 ) can be expressed as[8]:
10th Asian Symposium on Visualization, KLCE, INDIA, 2009.
3
u '( z0 ) 

z0 z / 2
u ( z )c( z )dz
z0 z / 2
z0 z / 2

z0 z / 2
(9)
c( z )dz
where u(z) and c(z) are the distribution functions of the theoretical velocity and the measured
particle concentration respectively. The theoretical velocity Eq.4 is used as u(z), and Eq.7 or Eq.8 as
c(z) for 200nm or 50nm particles, respectively. Eq.9 shows clearly that the deviation in u '( z0 ) strongly
depends on the particle radius (due to c(z)) and the effective focus plane thickness z.
The average relative deviation  between the measured data and the predicted values
u '( z0 )
for
50nm particles at z=0.25m becomes 10.1% instead of 45.8%. Thus, for microPTV measurements
near a hydrophilic wall, biased velocity data will appear due to the non-uniform particle concentration
in the effective focus plane thickness.
3.2 Brownian motion measurement
(1) Trajectory length K
Based on K-step trajectories of one particle, the experimental diffusion coefficient Dj can be
calculated by Eq.2. Fig 3(a) shows the diffusion coefficient Dj as a function of K for a typical particle.
The average diffusion coefficient with total 140 step displacements is noted as the solid line. It shows
that the deviation of K-step diffusion coefficient from its average value is larger than 5% for K<45 and
the deviation limits between 5% for K>45. Then we define Kcr=45 as the critical trajectory length for
the particle. In view of analyses with more than 200 different particles, the probability density
distribution of Kcr is presented in Fig 3(b). For most of the particles with K > Kcr = 70, the deviation of
K-step diffusion coefficient from its expectation value is less than 5%.
Fig. 3. Diffusion coefficient of one particle versus its frames number K(a) and distribution of Kcr (b)
(2) Particle Number N
Generally, the dispersities of nano-particles are larger for smaller particles. The reliability of the
experimental diffusion coefficient depends on how many particles are tracked. In our experiment,
4000 particles were tracked. Fig 4 implies the relation between the measured diffusion coefficient Dexp
and particle number N, where the solid line is the global average for all particles and the dash-line is
its 2% deviation. It shows that the deviation of Dexp from its global average is less than 2% when
1600 particles are tracked. The experiment was repeated and similar results were obtained.
Fig. 4 The relation of diffusion coefficient versus particle’s number
10th Asian Symposium on Visualization, KLCE, INDIA, 2009.
4
4. Conclusions
The measurement of velocities near wall demonstrated that the particle sizes can significantly
influence near wall velocity measurement with microPIV/PTV, due to the biased particle
concentration distribution and the effective focal plane thickness.
The Brownian motion measurement shows the sample particle’s number and recorded image
number should be verified, considering the deviation of the particle’s diameters.
Acknowledgments
The authors gratefully thank the support by the NNSFC (10672172, 10872203), NBRP (2007CB714501) and HTRDPC (2007AA04Z302).
References
[1] Santiago JG, Wereley ST, Meinhart CD, Beebe DJ and Adrian RJ. (1998) A particle image velocimetry system for
microfluidics. Experiments in Fluids. 25, 316-319.
[2] Meinhart CD, Wereley ST and Santiago JG. (1999) PIV measurements of a microchannel flow. Experiments in Fluids.
25, 414-419.
[3] Devasenathipathy S, Santiago JG, Wereley ST, Meinhart CD, Takehara K. (2003) Particle imaging techniques for
microfabricated fluidic systems. Experiments in Fluids. 34, 504-514.
[4] Joseph P & Tabeling P. (2005) Direct measurement of the apparent slip length. Physical Review E. 71, 035303.
[5] Zheng X, Silber-Li ZH (2008) Measurement of velocity profiles in a rectangular microchannel with aspect ratio =0.35.
Experiments in Fluids. 44, 951-959.
[6] Olsen MG and Adrian RJ. (2000) Out-of-focus effects on particle image visibility and correlation in microPIV.
Experiments in Fluids. 29(7), S166-S174.
[7] Hartman Kok PJA, Kazarian SG, Briscoe BJ, Lawrence CJ. (2004) Effects of particle size on near-wall depletion in
mono-dispersed colloidal suspensions. J Colloid and Interface Science 280, 511-517.
[8] Zheng X, Silber-Li ZH (2009) The influence of Saffman lift force on nanoparticle concentration distribution, Applied
Physics Letter, 95, 124105
10th Asian Symposium on Visualization, KLCE, INDIA, 2009.
3