Extended Abstracts of The Second Pacific Rim Thermal Engineering Conference
December 13-17, 2019, Maui, Hawaii, USA

PRTEC- 24152

TIMING CONTROL AND ALIGNMENT OF PARTICLES IN
MICROCHANNEL FLOW USING DIELECTROPHORETIC FORCES
Kazuya Tatsumi, Atasushi Noma, Renato Honma, Reiko Kuriyama, Kazuyoshi Nakabe
Department of Mechanical Engineering and Science, Kyoto University, Japan

ABSTRACTControlling the timing, interval (spacing), and velocity of the particles and cells in microchannel flows has
been an important issue to develop a high-throughput system in microfluidic devices for sensing, sorting, andencapsulating. We developed a technique that can control the timing of particles crossing a certain location in
the microchannel, interval between each particle, and particle velocity for particles flowing in the microchannel
by exerting forces on the particles in periodic form over time and space. In this study, we use the boxcar-type
electrodes to generate the dielectrophoretic (DEP) force and control the timing of the particles and align themin the streamwise direction. Analysis based on the perturbation theory is introduced to investigate theconvergence of the particle motion to the equilibrium state for the present method. We measure the particle
motion in the boxcar-electrode region in the microchannel flow, and present the probability density functionof the spacing (interval), velocity, and timing in relation to the applied voltage signal. The distribution
demonstrates the performance of the alignment and timing control in which the variation to the target value
falls in the range of several percent.

KEYWORDS: Microchannel flow, Particles, Position control, Timing control, Alignment, Focusing, Convection
1. INTRODUCTION
Controlling the position, interval (spacing), velocity, and timing of particles and cells in microchannel flows
is one of the important techniques in microfluidic devices to develop a high-throughput sensing, sorting, andencapsulation systems for lab-on-a-chip and micro-total-analysis-systems. [1-2] Particles and cells mixed in
fluids are supplied to the channel with the position randomly dispersed. The position of the particles and cells
should be controlled to make them locate at the specific position in the channel cross-section where the sensors
and sorters can perform effectively and accurately. This is called focusing of the particle and cells in the
microchannel flow. Further, the spacing between the particles and cells should sufficiently be taken as several
particles and cells located in the same region will incur measurement and sorting errors. Controlling thestreamwise distance (interval) between the particles and cells with equal spacing (alignment) and knowing thetiming when it will cross the sensor and sorting region will allow better calibration of the sensors and sorters
which will result in higher accuracy. In addition to this, the alignment and timing control will also contributesignificantly to the encapsulation technique. Microfluidic encapsulation generates micro-droplets sequentiallyin the channel and encapsulate the particles, cells, and chemical components in them. [3,4] The particles andcell should be delivered and injected to the droplets at the timing of the droplet generation with the precise
number required. In the case of particles and cells supplied randomly in the channel, droplets with undesired
number of particles and cells encapsulated are generated. Controlling the interval and timing, therefore, canmarkedly reduce the errors. From this background, controlling the timing and spacing of the particles and cells
has been an essential problem and yet is a challenging issue to be solved. [5-8]In this study, we developed a technique that can control the particle interval (spacing), velocity and the exact
timing of particles crossing a certain location in the channel by applying dielectrophoretic (DEP) force to the*Corresponding Author: tatsumi@me.kyoto-u.ac.jp
Copyright © 2019 by The Author(s). Distributed by JSME, KSME, and ASTFE with permission.

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Fig. 1 Schematic of the microfluidic device and the boxcar-electrodes, and the concept of the particlealignment and timing control by applying periodic force to the particles over space and time.
particles periodically with time and space. We designed the boxcar-type electrodes to produce regions of DEP
force in which particles are accelerate and decelerate periodically in the streamwise direction. The schematicof the boxcar-electrodes and the concept of the particle alignment and timing control are shown in Fig. 1.
Compared to the ladder-type electrodes previously presented by the authors, [7,8] the boxcar- electrode cancontrol the motion of the particles distributed over a wider area in the channel cross-section. It also requires
less complicated process for fabrication. In this presentation, the principle of the alignment, velocity control,
and the timing control of the particles is first examined based on the perturbation theory. We will thendemonstrate the performance of the present technique using the boxcar- electrode by measuring the particle
motion in the microchannel flow, and showing the probability density function of the deviation of the particle
interval, velocity, and timing from the target value.

2. PRINCIPLE OF THE PARTICLE ALIGNMENT
To discuss the particle motion characteristic and its convergence to the equilibrium state in simplified form,
we will consider a one-dimensional problem of the force distribution and particle motion. As shown in Fig. 2,
the force exerted on the particle decreases linearly from positive to negative in the streamwise direction for
one periodic region. The force is activated periodically for a certain period of –0 x 0. We will start fromthe equilibrium position at which zero work will be made on the particle during one periodic cycle. We now
assume that the phase of the particle against the equilibrium position is perturbed. In this case, the work applied
to the particle during this cycle WDEP can be written as Eq. (1), where  and (i) (i=1, 2, 3 ) are theperturbation coefficient and high order terms for the order of i.
𝑊DEP = 𝑊𝐷𝐸𝑃,0 +

𝜕𝑊𝐷𝐸𝑃
𝜕𝑊
𝑑𝜃 = 𝑊𝐷𝐸𝑃,0 + 𝐷𝐸𝑃 (𝜀𝜃 (1) + 𝜀 2 𝜃 (2) + ⋯ )𝜕𝜃𝜕𝜃= 𝑊𝐷𝐸𝑃,0 − 2𝜃0 𝜃 (1) 𝜀 − 2𝜃0 𝜃 (2) 𝜀 2 + ⋯(1)

WDEP,0 is zero and if we consider only the first order correction term, WDEP is written as Eq. (2).
𝑊DEP ≅ −2𝜃0 𝜃’(2)

We then consider the particle kinetic energy U. Having 𝑢̂p,0 be the particle average velocity in one periodic
region at equilibrium state, U can be expressed as Eq. (3) with the perturbation series.

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Fig. 2 Schematic of the force distribution and the force exerted on the particle when phase deviates fromthe equilibrium state described in a one-dimensional model.
1
𝜕𝑈
1 𝜕2𝑈
1
(1)
(2)
2
2
𝑈 = 𝑚𝑢̂𝑝,0+| 𝑢̂𝑝 +| 𝑑𝑢̂𝑝 2 + ⋯ = 𝑚𝑢̂𝑝,0+ 𝑚𝑢̂𝑝,0 (𝜀𝑢̂𝑝 + 𝜀 2 𝑢̂𝑝 + ⋯ )22𝜕𝑢̂𝑝 02 𝜕𝑢̂𝑝
2
0

1
2

(1)

(2)

2

+ 𝑚 (𝜀𝑢̂𝑝 + 𝜀 2 𝑢̂𝑝 + ⋯ )(3)Therefore, deviation from the equilibrium state U can be written as ∆𝑈 ≅ m𝑢̂𝑝 𝑢̂𝑝 ′, where 𝑢̂𝑝 ′ is thedeviation from the velocity of equilibrium state 𝑢̂𝑝,0 . m is the mass of the particle.
We then define the variation of 𝑢̂𝑝 ′ in one periodic region as 𝑑𝑢̂𝑝 ′. The variation of U due to this change,
which is defined here as dU, can be expressed as d𝑈 ≅ 𝑚𝑢̂𝑝 𝑑𝑢̂𝑝 ′.
As dU should be equal to WDEP, the following relationship can be derived.
2𝜃 𝜃′0𝑑𝑢̂𝑝 ′ = − 𝑚𝑢
̂

0

(4)

We will now define the variation of ’ in one periodic region as ’. ’ can be approximated as ∆𝜃′ ≅ 𝑢̂𝑝 ′∆𝑡,where t is the period of one cycle. If one periodic length is negligibly small compared with the total lengthof the region of interest, this can be rewritten as 𝑢̂𝑝 ′ = −𝑑𝜃 ′ /𝑑𝑡. Substituting this relationship in Eq. (5), thedeferential equation shown as Eq. (7) can be derived.
𝑑 2 𝜃′
2𝜃
= − 𝑚𝑢̂ 0 𝜃′
𝑑𝑡 2
p,0

(5)

This gives us an oscillatory solution for  ’. As the particle will receive the drag force from the fluid, thedamping term should be added to Eq. (5) which naturally gives us a solution converging to ’=0. This formula,which holds for –0< x <0, is based on the condition that the flow velocity is equal to the controlled particle
velocity 𝑢̂𝑝 ∗ = 𝐿pitch 𝑓on−off . However, this discussion can be applied also for flow velocity different from𝑢̂𝑝 ∗. In this case, the equilibrium position will move in the positive or negative direction to apply additional
work on the particle so that the particle will match 𝑢̂𝑝 ∗ = 𝐿pitch 𝑓on−off.
We can control the time interval between the particles and the particle velocity by changing 𝑓on−off. The timerequired for the particle to move one periodic unit 𝐿pitch /𝑢̂𝑝 should be same with the on-off cycle 1/𝑓on−off .
This leads to the fact that 𝑢̂𝑝 will be 𝐿pitch 𝑓on−off and can be changed by controlling 𝑓on−off.

3. MEASUREMENT METHODS
Boxcar-type electrodes was patterned on the channel bottom wall as shown in Fig. 1. The ground electrode
was attached to the top wall covering the whole area of the top wall. The distance between parallel electrodes
was 60 m and the pitch of the crosstie electrodes was 50 m. The top and bottom walls were glass substrates
on which the Pt electrodes were patterned. The layer between these substrates composing the microchannel
wall was made of SU-8 (Microchem, Su-8 3050), and was fabricated through soft lithography process.

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Table 1 Measurement conditions.
Vp-p (V)20

fon-of (Hz)125fV (Hz)10M

Um (mm/s)
7.74

Re
0.54

0.6

0.6

0.5

0.5

0.4

0.4

P(p/ton-off)P(p/ton-off)Fig. 3 Snapshots of the particles at the inlet and outlet of the boxcar-electrode.

0.3
0.2

0.2
0.1

0.1
0.0
0.00

0.3

0.25

0.50

0.75

1.00

0.0
0.00

0.25

p/ton-off

0.50

0.75

1.00

p/ton-off

Fig. 4 Probability density function for time difference between particles located at the middle of the boxcarelectrode region and the signal rise of the applied voltage: measured at inlet (left) and outlet (right).
The channel height is 42 m and width is 200 m at the boxcar-electrode region. Fluid was supplied to theinlets of the channel by a pump driven by pressurized air. Particles flowing from the center channel werefocused and guided to the inlet of the boxcar-electrode region by rail-type electrodes, which were placed in
the upstream of the boxcar-electrode region. The details of the structure and function of the microchannel flow
and rail-electrode are presented in the authors’ previous works [7,8].
Polystyrene micro particles of 12m diameters (Thermoscientific Co., 4212A) were used. The working fluid
was water (Milli-Q water) to which sodium lauryl sulfate (SLS) was mixed with 0.1wt%. The motion of theparticles was recorded by a high speed video camera and microscope. The frame rate and resolution of themeasurement were 10,000fps and 0.88m, respectively. We applied alternate current voltage to the electrodeusing a function generator with peak-to-peak voltage of Vp-p=20V and frequency of fV=10MHz. This voltage
was turned on and off periodically with frequency of fon-off=125Hz. The particle position and velocity in thechannel was obtained from the series of images by motion analysis software (Library Co. Ltd., Move-tr/2Dver. 7.90). Table 1 shows the representative experimental conditions. The characteristic length and velocity of
the Reynolds number are the channel hydraulic diameter and the cross-sectional average velocity.

4. RESULTS AND DISCUSSION
Figure 3 shows the snapshots of the particles flowing over the boxcar-electrode at the inlet and outlet regions,
respectively. In Fig. 3 (a), the particles are entering the region with random spacing, and some particles form
groups (clusters) having the spanwise position not fully focused. On the other hand, in Fig. 3 (b), clusters are
not observed and the particles are focused at the centerline accurately. Moreover, the particles are equally
spaced in the streamwise direction with distance equal to the pitch of the boxcar-electrodes, Lpitch, or its
multiples. Although not shown here but will in the presentation, the probability density function of the interval
between the particles showed a peak distribution with 95% confidence interval falling inside the range of1.9% of ton-off =1/fon-off. Furthermore, the probability density function of the particle velocity showed amaximum peak at the value equal to Lpitchfon-off , and the deviation was 2.6% with the 95% confidence interval.

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The relative position to the traverse electrodes are the same for all particles shown in Fig. 3 (b). This
characteristics having identical relative position to the electrode was same for other time (phases). This implies
that if the particle motion and the voltage signal applied to the electrode are synchronized, we can predict andcontrol the timing of the particles passing a specific streamwise positon from/with the voltage signal. To
evaluate the capability of the timing control using the present technique, we measured the particle motion withsynchronizing the camera recording with the voltage signal. The time difference between the signal rise of thevoltage and the time when the particles crosses the middle of the boxcar-electrode region (x/Lpitch=0.5) isdefined as p [s]. The probability density function (PDF) of p/ton-off is shown in Fig. 4. At the inlet of theboxcar-electrode, the PDF of p/ton-off shows a uniform distribution indicating that the timing in relation to theapplied voltage is random. On the other hand, the PDF of p/ton-off shows a maximum peak at p/ton-off =0.46
with the 95% confidence interval falling inside the range of 2.5%. This represents the fact that we can predict
the exact timing when the particle passes a certain position from the applied voltage signal within this accuracy.
Further, if a specific timing is required for the particles, e.g. the timing when the particle should cross thesensor region or enter the droplet, we can match the timing by adjusting the phase of the voltage signal.
As mentioned previously, the PDF of the time interval and velocity will be discussed in the presentation.
Further, the relationship between the phase deviation from the equilibrium state and the particle velocity ismeasured and will be shown to verify the analytical results and evaluate the particle motion characteristics:
how the force is exerted on the particles and how the particles move as they converge to the equilibrium state.

5. CONCLUSIONSTiming, interval (spacing), and velocity of the particles flowing in the microchannel was controlled by exerting
dielectrophoretic forces on the particles in periodic form over space and time using boxcar-type electrodes.
The analytical results showed that the present method can control the particle position to the equilibrium
positon at which the interval (spacing) and the velocity of particles are equal to the cycle (pitch) of theperiodicity 1/fon-off (Lpitch) and Lpitchfon-off. The measured probability density distribution for the deviation of thetiming, spacing (interval), and velocity from the target value showed that the values can be controlled within
the accuracy of 2.5%, 1.9%, and 2.6%, respectively. Although not shown here but will in the presentation,
the numerical results and the measurement for the phase deviation from the equilibrium state of the particles
showed that the particles with larger/smaller spacing (interval) or velocity compared with the target value will
give a phase shift leading to additional acceleration and deceleration of the particle motion. This agreed wellwith the analytical results.

ACKNOWLEDGMENTS
This work was supported by the Japan Society for the Promotion of Science KAKENHI Grant Number 17K18841, and partially byMicro/Nano Fabrication Hub in Kyoto University of "Low-Carbon Research Network" funded by the Ministry of Education, Culture,
Sports, Science and Technology (MEXT), Japan.

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