Measuring the Effectiveness of Three Dimensional
Deterministic Lateral Displacement in Low
Viscosity Liquids
Brandon Gomes
[email protected]
Sophie Slutzky
[email protected]
Kaley Ubellacker
[email protected]
Jackson Weaver
[email protected]
Sharon Zhang
[email protected]
New Jersey Governor’s School of Engineering and Technology 2016
July 21, 2016
Abstract
by analyzing particle motion in a different
fluid, namely, water. Analyzing disparities
between the data sets revealed the effects on
particle motion through a fluid with a high
Reynolds number, as well as how the separation mechanics of the passing fluid were
altered according to 3D DLD.
With more research, three dimensional deterministic lateral displacement
(3D DLD) has the potential to greatly improve the efficacy and flexibility of microfluidic devices for separation within various fields of science, notably microbiology.
As a particle passes through a set array of
obstacles submerged in liquid, its type of
motion varies according to its specific properties. Utilizing the differing movements,
3D DLD can be used to separate various
particles according to size, deformability,
and other properties. The project focuses
on testing the competence of 3D DLD systems in a low viscosity liquid. Similar to the
data collecting and data processing procedure used in a previous 3D DLD experiment
utilizing corn oil, this was accomplished
Analysis of the experimental data revealed important notes regarding particle
sorting in lower viscosity fluids, many of
which directly correlate with similar corn
oil results. Studies in two planes of motion revealed distinct points for particle separation regardless of the type of motion,
and further comparisons of forcing, critical,
and migration angles demonstrated sophisticated relationships that are especially useful in particle separation. A prominent issue with the trials included the formation
of rust, requiring the addition of vinegar
1
to counter and forestall the effects. Ultimately, the research supported the increased
efficiency and accuracy of 3D DLD mechanisms but demonstrated that water is much
less consistent in comparison to corn oil as
a separating fluid.
1
1.1
lated to a microscopic set-up to function in
the same way based on larger scale research.
Another goal of this experiment is to
compare the results of 3D DLD when used
with water, a low viscosity liquid, with the
results obtained using corn oil, a much more
viscous liquid. Due to water’s low viscosity, the system has a higher Reynolds number, and the driving force, specifically gravity, has a much more significant effect on the
movement of the particles.
Introduction
Goals
The study focuses on the effectiveness
of a 3D DLD system in separating particles
based on size. 3D DLD is an expansion
of two dimensional deterministic lateral displacement (2D DLD), a separation method
used in microfluidics. 2D DLD is often used
in binary separation, where it creates two
different streams of distinct particles, often
separating them by size, shape, texture, or
material. However, because of the planar
motion of particles within a 2D DLD setup, separating more than two different types
of particles in a single fluid is extremely difficult and inaccurate.
The primary purpose of the experiment
is to overcome the limitations of 2D DLD
by adding a third range of motion for the
particles to move through. In order to accomplish the task, particles of three different sizes are sent through a 3D DLD system,
and their relative pathways are recorded to
determine the three distinct streams of particles. The 3D DLD system consists of
an obstacle array with long cylindrical rods
placed in a rectangular grid. The experiment is conducted in a macroscopic set-up,
which allows for the manipulation of both
the slope angle and the orientation of the array. This directly relates to a main ambition
of microfluidics as a whole to create a feasible macroscopic model which can be trans-
1.2
Reasons for Development of
3D DLD
A major motivation for the development of 3D DLD is that it can easily be
applied to the purification of environmental
and biological fluids [1]. One specific application is separating healthy and diseased
blood cells, which is possible due to blood’s
low viscosity and ability to move through
microchannels without clogging [1]. Another advantage to 3D DLD is that it has the
ability to separate many varieties of particles at a time and to replace the more complex and expensive separation methods that
are currently in use. As a result of its simple
design, 3D DLD has the potential to separate particles in a large variety of liquids, regardless of their composition and viscosity.
2
2.1
Background
Microfluidics
The principles of 3D DLD are founded
on microfluidics, which focuses on the manipulation of fluids typically in the range
of microliters to picoliters through channel
networks [2]. Microfluidics seeks to control fluid flow on the microscale to provide
2
several advantages, such as increased range
of capabilities, less material requirements,
and more manageable compact units. Microfluidics additionally allows for detection
with higher resolution and sensitivity, as
well as improved cost efficiency. Exploiting
smaller scale management and established
characteristics of fluids, microfluidic mechanisms offer increased control and overall
effectiveness. One of the characteristics of
fluids vital to the principles of microfluidics
and particularly relevant to this research is
laminar flow. In laminar flow, fluids flow in
parallel, and the only mixing that occurs results from the diffusion of molecules across
the interface [2]. All in all, the networks of
channels capitalizing on the varying properties of liquids and particles in microfluidics
are a key component of separation during
3D DLD.
2.2
inertial microfluidic techniques, in addition
to hydrodynamic filtration and pinched
flow fractionation. Hydrodynamic filtration
withdraws a small amount of liquid from
a mainstream to align particles with side
branch channels [3], and pinched flow fractionation introduces particles to a pinched
segment where they are isolated with a
spreading flow profile [4]. 3D DLD draws
on the results of the various methods to
improve upon prior techniques and optimize
efficiency and accuracy in separation.
2.3
Two Dimensional Deterministic Lateral Displacement
The most basic form of deterministic
lateral displacement implements two ranges
of motion along the x-axis and y-axis. The
main focus of the separation technique is to
create equivalent migration paths using laminar flow to process particles through an array of obstacles. A set of obstacles is arranged on one plane, and each successive
row of obstacles is shifted horizontally by a
steady factor: ∆λ , where λ is the center-tocenter distance between obstacles [5]. Ideally, in 2D DLD, particles experience a consistent routine of motion as they progress
through the gaps between obstacles. The
routine of motion, developed by each specific particle as it passes through the array, varies depending on individual properties, thereby contributing a key component
to particle separation utilizing 2D DLD. The
ultimate goal is to understand various particle interactions with the array and take advantage of them within the context of characteristic separation in order to improve the
functionality of that separation.
Compared to other sorting methods,
2D DLD offers various crucial advantages.
Unlike other systems, it does not depend on
Methods of Particle Separation
Separation in microfluidics utilizes two
different types of methods: active and passive. The sole difference between active
methods and passive methods is that active
methods involve the use of external fields
to drive the separative displacement, while
passive methods do not. Active methods
include dielectrophoresis, magnetophoresis,
and acoustophoresis, implementing electric
charges, magnetic fields, and ultrasound
waves, respectively, to separate particles.
While active methods hone in on flow field
fractionation, passive methods incorporate
hydrodynamics and particle-solid interactions based on inertial motion as a means to
separate particles within the fluidic system
[1].
Deterministic lateral displacement
serves as one passive method among other
3
diffusion or multipath averaging, eliminating the randomness and presenting a highly
deterministic event. Additionally, DLD is
much less susceptible to clogging, which is
especially useful in biological settings and
allows for continuous particle separation.
However, the efficiency of the deterministic lateral displacement method can
still be further maximized. One of the areas for improvement is precision. Although
2D DLD is far more exact compared to
other separation techniques, there still remains a fair margin of error. Random diffusion across streamlines continues to moderately degrade resolution. Although high
flow speeds would minimize the issue, separation in a 2D DLD system functions best at
low flow speeds. Furthermore, the systems
are not immune to jamming and cannot support non spherical particles without utilizing
complicated post structures. There is much
room for deterministic lateral displacement
methods to be further researched, consolidated, and ultimately finalized.
2.4
Therefore, the combination of the two angles would allow for three separate critical
angles to be found for three different particles. When a certain size particle’s critical angle is below the forcing angle, it will
experience locked motion. If the other two
particles have greater critical angles than the
same forcing angle, the three dimensional
geometry allows for the two other particles
to be separated by their out-of-plane motion
in the xz-plane, allowing for more specificity than 2D DLD [1].
2.5
Collision Interactions
The collision model assumes two different types of interactions with the posts:
purely hydrodynamic or physical contact.
Purely hydrodynamic interactions describe
interactions in which the displacement going into the collision is equivalent to the displacement out. For the touching collision,
the two displacements will be asymmetrical,
with the position at which the particle exists
the apparatus being set at one specific value
[7]. For each given interaction, the particle
trajectory is considered either reversible or
irreversible. A particle’s trajectory is considered reversible in scenarios where the obstacle does not affect the particle’s intended
motion. However, for each irreversible collision, there exists a critical offset which differs from the initial offset prior to interaction with an obstacle, giving rise to a net lateral displacement necessary for particle separation [7].
Overall Concept
The deterministic lateral displacement
is formed using cylindrical obstacles to affect the in-plane and out-of-plane motion of
particles. The motion is altered by two angles: a rotation angle and the slope angle.
Therefore, the gravitational force, which
drives each particle through the system, becomes a three dimensional vector based
on the two angles. The particles’ interactions with the rods are calculated in threedimensions due to the gravitational force,
thus creating 3D DLD [6].
For 3D DLD, the forcing angle α, defined as the angle between the particle path
vector and the z-axis in the yz-plane, is
based on both the rotation and slope angle.
2.6
Types of Motion
The particles exhibit two types of motion as they travel through the rods: zigzag
and locked (see Figure 1). The two forms
of motion allow for the separation of parti4
cles, as they create two different streams and
points of exit from the cylindrical array.
work of Dr. German Drazer and Siqi Du,
as the system uses water as the liquid that
the particle flows through, rather than corn
oil. Corn oil has a much higher density
and therefore a much lower Reynolds number. The Reynolds number is a measurement of turbulence within a system, and
plays a significant role in the inertia of the
particles. The Reynolds number also plays a
role in the Navier-Stokes Equations, which
describes the motion of a particle in a fluid.
The Reynolds number measures the proportions of the viscous forces to inertial forces
acting on a particle traversing the system.
It helps to indicate above which values the
particle will experience turbulent flow and
below which it will experience laminar flow
through the system. With water having a
lower density and higher Reynolds number,
a higher degree of chaos is expected, which
may cause the particle to act differently
within the system from the system with corn
oil. The force angles may have different effects on the particles because there will be a
different critical velocity value for the particle at which it switches types of movement
through the system. Therefore, the critical
angle of each particle will differ based on
the fluid it flows through [6].
Figure 1: Adapted from [1]. Particle motion
projected onto the yz-plane shows the migration angle β and the forcing angle α. The red
particle moves in locked mode and is confined
to a single column, whereas the blue particle
moves in zigzag mode and travels across multiple columns.
Both models of motion are made possible by the phenomenon called directional
locking, where if the force angle is less than
a specific value, known as the critical angle, the particles will follow the array of
poles, creating a diagonal path. Directional
locking is due to the touching force, where
all particles will exit the collision at the exact same point, creating a specific pathway,
which they will follow. When the angle is
greater than or equal to the specific critical
angle, the particles will bounce around and
follow a zigzag pattern similar to a pinball
machine [7].
2.7
3
3.1
Separation Using Three
Dimensional Deterministic Lateral Displacement
Apparatus Preparation
First, the apparatus that would be used
in the 3D DLD system was assembled.
Stainless steel poles, six feet in length, were
cut into 15 centimeter rods, which would
act as the cylindrical obstacles in the array.
Theory
For the experiment specifically, different results are expected from the previous
5
Two acrylic plates (see Figure 2a) designed
in Solidworksr were constructed, each with
a 20 x 20 grid of holes. The holes were
spaced 4 mm apart, each with a diameter of
2 mm. A total of 200 cut rods were then
inserted into both acrylic plates in the central 10 columns of the array, creating a 10 x
20 grid of rods. The array plates were then
drilled into place, at a separation of 14 cm,
into a square acrylic plate (see Figure 2b).
Another acrylic plate was attached to
the largest base plate by hinges, allowing
for the array to be lifted at various slope angles. The square plate and base plate were
loosely screwed together to allow for the rotation angle to be adjusted.
A large rectangular acrylic plate was
used as a base plate, and its surface was
marked with angles in 10◦ increments, ranging from 0◦ to 90◦ . Another acrylic plate
was attached to the base plate by hinges, allowing for the entire array to be lifted at various slope angles while still maintaining a
flat bottom surface. The square plate with
the array mounted on it and the base plate
were loosely screwed together to allow for
the rotation angle to be easily adjusted using manual force (see Figure 2b).
A small hole was drilled into both of
the unhinged corners of the base plate, and
floss was threaded through and tied to a
long metal bar. To adjust the slope angle,
the floss was either wound, increasing the
angle, or unwound, decreasing the angle.
Then, a tank with a total volume of one cubic foot was filled to a height of eight inches
with tap water, and the completed apparatus
was entirely submerged in the liquid. The
floss and rod were placed outside the tank,
and the floss was made taut, acting as a type
of pulley. In order to adjust the slope angle,
the floss was either wound, increasing the
angle, or unwound, decreasing the angle.
(a)
(b)
Figure 2: (a) The two acrylic plates holding
the stainless steel rods were designed using
Solidworksr . (b) The apparatus from the view
of the camera. The slope angle φ is measured
along the center of the bottom acrylic plate.
6
Figure 3: The assembled rod array and the two
other acrylic plates. The plate in the top left is
marked with angles in increments of 10◦ .
3.2
(a)
Rust Removal and Prevention
After submerging the apparatus in the
water, oxygen bubbles formed on the steel
rods of the array, revealing the presence of
an oxidation reaction (see Figure 4c). The
oxidation as a result of the water’s reaction
with the steel thus produced rust, a significant issue to the function of the apparatus
as a whole. Due to the change in texture
of the rods, particles became attached to the
steel rods upon impact rather than passing
through the array, dramatically varying the
results of the trials. The presence of rust
clearly affected the roughness of the steel
rods, thereby altering the path of particles
and leading to inaccuracy.
In order to remove the rust from the
steel rods, the entire apparatus was placed
in a vinegar-water solution and cleaned with
gauze. To prevent rust from appearing
again, the water in the tank was replaced
with a vinegar-water solution consisting of
21.48 L water and 100 mL vinegar, approximately a 215:1 water to vinegar ratio. The
addition of vinegar lowered the slightly basic pH of the water into a neutral range,
eliminating the potential for oxidation reac-
(b)
(c)
Figure 4: (a) The apparatus submerged in water in the fish tank. A stand was used to make
maintain balance of the tank. (b) Washing the
apparatus in a vinegar-water bath to clean the
rust off of the steel rods. (c) Oxidation of the
steel rods was detectable by the bubbles forming around the rods.
7
tions without drastically impacting the viscosity. Additionally, the vinegar-water solution was monitored closely and changed
daily in an attempt to maintain the cleanliness and quality of the liquid.
3.3
ment within the array and their point of exit
was captured by the camera to allow for further review and analysis. The type of particle movement, zigzag or locked, was also
observed in order to determine the value of
the critical angle for each particle size at the
given slope angle. At the smaller rotation
angles, the vast majority of particles exhibited the properties of zigzag motion. The
later transition from zigzag to locked motion signaled that the angle of displacement
of the particles was approaching the value of
the critical angle. Therefore, as the rotation
angle was increased in increments of 10◦ ,
the particles passed through the intermediary state, where they switched from zigzag
to locked motion. During the intermediary
states, an additional trial was conducted at
a 5◦ increase in order to find a more accurate value for the critical angle and locate a
more exact point at which the motion of the
particles underwent the transition.
Once the particles of a certain size had
sufficiently transitioned into locked motion,
with the vast majority of the trial particles
following the path along the rods, no more
trials were conducted for that specific size
and slope angle. Locked motion indicated
the critical angle had already been achieved,
meaning additional trials at larger rotational
angles would have yielded the same result.
Completion of Trials
The testing process for 3D DLD involved manipulating three different variables: the particle size, the rotation angle,
and the slope angle. A total of 44 trials
were completed, consisting of three different sizes of particles, 22 rotation angles,
and two slope angles. The particle diameters varied between 1.59◦ , 2.88◦ , and 3.16◦ ,
with Particle 1 being the smallest and Particle 3 being the largest. In each trial, 20
spherical Nylon particles of the predetermined size were inserted into the first column to the right of the array, and their motion through the apparatus was recorded.
First, the mechanism constructed from
dental floss attached to the base of the apparatus was rewound to the appropriate slope
angle. The trials began by testing a constant
slope angle of approximately 28◦ in conjunction with the manipulation of the other
two variables. Afterwards, another series of
trials mimicked the first set but instead used
a slope angle of approximately 37◦ . The
slope angles were deliberately chosen at an
assumed safe range above the particles’ hypothesized critical angles. For each given
slope angle, the rotation angle was adjusted
beginning with 10◦ followed by steadily increasing 10◦ intervals until the last trial with
a rotation angle of 80◦ .
Before each session, a camera was set
to record the trial. After visually specifying
which particle size was being tested, the 20
particles were individually dropped into the
array using tweezers. The particles’ move-
3.4
Review and Analysis Process
Once data collection was complete, the
analysis was split into two sections. The
first part consisted of motion analysis in two
dimensions, specifically within the in-plane
(yz) motion.
The forcing angle can be determined in
terms of the components of gravity on the xand y-axes (see Figure) as follows [6]:
8
where C is the number of columns that
the particle traversed and R is the number of
rows that the particle traversed.
The second part of analysis consisted
of video analysis of particle motion in the
xy-plane. Each trial was videotaped individually, with a total of twenty particles per
trial. The camera was positioned parallel to
the top of the apparatus so that the video
could later be analyzed digitally in order to
determine the path of the particles. Furthermore, the distance traveled by the particles in the x- and z-directions allowed for
additional separation of the particles which
were indistinguishable in the xz-plane analysis. Comparing the out-of-plane motion
was accomplished by projecting the particle path vector in the xy-plane onto the xaxis and taking the magnitude of that vector.
Videos were filtered after compilation from
the camera, and a program written in MATLAB was used to generate frames from each
video. Every fifth frame was saved as an
image, and all saved images from the same
video were saved into a folder with a unique
video ID. The images were then further filtered so that the final image sequences consisted of only the frames showing the particles entering and exiting the grid. The
data was then collected by manually analyzing the images in an open source image
processing software, ImageJ, using manual
tracking. The manual tracking process for
each video sequence recorded the path vector of each particle, as well as the vector in
the x-direction along the steel rods. In order to convert the projection length calculated by the ImageJ tracking from pixels to
millimeters, another standard vector spanning the distance between four steel rods
was recorded for each video. The length of
this vector, which was known to be 18 mm,
was then used to scale the projection length
Figure 5: Adapted from [1]. The components
of the gravitational force in the axis defined by
the apparatus, as well as the slope angle θ and
rotation angle φ .
gz = g cos θ
gx = g sin θ cos φ
gy = g sin θ sin φ
(1a)
(1b)
(1c)
gy /gz = tan α = tan θ sin φ
(2)
The entrance and exit points of each
particle in the array were recorded. Compilation of the row and column exit data enabled estimation of the critical angle for initial separation of particles into two streams,
one containing a particle of one size and
the other containing particles of the two remaining sizes. Three different critical angles were calculated for each slope angle,
one corresponding to each specific particle
size. The exit point was also used to find
the migration angle of each particle, which
was calculated by:
β = arctan
C
R
(3)
9
10◦ increments, the forcing angle decreased.
Once the forcing angle approached a certain
range bounding the critical angle, the particles’ tendencies to travel in locked mode
increased abruptly.
into millimeters. The particle’s displacement along the x-axis could then be calculated by the projection equation:
|projb x| =
x·b
|x|
18 mm
|s|
(4)
4.2
where x represents the particle’s path
vector, b represents a directional vector
along the steel rods, and s represents the
standard vector.
4
4.1
Separation Streams in 2D
In order to determine the critical angle, a range was first pinpointed from the
experimental data by calculating the probability of crossing (Pc ), defined as the ratio
of the number of particles in zigzag motion
to the total number of particles in a trial[1]
[1]. The data showed clear transitions from
a very large probability of crossing (Pc =
1) to a seemingly unapparent probability of
crossing zero (Pc = 0) over two or three
consecutive rotation angles for each particle
size under a fixed slope angle.
Results and Discussion
Tracking Particle Motion
Through Steel Rods
The out-of-plane motion of each particle was recorded by the row or column
which the particle exited from at the end of
each run, and the motion in the y-direction
was tracked by the video recording. Within
the steel rod grid, two modes of particle
motion were evident. Initially, the particle
moved in zigzag motion, in which it followed the direction of the gravitational force
pulling down on it, thus following a generally downwards path that spanned multiple columns and crossed a large portion of
the array. The particles usually exited on
the side of the array or in one of the leftmost columns at the bottom of the array.
Particles may also travel in locked motion,
following the direction of the lattice rather
than that of gravity. Particles in locked motion moved through all nineteen rows of lattice but stayed strictly within the first column. The critical angle was the angle at
which particles of a certain size switched
from zigzag mode to locked mode and was
the primary method of separation in two dimensions. As the rotation angle increased in
Figure 6: The probability of crossing Pc for each
particle size in different combinations of slope
angles and rotation angles. Trials highlighted in
green indicate when the particle is traveling in
or close to locked mode, and trials highlighted
in yellow indicate when the particle is traveling
in zigzag mode. The trial highlighted in red indicates a potentially faulty result.
Experimentally determined ranges for
the critical angle α of a certain particle
size can be found by taking the corresponding forcing angles of the trials where
Pc most closely bound 0.5. For a slope
angle of 28◦ and particles of diameter
1.59 mm, 2.38 mm, and 3.16 mm the respective ranges for α are:
10
respectively:
10.3◦ < α < 14.9◦
18.9◦ < α < 21.3◦
◦
21.3 < α < 26.7
Particle Size
1.59 mm
2.38 mm
3.16 mm
◦
For a slope angle of 37◦ and particles of diameter 1.59 mm, 2.38 mm, and
3.16 mm the respective ranges for α are:
◦
7.5 < α < 14.5
Critical Angle in Water
11.6◦ ± 2.3◦
19.8◦ ± 1.6◦
25.4◦ ± 2.1◦
The estimated critical angles for the
same sizes of particles in corn oil are respectively [1]:
◦
14.5◦ < α < 17.7◦
20.6◦ < α < 30.0◦
Particle Size
1.59 mm
2.38 mm
3.16 mm
Critical Angle in Corn Oil
6.7◦ ± 1.7◦
10.0◦ ± 1.5◦
12.6◦ ± 1.7◦
Figure 7: The probability of crossing Pc against
the forcing angle α. Different particle sizes are
marked by different colors and shapes.
Plotting Pc against forcing angles and
isolating the transition stage trials produces
a linear regression. The regression enables
the estimation of the critical angle, determined by the value of the forcing angle
when the probability of crossing is 0.5
The graph also shows a distinct jump in Pc ,
indicating that the transition between modes
occurs at a specific range of angles for each
particle. The graph also shows that the
critical angle tends to increase as particle
size increases, which is consistent with
the previous experiment using corn oil [1].
The estimated critical angle for particles
of 1.59 mm, 2.38 mm, and 3.16 mm are
Figure 8: The migration angle β as a function of
the forcing angle α for all three particle sizes:
1.59 mm, 2.38 mm, and 3.16 mm.
Particle motion may also be studied
by plotting the migration angle β against
the forcing angle α, which shows that the
particles of each size begin to move in
zigzag motion only after the respective critical angle, which is consistent with the particle motion exhibited in oil [1]. With a
few exceptions, particles traveling at forcing angles less than the critical angle exhibit
locked motion, with β = 0◦ .
11
4.3
Separating Particles in Three
Dimensions
Figure 9 shows that in the xy-plane,
there existed critical angles in which one
particle size was split into a separate stream
but the remaining two particle sizes still experienced zigzag motion, highlighting the
ability of the experiment to choose specific
particles to separate into distinct streams.
While the in-plane motion of the particles could not have been distinguished, Figure 10 shows that their out-of-plane movements were clearly distinct. For instance,
at a forcing angle of 22◦ , particles of diameter 3.16 mm would be separated into
a zigzag stream, but particles of diameter
1.59 mm and 2.38 mm would both remain
in the same locked stream in the 2D DLD
plane. However, Fig. depicts a clear difference in ∆x/∆z between particles of diameter
1.59 mm and 2.38 mm, thus splitting them
into separate streams.
Further separation of the particles in
the third dimension is done in two planes.
First, the projection of the particle motion
vector in the xy-plane onto the x-axis is determined. The projection, or the particle’s
movement along the x-axis (∆x), can be normalized along the particle displacement in
the z-axis (∆z) to obtain ∆x/∆z. The ratio
is effectively describing the particle’s movement in the xz-plane. Plotting ∆x/∆z as a
function of the forcing angle α allows for
further separation of particles locked within
the same column, a motion that would be
indistinguishable in 2D DLD.
4.4
Comparing Particle Motion
in Water to Particle Motion
in Corn Oil
The critical angles for water are higher
for each particle size, which was expected
since the Reynolds number for water is significantly higher than that of oil. The difference in critical angle indicates that the gravitational force pulling on the particles met
less inertial resistance in water than in oil,
and the greater perturbations within the water allow the particles to remain in zigzag
motion at greater forcing angles. Conversely, the greater inertial forces present
in oil, which has a higher viscosity, minimize the perturbations caused by the force
of gravity moving the particle and locking
the particle within the steel rod lattice more
easily.
(a)
(b)
Figure 9: The xz-plane motion graphed as a
function of the forcing angle α for slope angles
of (a) 28◦ , and (b) 37◦ .
12
(a)
(b)
(c)
Figure 10: The migration angle β as a function of the forcing angle α for particles of diameter (a)
1.59 mm (b) 2.38 mm (c) 3.16 mm. Noticeable plateaus in migration angle are observed for certain
intervals of the forcing angle.
13
While the critical angles were greater
for particles traveling through water than in
oil, the general separation mechanism of 3D
DLD functioned similarly in both fluids. In
particular, an individual analysis of the migration angle β against the forcing angle α
of each particle shows the directional locking behavior, defined as the occurrence of a
fixed migration angle for a certain interval
of forcing angles [1]. Similar to oil, the directional locking intervals decrease in number but increase in range as particle size increases. The definition of the plateaus, however, is much clearer in the data for oil than
that of water. Additionally, it is evident that
particles have migration angles of approximately 0◦ at forcing angles less than the critical angle, which suggests that the turbulent
nature of water does not significantly alter
the separation mechanism from that in oil.
4.5
changed every day that new trials were completed. As a result, each new day of trials
may have had a slightly different viscosity
liquid to travel through.
Another potential source of error is
the initial dropping of the particles into the
array. Each particle was placed into the
apparatus using tweezers, and as a result,
they did not all enter with the same initial
force or velocity. Small changes in how the
tweezers were held or the location of the
tweezers could have affected the overall motion of the particles as well. Human error
is also present in the analysis of the particles using ImageJ. Due to the manual tracking process that was employed, some of the
motion vectors may have been inaccurate.
Some of the trial video recordings were not
completely in focus, and a small speck, air
bubble, or reflection in the tank could have
been mistaken for the particle, leading to an
incorrect reading.
Sources of Error
During the analysis of the collected
data, discrepancies were found in select trials concerning the type of movement and
the migration angle of particles. The error could be attributed to multiple possible
sources of error. First, due to the original rusting of the steel rods in the array, a
rice vinegar-water solution was composed
to clean the array and prevent future rust.
The vinegar present in the solution had a
slightly higher viscosity than water, which
could have affected the motion of the particles. In addition, the rust may have adjusted the texture of the rods. Such textural change would also have had an effect on
the movement of the particles, as they could
have stuck to the rods or changed their trajectory due to increased friction. The vinegar solution also posed a possible problem
because the liquid in the tank needed to be
5
Conclusions
As particles were placed into the array and passed through the series of obstacles, two types of motion were observed,
zigzag and locked, which enable particle
separation. Generally, particles demonstrated more inclination towards locked motion as the forcing angle approached the critical angle, often with greater rotation angles. The experimental data supported th,
revealing that the probability of crossing decreased suddenly from one to zero over the
span of the trials. After calculating critical
angles for given particle sizes according to
their forcing angles and plotting the probability of crossing against forcing angles isolated from the transition stage, a linear regression was observed. This further distin14
guished that the critical angle typically increases as particle size increases, strongly
suggesting that water serves as a successful
separation medium. Aside from the comparison of forcing and critical angles, the
relationship between forcing and migration
angles also revealed important notes concerning the data sets, namely, that particles
tended to lock at forcing angles less than the
critical angles. In general, particles moving according to forcing angles less than the
critical angle exhibited locked motion.
ing particles were blurry.
Acknowledgments
This paper and knowledge acquired
through research would not have been possible without the extensive time and effort
contributed by a great account of people
and institutions. Specifically, the authors of
this paper would like to express thorough
gratitude to all their mentors. The special
efforts of mentor and PhD candidate Siqi
Du were invaluable to the experimental process and deep analysis required for success,
and the authors would like to further acknowledge with great appreciation his considerable help, support, and enthusiasm in
all project matters. Additionally, they extend their thanks to Residential Teaching
Assistant Alissa Persad for her facilitation
in review and overall focus. Furthermore,
the authors express the utmost gratitude to
Dr. German Drazer for allowing the use of
his facilities, without which this opportunity
would not be possible.
They would also like to extend thanks
to all the staff of the Governor’s School of
Engineering and Technology for not only
the materials and basis creating thie research project, but also the remarkable experience as a whole. Their hard work
and detailed planning provided the foundation for all the studies described within
the paper. Particularly, the authors would
like to express deep appreciation to Dean
Jean Patrick Antoine and Dean Ilene Rosen,
without whom the research would not have
been pursued. Finally, they respectfully acknowledge the generous donations of the
sponsors of the Governor’s School of Engineering, enabling the pursuit of interests
in science, mathematics, engineering, and
Furthermore, utilizing the three dimensional coordinate system enabled greater
separation capabilities in a given column,
successfully expanding the range of motion
and accuracy in comparison to 2D DLD.
While there still remains areas for improvement in sorting particles according to DLD,
such as in cases where two particles experience the same type of motion, 3D DLD
permits analysis in two planes of separation
with distinct displacements. Additionally,
appealing to one of the primary goals of the
research to identify discontinuities between
oil and water used in 3D DLD, less inertial resistance was met in water due to lower
viscosity provided for higher critical angles,
also allowing zigzag motion in greater forcing angles. However, the difference in inertial resistance did not have a significant
impact on the mechanism as a whole, as
proven within the overall directional locking behavior of the particles. Even so, oil
exhibited more consistent separation, especially when separation involved smaller particle sizes. Possible sources of error include
material malfunctions, particularly viscosity
and trial reset discrepancies regarding the
water-vinegar solution and steel rod rusting, precision in original particle placement
within the array, and human error concerning analysis, especially when videos track15
technology: Rutgers, the State University of
New Jersey; Rutgers School of Engineering;
South Jersey Industries, Inc.; Printrbot; and
Lockheed Martin.
[4] M. Yamada et al., “Pinched Flow Fractionation: Continuous Size Separation
of Particles Utilizing a Laminar Flow
Profile in a Pinched Microchannel,”
Anal. Chem., vol. 76, pp. 5465-5471,
Sept. 2004.
References
[5] L. R. Huang et al., “Continuous Particle Separation Through Deterministic
Lateral Displacement,” Science, vol.
304, pp. 987-990, Dec. 2003.
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