NANO BIONIC SWIMMING ROBOTICS ANDAPPLICATIONS IN ENVIRONMENTALENGINEERING

Bioscience & Engineering: An International Journal (BIOEJ), December 2022, Volume 9, Number 1/2/3/4
DOI: 10.5121/bioej.2022.9401 1
NANO BIONIC SWIMMING ROBOTICS AND
APPLICATIONS IN ENVIRONMENTAL
ENGINEERING
Tianying Li1
1
Department of Civil and Environmental Engineering, Western University,
London, Ontario, Canada.
ABSTRACT
As microscopic swimmers survive in nature, they have evolved unique structures and swimming
patterns under the water, which has special advantages. The movement of bacteria at low
Reynolds number (Re) environment has aroused extensive research interest. The two typical
swimming methods of bacteria are introduced in this paper.
Based on this, we are inspired to design the bionic robot on a micro-scale, which is an artificial
structure that imitates the external shape, movement principle and behavior mode of organisms in
nature. Compared with traditional robots, nano bionic robots are easier to miniaturize[1]. They
also have higher maneuverability so that they can move continuously and flexibly. We expect to
simulate its motion at low Reynolds number (Re) fluids and explore complex future applications
in different fields.
KEYWORDS
Microscopic swimmers, Low Re, Bionic robots, Applications
1. INTRODUCTION
1.1. Background and Goals
The Nobel Prize winner Richard Feynman puts forward the concept of nano bionic robots. It is
based on the biological principle at the molecular level as the prototype to design a "molecular
device" that can operate in the nano space, also known as the molecular robot[2]. Nano robot is
the most attractive content of biomedicine, and the extreme environment is its main working
environment.
Some major applications of nano bionic robots will be widely implemented in a variety of fields,
from information technology to biotechnology, from medicine to aerospace and so on. Nowadays,
a number of previous research projects have explored the use of nano bionic robotics in the
medical field[3]. Those tiny nanoparticles have the ability to change the body’s dynamics with
minimal side effects, allowing them to perform specific tasks inside the body, including the
development of the nano robot assisted fertilization and the nano spider robot composed of DNA
molecules that move along membrane surface [4][5]. However, they are still in the research and
development stage, and some technical barriers remain to be solved. We are inspired by the
previous research and try to design the artificial nano bionic robot in order to apply it to the
wastewater control technology in the field of environmental engineering in this paper.

2
Fluid mechanics plays an important role in Environmental Engineering. In this field, we study the
static/ dynamic state of the fluid itself as well as the interaction when the fluid and solid boundary
are in relative motion under various forces. Here we introduce the definition of Reynolds number
(Re), a similarity criterion constant in fluid mechanics to characterize the influence of viscosity,
which is defined as the ratio of the inertial forces to the viscous forces.
�� =
��
��
=
��
�
=
��
�
(1)
Where：ρ and η: density and viscosity of the fluid;
ν: kinematic viscosity, ν = 10−2
cm2
/sec (for water);
a: dimension.
People, fish, and microbes, also swim in water, but the physical behavior and Re numbers of
various creatures are also quite different because of the huge differences in length scales. The
Renumber for a man swimming in a liquid may be 104
. However, when it comes to the microbial
world, the Re number for the animals that we're going to be talking about may get down to only
10-4
or 10-5
.
Normally, the force is proportional to the acceleration, but when the Re number is extremely low,
the viscous forces dominate, which means inertial force plays no role and the force is
proportional to the velocity only. We aim to find out why swimming at the micro-scaleis so
difficult and then try to design an artificial nano robot that can overcome the difficulties when
they swim at a low-Re number.
In summary, the objectives of the research were:
(1) Studying the physics of swimming problems at low-Re numbers;
(2) Designing the artificial micro-swimmer based on the theory part by analyzing,
programming, modeling, etc.;
Discussingfuture prospects of Nano Bionic Swimming Robotics.
2. THEORY AND METHOD
2.1. Scallop Theorem
The most significant difference in microbial movement is the reversibility in time, that is, any
motion is the result of the forces that are exerted on them currently and has nothing to do with the
past at a low Re number. Under this circumstance, we can even move backward by exerting
reverse forces. This makes it clear what a low Re number implies. Imagining scallops, they swim
by the shock of slowly opening their shells in the water and then quickly closing them together.
Finding that they have been doing reciprocating motion and the shells open and close
symmetrically in time, so they cannot swim at a low Re number unluckily[6]. Only if microbes
break time reversibility, can they swim at a low Re number. This is what we called the Scallop
Theorem. Based on this, we will explore how bacteria with micro-scale swim in a liquid
environment.
According to E.M. Purcell, an American physicist who shared, with Felix Bloch of the United
States, the Nobel Prize for Physics in 1952, there are two main methods to the problem of
swimming in the microbe world[6]. One way we may call flexible oar (fig.1), the fluttering of
their flexible flagella, like sperm. Another one might be a corkscrew (fig.1), rotating their helical
flagella filaments and helical cell bodies[6]. For example, the most common E. coli rotates its

3
flagella like a screw, and other microorganisms have their own special structures to meet their
swimming needs.
Figure 1. Solutions to the problem of swimming at a low Re number[6]
In the following part, we are going to talk about how a rotating corkscrew propels something first.
Remember everything is linear at a low Re number, so we see matrices come in.
2.2. Matrix Method
For low-Re number swimmer:
F=Av+BΩ (2)
N=Cv+DΩ (3)
Here we regard this matrix as a propulsion matrix, known as its elements A, B, C and D, which is
applicable to the motion of any shape of the object at a low Re number. The respective number of
A, B, C and D depends on the shape of the object. The total matrix of the system can be equal to
the sum of each individual in a series.
We aim to develop a mathematical explanation of bacterial swimming speed with viscosity in
linear-polymer solutions, therefore the traditional hydrodynamic solutions do not apply to the
motion of microorganisms in solutions containing viscous components[7]. Here we see a
mathematical expression of force theory comes in.
2.3. Mathematical Expression of Force Theory
Equations of motion.
�� + �� = 0 (4)
�� + �� = 0 (5)
Where：Fc and Tc: Hydrodynamic force and torque acting on cell body;
Ff and Tf: Hydrodynamic force and torque acting on flagella filament;
Drag force and torque act on a cell body.
�� = �� (6)
�� = �� (7)
Where:αc and βc: Drag coefficients of cell body;
ωc: Rotation rates of cell body;
V: Swimming speed;
Drag force and torque on a flagella filament.

4
�� = �� + �� (8)
�� = �� + �� (9)
where：αf , βf and γf: Drag coefficients of flagella filament;
ωf: Rotation rates of flagella filament.
Drag coefficients αc,βc; αf , βf and γf were written as follows[8]
:
�� =− 6�� 1 −
1
5
1 −
�
�
(10)
�� =− 8��3
1 −
3
5
1 −
�
�
(11)
�� =
2��
��
�
2�
+
1
2
4�2�2+�2
(8�2
�2
+ �2
) (12)
�� =
2��
��
�
2�
+
1
2
4�2�2+�2
(4�2�2 + 2�2
)�2
(13)
�� =
2��
��
�
2�
+
1
2
4�2�2+�2
( − 2�2�2
�) (14)
Where：μ: Viscosity, μ = 0.8973 × 10−3pa. s (under 25℃);
2a, 2b: Cell width and cell length;
2d: Diameter of flagella filament;
L: Length of flagella filament.;
R: Radius of flagella filament;
P: pitch angle, tan θ =
p
2πr
.
3. RESULTS
3.1. Programming Part
Our purpose is to implement the theory by programming method. So here we use Matlab to
program the calculations mentioned above. The known micro swimmer（fig.2）, as an example:
Figure 2. The schematic of the example
The relation between velocity versus pitch angle is shown in the figure below (fig.3).
When the pitch angle changes from 0 to
π
4
, the velocity increases with the increase of the
pitch angle and reaches the maximum value at
π
4
. When pitch angle changes from
π
4
to
π
2
, the
velocity decreases with the change of the pitch angle

5
Figure 3. The plot of velocity versus pitch angle
After this work, we still use Matlab to simulate the swimming process of an E. coli with 2D,
which swims following a run-and-tumble process. Knowing the run speed of E. coli is 25μm/s,
the average run time is 1s and follows an exponential distribution, average tumble time is 0.1s,
which also follows an exponential distribution. In short, there is a tumble event between two run
events in the swimming process of E. coli. Using two random arrays for run and tumble to plot
the speed vs time as well as the Vy vs Vx (add white noises language). From this work, we
finally plotted the swimming trajectory with 2D. The results (random) are as followed (fig.4-
fig.6):
Figure 4. The plot between speed (um/s) versus Time (s)
Figure 5. The plot between Vy (um/s) versus Vx (um/s)

6
Figure 6. The plot between Y (um) versus X (um)
Based on all the work mentioned above, we finally come to the most challenging but interesting
part, the design of artificial micro-swimmers, which is also known as bionic swimming robotics
design. Two of the most common models for doing this are 3D printouts and 3D modeling to
simulate the animation of its trajectory. Here we are going to talk about the way of 3D modeling.
3.2. Modeling Part
Using Pro engineering to Model E. coli in 3D (fig.7), the cilium on its cell body and its flagella
should be flexible, but Pro engineering cannot manage as vivid as the real thing. Then, based on
the plot of Y vs X drawn by Matlab, we could simulate its swimming trajectory as is shown in the
video . The screenshot of its swimming trajectory in the video is shown below (fig.8). The cell
body rotates in the opposite direction to the flagellum, and the difference in speed should be large
even though it is not obvious in the video.
Figure 7. The 3D modeling of E. coli
Please check this link at https://youtu.be/W-lNw1iWHU4 for your convenience.

7
Figure 8. Swimming trajectory of E. coli modeled by Pro Engineering
4. DISCUSSION
4.1. Nanotechnology and Nano Bionic Robotics
With the development of technology, nano-scale substances are widely used in human life.
Nanotechnology turns underwater bionic robots to enter a flexible era instead of the traditional
rigid era. We intend to design a nano bionic robot by using E. coli as a model in this paper. The
combination of these two enables the nano bionic robot to move continuously and flexibly, better
mimicking the movement of bacteria at low Re number fluids.
4.2. Prospects of Nano Bionic Robotics in Wastewater Treatment Engineering
Generally speaking, there are two kinds of water pollution sources: human factors and natural
factors. Water pollution caused by human activities accounts for two-thirds of the total due to the
development of urbanization and Industry. Urban and industrial wastewater is a serious threat to
the ecological environment, so it is very important to accurately monitor and quickly target the
pollutants in polluted water bodies. We are inspired to apply nano bionic robots to wastewater
control engineering, which do not need to have extremely complicated structures but need to have
the ability to receive radio wave signals. They can still move around as well as monitor
contaminants in poor condition fluids without creating additional pollution by self-propelling,
just like those microscopic swimmers in nature. By conveying the information they detect to the
nearest robot through radio waves, the detection information will be transmitted to the central
control system in the end. In this way, The bionic robot only acts as a medium for information
transmission, so that we are able to treat polluted water bodies quickly.
4.3. Improvement and Innovation
The future development trend of nano bionic robots using in wastewater control engineering will
be more flexible, efficient, stable, and will be applied to more aspects of the wastewater treatment
process. Currently, wastewater testing mainly uses the sampling method, then is analyzed in the
laboratory, which is still mainly based on chemical agents for a variety of experimental data
comparisons. Therefore, the process is generally complex, time-consuming, and not flexible
enough. However, the new technology supports the collection and analysis of data directly,
especially in extremely viscous fluid bodies, offering the advantages of faster calculations,
reducing device requirements, and allowing for remote control as well.

8
In addition to obtaining inspiration from the physical characteristics and propulsion of the
creature, it is also necessary to emphasize the self-perception, self-control and other performance
characteristics, positioning in the water and environmental perception for example, much closer
to the micro creatures in nature[9][10][11].
However, due to the complexity of the wastewater environment, the material requirements of
nano bionic robotics are very strict, we may have to add antibodies to their surfaces to prevent
them from being eroded by contaminants.
Finally, considering they are nano-scale devices, their computing power is still limited. Therefore,
our aim is to reduce their manufacturing costs and produce them on a large scale in order to let
them work together. On this basis, we then need to establish a complete information transmission
system, which can be controlled by a small programmable logic controller (PLC) that can detect
various parameters instantly and adjust the operation status of each part automatically. Once this
design is successful, it will bring a great breakthrough in the fight against water pollution.
However further research is still needed to pursue sustainability along the way to make this
technology more mature.
As for the innovation, I think we may study the bionic robot with two tails and the rotation of two
tails, arranged at each end of the robot body. I think the design enables the robot to have multiple
degrees of freedom such as forward, backward and turning. By optimizing the structure of the
spiral tail, the shape of the robot body and the distance between the two spiral tails, in order to
achieve good performance. We may figure it out in the future research work.
5. CONCLUSION
In this paper, E. coli was used as the model of a nano bionic swimming robot to analyze each
characteristic value of the artificial nano bionic robot by programming, and the final result was
presented by modeling animation. In conclusion, the following points need to be highlighted:
(1)The overall design is based on the physics of micro-organism swimming mechanisms at low-
Re number;
(2)When the pitch angle of the tail is about 45 degrees, its swimming speed reaches the maximum;
(3)The whole process follows a run-and-tumble process. We programmed it with random arrays,
the pattern shown above is just one of those random cases;
(4)In order to put the design into practice, we discussed the possibility of using nano bionic
swimming robots in sewage treatment engineering.
In the twenty-first century, research in the fields of nanotechnology, biology and environmental
engineering should be developed in conjunction with social development. In this way, we can get
a deeper understanding of the integrate field and put forward more innovative ideas, so as to
always have hope for a “artificial nano bionic robotics revolution” in the future.
ACKNOWLEDGMENTS
I would like to express my sincere gratitude to my supervisor, Professor Jason, Qu, who has
given me this valuable research opportunity and his selfless support. With his sincere help and
useful advice, I had a certain understanding of computer programming, such as MATLAB, and
overcame various difficulties. Thanks to his guidance, it has gradually become possible for me to
do further research on a series of properties and applications of nano bionic robots in Wastewater

9
Treatment Engineering. My gratitude also goes to everyone who helped me, shared with me my
worries and was always be patient with me.
True talents always shine through. I will always cherish this valuable experience as it led me into
a challenging yet fascinating field of academic research, which was, is and will be of great
significant to my whole studying life.
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AUTHORS
Tianying Li, M.Eng., Civil & Environmental Engineering, Western University, ON
Canada. Bachelor of Engineering, Environmental Protection Equipment Engineering,
Yantai University, China.

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