IONIC POLYMER-METAL COMPOSITE (IPMC): MODELING AND BIO-INSPIRED

SENSING APPLICATIONS

By

Montassar Aidi Sharif

A DISSERTATION

Submitted to

Michigan State University

in partial fulﬁllment of the requirements

for the degree of

Electrical Engineering - Doctor of Philosophy

2019

ABSTRACT

IONIC POLYMER-METAL COMPOSITE (IPMC): MODELING AND BIO-INSPIRED

SENSING APPLICATIONS

By

Montassar Aidi Sharif

Ionic polymer-metal composite (IPMC) is a class of electroactive polymers with built-in actu-

ation and sensing capabilities. In this dissertation, the modeling and several bio-inspired sensing

applications of IPMC are investigated computationally and experimentally. First, physics-based

modeling is studied for a tubular IPMC sensor under pure torsional stimulus. With inspiration

from the ﬁsh lateral line system, IPMC is then explored for several ﬂow-sensing applications,

where modeling of ﬂuid-structure interactions, sensor design, and experimental validation are con-

ducted. Speciﬁcally, the sensitivities of IPMC-based artiﬁcial superﬁcial and canal neuromasts

are examined in terms of their dimensions, shapes, and stiffness properties. A canal lateral line-

inspired pressure sensor is further proposed and developed. Another novel ﬂow velocity sensor is

proposed, which exploits self-generated von Krmn vortices to produce vibrations that are corre-

lated with the ﬂow speed. Finally, inspired by the vestibular system, an angular acceleration sensor

is proposed.

Firstly, the Poisson-Nernst-Planck (PNP) model is used to describe the fundamental physics

within the tubular IPMC under torsional excitation, where it is hypothesized that the anion con-

centration is coupled to the sum of shear strains induced by the torsional stimulus. Finite element

simulation is conducted to solve for the torsional sensing response, where some of the key pa-

rameters are identiﬁed based on experimental measurements using an artiﬁcial neural network.

Additional experimental results suggest that the proposed model is able to capture the torsional

sensing dynamics for different amplitudes and rates of the torsional stimulus.

Secondly, Inspired by the ﬁsh lateral line system, the sensitivity of IPMC-based artiﬁcial su-

perﬁcial and canal neuromasts are examined in terms of their dimensions, shapes, and stiffness

properties. The PNP model is again used to describe the fundamental physics within the IPMC,

where the bending stimulus due to the cupula displacement is coupled to the PNP model through

the cation convective ﬂux term. Comparison of the numerically computed cupula displacement

with an analytical approximation is conducted.

Thirdly, a novel pressure difference sensor inspired by the canal lateral line is proposed. The

sensor output is experimentally characterized as the ﬁsh-like body is rotated with respect to a dipole

source, which conﬁrms that the sensor is capable of capturing the pressure between the two pores.

Finite element modeling that capture ﬂuid-structure interactions and IPMC physics are conducted

to shed light on the sensor behavior. Finally, the utility of the sensor in underwater robotics is

illustrated via orientation of the ﬁsh-like body towards the dipole source using feedback from the

proposed sensor.

Fourthly, a novel IPMC ﬂow sensor is proposed that exploits self-generated von Krmn vortices

to produce vibrations, the frequency and amplitude of which are correlated with the stream ﬂow.

Experiments are conducted in a ﬂow channel to measure the IPMC output and the free-end dis-

placement of the sheath under different ﬂow speeds. The results indicate that the proposed sensor

structure can produce signiﬁcant oscillatory signals for effectively decoding the ﬂow speed.

Finally, inspired by the vestibular system, an angular acceleration sensor by exploiting IPMC

sensor is proposed. The sensor has one 3D-printed canal ﬁlled with a viscous ﬂuid. Finite-element

simulation based Experimental results involving different angular acceleration stimuli show that

the sensor is able to capture the angular acceleration for different rates of rotational stimulus.

Copyright by
MONTASSAR AIDI SHARIF
2019

Dedicated to my parents, my wife, and my kids with
all my love and gratitude.

v

ACKNOWLEDGMENTS

I would like to express my sincere gratitude to my advisor, Prof. Xiaobo Tan, for providing

me the opportunity to be part of his team in Smart Microsystems Lab during my doctoral study.

His valuable guidance and generous encouragement beneﬁted me a lot in my research and will

continue to beneﬁt me for my future career.

I want to thank all my Ph.D. committee members: Prof. Guoming Zhu, Prof. Linxin Dong,

and Prof. Wen Li at Michigan State University, for kindly joining my advisory committee and

offering me insightful comments. I also thank our research collaborators, Prof. Matthew McHenry

at University of California, Irvine, Prof. Derek A. Paley at University of Maryland, and Prof.

Kalyanmoy Deb at Michigan State University, for their constant support and kind help in my

research projects.

I would like to thank the ECE technical staff, ECE cleanroom committee, and ECE cleanroom

colleagues for their advice and assistance on my fabrication work in ECE cleanroom at Michigan

State University, in particular, Brian Wright and Karl Dersch.

I would also like to thank Dr.

Sandrine Martin in the Lurie Nanofabrication Facility (LNF) for her help on my fabrication work

in LNF at University of Michigan.

I am grateful to all my colleagues and friends who have offered help in various ways, especially

to Mohammed Al-Rubaiai, Dr. Hong Lei, John Thon, Dr. Feitian Zhang, Dr. Jianxun Wang, Dr.

Sanaz Behbahani, Dr. Jun Zhang, Dr. Ali Ahrari, Jason Freeberg, Demetris Coleman, Hongyang

Shi, Maria Castano, Thassyo Pinto, Pratap Bhanu Solanki, Osama En-Nasr, Cody Thon, Husien

Hasan, Ameer Janabi, Ali Al-Awadi, and Maher Al-Sahlani. Their encourgments, comments, and

collaboration have helped my research a lot. Thanks also to all of the administrators and staff

vi

members in the ECE department for their assistance over the years.

I would also like to acknowledge the ﬁnancial support from the Ofﬁce of Naval Research

(N000141512246) and the Higher Committee for Educational Development in Iraq (HCED).

Most of all, I am foremost thankful for my family. I would like to thank my mother, Kareema

Khudier Faraj, my father, Aidi Sharif, and my brother, Dr. Montadher Aidi Sharif, for their all-

enduring love and everlasting support in this life journey. I would like to express my ultimate

gratitude to my brothers and sisters for their everlasting support to pursue my dreams. Special

thanks to my wife, Shaimaa Faisal Jasim – I am deeply grateful for her selﬂess love, support, and

encouragement, and to my kids for their love. This dissertation would not have been possible

without their years of encouragement and continuous support in both good times and bad times.

vii

TABLE OF CONTENTS

LIST OF TABLES .

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LIST OF FIGURES .

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xi

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. xii

Chapter 1 Introduction .

1.1
1.2

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.

.

1
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
Ionic Polymer-Metal Composites . . . . . . . . . . . . . . . . . . . . . . . . . . .
3
IPMC - based Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3
1.2.1
Ionic Polymer-Metal Composite Torsional Sensor . . . . . . . . . . . . . .
4
1.2.2 A Bio-inspired Artiﬁcial Lateral Line System . . . . . . . . . . . . . . . .
9
1.2.3 A Pressure Gradient Sensor Inspired by the Canal Neuromasts of Fish . . .
1.2.4
IPMC Flow Sensor Exploiting Self-Generated Vortices . . . . . . . . . . . 12
1.2.5 Angular Acceleration Sensor Inspired by the Vestibular System . . . . . . . 13
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

1.3 Overview of Contributions

Chapter 2 Ionic Polymer-Metal Composite Torsional Sensor: Physics-based Model-

.

.

.

.

PNP Model

2.1.1
2.1.2 Mechano-electrical Coupling

ing and Experimental Validation . . . . . . . . . . . . . . . . . . . . . . . . 16
2.1 Physics-based Modeling of the Tubular IPMC Sensor under Torsion . . . . . . . . 16
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
. . . . . . . . . . . . . . . . . . . . . . . . 18
2.2 Sensor Fabrication and Experimental Characterization . . . . . . . . . . . . . . . . 19
2.2.1
. . . . . . . . . . . . . . . . . . . . 19
2.2.2 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
Sensor Characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.2.3
2.3 Parameter Identiﬁcation and Model Validation . . . . . . . . . . . . . . . . . . . . 23
2.3.1
Parameter Identiﬁcation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.3.2 Model Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

Fabrication of Tubular IPMC Sensors

Chapter 3 A Bio-inspired Artiﬁcial Superﬁcial Lateral Line System . . . . . . . . . . 33
3.1 Modeling of the Superﬁcial Neuromast . . . . . . . . . . . . . . . . . . . . . . . . 33
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
Simulation Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.3 Comparison between Numerical and Analytical Results . . . . . . . . . . . . . . . 38

3.1.1 Analytical Model
.

3.2 Finite Element Model .

3.2.1

Chapter 4 A Bio-inspired Artiﬁcial Canal-type Lateral Line System . . . . . . . . . . 43
4.1 Modeling of the Canal-type Neuromast . . . . . . . . . . . . . . . . . . . . . . . . 44
Physics-based Modeling of the Canal Neuromast Under Oscillatory Flow . 44
. . . . . . . . . . . . . . . . 47

4.1.1
4.1.2 Analytical Modeling of Cupula Displacement

viii

.

IPMC Flow Sensor Output

4.2 Finite Element Model .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Simulation Setup .
Simulation Results: Cupula Displacement

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
. 48
4.2.1
. . . . . . . . . . . . . . . . . . 51
4.2.2
4.2.3 Comparison between Numerical and Analytical Results . . . . . . . . . . . 58
4.2.4
. 64
4.3 Fabrication of Artiﬁcial Canal Neuromast
. . . . . . . . . . . . . . . . . . . . . . 66
4.4 Characterizations of Artiﬁcial Canal Neuromast in a Dipole Flow . . . . . . . . . . 68
. 68
. 70
4.5 Parameter Identiﬁcation and Model Validation . . . . . . . . . . . . . . . . . . . . 70
. 70
. 73

4.4.1 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4.2 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . .

Parameter Identiﬁcation . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.5.1
4.5.2 Model Validation .

. . . . . . . . . . . . . . . . . . . . . . . . .

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.

5.3 Finite Element Model and Simulation . . . . . . . . . . . . . . . . . . . . . . .

5.1 System Development
5.2 Experimental Characterization . . . . . . . . . . . . . . . . . . . . . . . . . . .

Chapter 5 A Pressure Gradient Sensor Inspired by the Canal Neuromasts of Fish . . 76
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
. 77
5.2.1 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
5.2.2 Experimental Results and Discussion . . . . . . . . . . . . . . . . . . . . 80
. 83
Finite Element Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
Parameter Identiﬁcation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
Simulation Results
5.4 Orientation Control of Fish-like Body with Sensor Feedback . . . . . . . . . . . . 91
Sliding Discrete Fourier Transform (SDFT) Algorithm . . . . . . . . . . . 91
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
Feedback Controller

5.3.1
5.3.2
5.3.3

5.4.1
5.4.2

.

.

.

6.1 Sensor Fabrication .

Chapter 6 IPMC Flow Sensor Exploiting Self-Generated Vortices

. . . . . . . . . . . 97
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
IPMC Flow Sensor Fabrication . . . . . . . . . . . . . . . . . . . . . . . . 97
Sensor Structure Fabrication . . . . . . . . . . . . . . . . . . . . . . . . . 98
. 100
6.2.1 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
6.2.2 Experimental Results and Discussion . . . . . . . . . . . . . . . . . . . . 100

6.2 Experimental Results on Flow Sensing . . . . . . . . . . . . . . . . . . . . . . .

6.1.1
6.1.2

.

.

.

.

. .

Sensor fabrication .

7.1 The Approach .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Chapter 7 Angular Acceleration Sensor Inspired by the Vestibular System . . . . . . 108
. 109
7.1.1
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
7.1.2 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
Sensor Characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
7.1.3
7.1.4
Finite Element Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . 113
7.1.5 Modeling and Simulation Setup . . . . . . . . . . . . . . . . . . . . . . . 117
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
7.1.6
7.2 Comparison between Experimental Measurements and Simulation Results . . . . . 121

Simulation Results

ix

Chapter 8 Conclusions and Future Work . . . . . . . . . . . . . . . . . . . . . . . . . 123
. 123
. 125

.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

8.1 Conclusion .
8.2 Future Work . .

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BIBLIOGRAPHY .

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x

LIST OF TABLES

Table 2.1: Model Parameters of the Tubular IPMC Sensor.

. . . . . . . . . . . . . . . 27

Table 4.1: Model Parameters of Canal-type Neuromasts.

. . . . . . . . . . . . . . . . 74

Table 5.1: Model Parameters of the Pressure Difference Sensor.

. . . . . . . . . . .

. 90

xi

LIST OF FIGURES

Figure1.1:

Illustration of IPMC sensing principle.

. . . . . . . . . . . . . . . . . . . .

2

Figure1.2: Distribution of a lateral line system [1], (a) A ﬁsh with lateral line systems;
(b) The lateral line system with the superﬁcial and canal neuromasts; (c)
Canal neuromasts (CN). . . . . . . . . . . . . . . . . . . . . . . . . . . .

.

5

Figure1.3: The schematic of a lateral line system, showing a single superﬁcial neuro-

mast and a hair cell sensor under oscillatory ﬂow.

. . . . . . . . . . . . . .

7

Figure1.4: The schematic of a canal-type lateral line system schematic, showing a

canal neuromast containing a hair cell-like sensor. . . . . . . . . . . . . . .

9

Figure1.5: The schematic of the proposed sensor, showing a ﬁsh-like structure with
two pores on the front and the artiﬁcial canal neuromast consisting of an
IPMC sensor embedded in a cupula-like structure. . . . . . . . . . . . . . . 11

Figure1.6: The schematic of the proposed IPMC ﬂow sensing structure with self-
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

generated vortices.

. 12

Figure1.7: The schematic of the proposed sensor, showing a circular canal consisting

of an IPMC sensor embedded in cupula-like structure. . . . . . . . . . . . . 13

Figure2.1:

Fabricated tubular IPMC sensor.

. . . . . . . . . . . . . . . . . . . . . . . 21

Figure2.2:

(a) Experimental setup involving the torsion assembly, conditioning circuit
for the sensing output, and dSPACE system for data acquisition;(b) Details
of the torsion assembly. . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 22

Figure2.3: The applied sequence of motor inputs in loading/unloading the torsion, ﬁrst
in one direction and then in the other, and the corresponding sensing signal.
Here the motor speed in ramping up/down is 360 ◦/s and the twist angle
magnitude is 10◦.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

xii

Figure2.4: Testing results: a comparison between the experimental measurement and

the simulation model after applying 10◦ twisting angle.

. . . . . . . . . . . 27

Figure2.5:

Input trajectory: two different stepper motor speeds to reach a speciﬁc angle 28

Figure2.6: Comparison between the experimental measurement and model prediction
of the sensor response under different torsional stimuli: (a) Torsion mag-
nitude 10◦, speed 360◦/s; (b) Torsion magnitude 10◦, speed 180◦/s; (c)
Torsion magnitude 15◦, speed 360◦/s; (d) Torsion magnitude 15◦, speed
180◦/s; (e) Torsion magnitude 20◦, speed 360◦/s; (f) Torsion magnitude
20◦, speed 180◦/s.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

Figure2.7: The simulated sensing response when the model in [2] is adopted for the

stimulus of magnitude of 10◦ and rate of 360◦/s.

. . . . . . . . . . . . . . 30

Figure3.1: The ﬁnite-element modeling of a superﬁcial neuromast in the presence of
a dipole stimulus, where the cupula in the cylindrical shape. The top color
bar represents deﬂection of the IPMC sensor beam while the lower color
bar represents the ﬂow velocity around the cupula. . . . . . . . . . . . . . . 36

Figure3.2: The ﬁnite-element modeling of a superﬁcial neuromast in the presence of
a dipole stimulus, where the cupula in the cone shape. The top color bar
represents deﬂection of the IPMC sensor beam while the lower color bar
represents the ﬂow velocity around the cupula. . . . . . . . . . . . . . . . . 37

Figure3.3: Displacement magnitude of the cupula structure with four different shapes
as a function of the dipole frequency, where two Young’s moduli were used
10 KPa (ﬂex) and 0.2 MPa (stiff). . . . . . . . . . . . . . . . . . . . . . . . 38

Figure3.4: Comparison between the FE model and the analytical model cm-scale cupula

structures.

.

.

.

.

.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

Figure3.5: Comparison between the FE model and the analytical model µm-scale
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

cupula structures.

.

. 42

xiii

Figure4.1:

Finite-element modeling of a canal neuromast in the presence of a dipole
stimulus. The left color bar represents the ﬂow velocity within the canal.
The upper right color bar represents deﬂection of the IPMC sensor beam
while the lower right color bar represents the deﬂection of the cupula-like
structure.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

.

.

.

.

Figure4.2: An example of cupula displacement trajectory for a 280 Hz dipole stimulus,
where the radius of the cupula was 0.7 mm and the Young’s modulus was
2000 Pa. .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

.

.

.

.

Figure4.3: Exacted amplitude of cupula movement, where the radius of the cupula was

0.7 mm and the Young’s modulus was 2000 Pa.

. . . . . . . . . . . . . . . 52

Figure4.4: Displacement magnitude of the cupula structure with radius 0.7 mm as a
function of the dipole frequency, where the Young’s modulus was 300 Pa.

. 53

Figure4.5: The comparison with radius 0.7 mm as a function of the dipole frequency,

where the Young’s modulus was 2000 Pa for both. . . . . . . . . . . . . . . 54

Figure4.6: The comparison of the displacement responses between the two mm scale

cupula structures, where the Young’s modulus was set to be 5000 Pa for both. 55

Figure4.7: Comparison of the displacement responses of cupula structures (radius of

0.7 cm) with different Young’s moduli (300 Pa and 600 Pa). . . . . . . . . . 56

Figure4.8: Comparison between the FE model and the analytical model for capula
radius of 0.7 mm and Young’s modulus of 2000 Pa. The sliding stiffness in
the analytical model = 2.6 N/m. . . . . . . . . . . . . . . . . . . . . . . .

. 58

Figure4.9: Comparison between the FE model and the analytical model for capula
radius of 0.35 mm and Young’s modulus of 2000 Pa. The sliding stiffness
in the analytical model = 1.2 N/m.

. . . . . . . . . . . . . . . . . . . . . . 59

xiv

Figure4.10: Comparison between the FE model and the analytical model for capula
radius of 0.7 mm and Young’s modulus of 5000 Pa. The sliding stiffness in
the analytical model = 5.4 N/m. . . . . . . . . . . . . . . . . . . . . . . .

. 60

Figure4.11: Comparison between the FE model and the analytical model for capula
radius of 0.35 mm and Young’s modulus of 5000 Pa. The sliding stiffness
in the analytical model = 1.9 N/m.

. . . . . . . . . . . . . . . . . . . . . . 61

Figure4.12: Comparison between the FE model and the analytical model for capula
radius of 0.7 cm and Young’s modulus of 300 Pa. The sliding stiffness in
the analytical model = 1.52 N/m.
. . . . . . . . . . . . . . . . . . . . . .

. 62

Figure4.13: Comparison between the FE model and the analytical model for capula
radius of 0.7 cm and Young’s modulus of 600 Pa. The sliding stiffness in
the analytical model = 3.6 N/m. . . . . . . . . . . . . . . . . . . . . . . .

. 63

Figure4.14: Simulation results on the IPMC sensor beam embedded in the cupula: (a)
Sensor beam displacement; (b) Electrical potential distribution within the
Naﬁon polymer; (c) Electrical charge density distribution in the vicinity of
the IPMC electrodes.
. . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 65

Figure4.15: Fabrication of cupula-like structure: (a) design schematic of the cupula-like
structure; (b) 3D-printed mold parts; (c) fabricated IPMC ﬂow sensor (1 cm
long, 1 mm wide); (d) cupula-like structure-inspired IPMC ﬂow sensor.

. . 67

Figure4.16: Experimental setup: (a) the canal assembly, mini shaker to apply a vibrating
motion, laser sensor to measure the mini-shaker displacement; (b) Details
of the canal assembly. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 69

Figure4.17: Measured stress-strain relationship curve for identifying the Young modu-

lus of the artiﬁcial canal neuromast.

. . . . . . . . . . . . . . . . . . . . . 72

Figure4.18: Comparison between the experimental and the simulation sensing signal
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

for two distances.

.

. 75

xv

Figure5.1:

3D-printed ﬁsh-like structure with two pores to be covered with natural
latex rubber membranes.
. . . . . . . . . . . . . . . . . . . . . . . . . .

. 78

Figure5.2:

Fabrication of the proposed sensor: (a) fabricated IPMC ﬂow sensor (1.5
cm long, 2 mm wide); (b) 3D-printed cupula-structure with the IPMC sen-
sor inserted.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

.

.

.

Figure5.3:

Picture of the experimental setup. . . . . . . . . . . . . . . . . . . . . . . . 80

Figure5.4: Experimental measurements of the sensor output where the ﬁsh-like struc-

ture is at different angles relative to a dipole source.

. . . . . . . . . . . . . 82

Figure5.5: The dipole displacement and the acceleration in the frequency range 2 to

30 Hz.

.

.

.

.

.

.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

Figure5.6: Comparison of the sensor frequency response at different angles relative to
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

the dipole source.

.

. 84

Figure5.7: The ﬁnite-element modeling of a ﬁsh-like pressure difference sensor in the
presence of a dipole source. The upper color bar represents the ﬂow veloc-
ity within and around the sensor while the lower color bar represents the
deﬂection of the membrane and the cupula-inspired IPMC ﬂow sensor. . .

. 85

Figure5.8: Experimentally obtained stress-strain curve of the cupula structure for esti-
mating Young’s modulus. . . . . . . . . . . . . . . . . . . . . . . . . . .

. 88

Figure5.9:

Snapshots of simulation showing the membrane and the cupula displace-
ment (units in mm) when the ﬁsh-like structure is oriented with different
angles relative to the dipole stimulus, where the upper color bar represents
the membrane displacement and the bottom color bar represents the cupula
displacement: (a) 0◦; (b) 30◦; (c) 45◦ (d) 60◦; (e) 75◦ (f) 90◦. . . . . . . . . 92

Figure5.10: Computed magnitudes for the displacement of the membrane and for the

tip displacement of the cupula, respectively.

. . . . . . . . . . . . . . . . . 93

xvi

Figure5.11: Comparison between the experimental and the simulation sensing signal. . . 94

Figure5.12: Magnitude trajectory of the IPMC sensor under the feedback control, acti-

vated at about t = 1.3 seconds.

. . . . . . . . . . . . . . . . . . . . . . . . 96

Figure6.1:

Fabrication of the IPMC ﬂow-sensing structure with self-generated vor-
tices: (a) a parylene-encapsulated IPMC sensor; (b) design schematic of
the ﬂow-sensing structure; (c) 3D-printed structure with a sphere, a sheath,
and a mounting shaft.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

Figure6.2: Experimental measurements of the sensor tip displacement and current out-
put, in response to sheath laminar ﬂow of 35 cm/s: (a) measured sheath tip
displacement; (b) measured short-circuit current of the IPMC ﬂow sensor.

. 102

Figure6.3: Experimental measurements of the sensor tip displacement and current out-
put, in response to sheath laminar ﬂow of 35 cm/s: (a) spectral content of
the sheath tip displacement; (b) spectral content of the IPMC current output. 103

Figure6.4: Experimental measurements of the sensor tip displacement and current out-
put, in response to sheath laminar ﬂow of 70 cm/s: (a) measured sheath tip
displacement; (b) measured short-circuit current of the IPMC ﬂow sensor.

. 104

Figure6.5: Experimental measurements of the sensor tip displacement and current out-
put, in response to sheath laminar ﬂow of 70 cm/s: (a) spectral content of
the sheath tip displacement; (b) spectral content of the IPMC current output. 105

Figure6.6: Average amplitude of the sheath displacement and the IPMC sensing signal. 106

Figure6.7: Average frequency of the sheath displacement and the IPMC sensing signal. 107

Figure7.1:

Fabrication of the proposed sensor: (a) 3D-printed vestibular system circu-
lar canal device; (c) fabricated IPMC ﬂow sensor (1 cm long, 1 mm wide);
(d) 3D-printed cupula-structure with the IPMC sensor inserted.

. . . . . . . 110

xvii

Figure7.2: Experimental setup involving a details of the rotational assembly. . . . . . . 111

Figure7.3: The applied sequence of the stepper motor inputs in acceleration/decelera-
tion and the corresponding sensing signal from the IPMC. Here the constant
angular velocity is 31 rad/s and the acceleration/deceleration is 62 rad/s2.

. 112

Figure7.4: Experimental measurements of the sensor response under different acceler-
ation stimuli and one angular velocity which is 31 rad/s: (a) Angular accel-
eration 62 rad/s2 with viscous ﬂuid; (b) Angular acceleration is 62 rad/s2
with water; (c) Angular acceleration is 62 rad/s2 with air; (d) Angular
acceleration 125 rad/s2 with viscous ﬂuid; (e) Angular acceleration is
125 rad/s2 with water; (f) Angular acceleration is 125 rad/s2 with air;(g)
Angular acceleration 188 rad/s2 with viscous ﬂuid; (h) Angular accelera-
tion is 188 rad/s2 with water; (i) Angular acceleration is 188 rad/s2 with
air. .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

.

.

.

.

.

.

.

Figure7.5: Experimental measurements of the sensor response under different accel-
eration stimuli and one angular velocity which is 31 rad/s: (a) Angular
acceleration 251 rad/s2 with viscous ﬂuid; (b) Angular acceleration is
251 rad/s2 with water; (c) Angular acceleration is 251 rad/s2 with air;
(d) Angular acceleration 314 rad/s2 with viscous ﬂuid; (e) Angular accel-
eration is 314 rad/s2 with water; (f) Angular acceleration is 314 rad/s2
with air.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

.

.

.

.

.

. 114

. 115

Figure7.6:

Frequency response of the IPMC sensor output under sinusoidal stimuli
with different angular accelerations.

. . . . . . . . . . . . . . . . . . . . . 116

Figure7.7: The schematic of the proposed sensor, showing a circular canal consisting

of an IPMC sensor embedded in cupula-like structure. . . . . . . . . . . . . 118

Figure7.8: The schematic of the proposed sensor, showing a circular canal consisting

of an IPMC sensor embedded in cupula-like structure. . . . . . . . . . . . . 119

Figure7.9: The input trajectory to the circular canal with the correspondence sensor

displacements. . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

xviii

Figure7.10: The IPMC sensor tip displacement and the IPMC sensor output (short cir-
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

cuit current). .

. .

. 120

Figure7.11: Comparison between the FE model and the experimental measurements of
the sensor response under different acceleration stimuli and one angular
velocity which is 16 rad/s: (a) Angular acceleration 15.6 rad/s2 with vis-
cous ﬂuid; (b) Angular acceleration is 31.2 rad/s2 with viscous ﬂuid; (c)
Angular acceleration is 40.3 rad/s2 with viscous ﬂuid.

. . . . . . . . . . . 122

xix

Chapter 1

Introduction

Ionic polymer-metal composites (IPMCs) have inherent sensing properties. They hold strong

promise for versatile applications as sensors for their direct mechanosensory property and inherent

polarity. A physics-based dynamic model and novel bio-inspired sensing applications of IPMCs

are presented in this dissertation. In this introduction, a brief background is ﬁrst presented, fol-

lowed by a summary of contributions of this work.

1.1

Ionic Polymer-Metal Composites

Ionic-polymer metal composites (IPMCs) represent a class of electroactive polymers (EAPs), and

have built-in actuation and sensing capabilities [3–5]. Basically, IPMCs can convert mechanical

energy into electrical energy and vice versa [6]. In the past two decades, they have received sig-

niﬁcant interest because of their inherent polarity, high sensitivity, and ability to work in wet and

dry environments. They are also bio-compatible and amenable to microfabrication [7–11].

In

particular, they hold strong promise for versatile applications because they require low-actuation

voltages to generate large bending deformation, work in both air and water without stringent pack-

aging requirements, and exhibit direct electromechanical and mechanoelectric transduction, which

minimizes the structural complexity in implementation as actuators and sensors [12, 13].

An IPMC typically consists of a thin ion-exchange membrane (e.g., Naﬁon), chemically plated

1

Figure 1.1: Illustration of IPMC sensing principle.

with a layer of noble metal (e.g., platinum) as electrodes on both surfaces [7, 14], as shown in

Fig. 1.1. The traditional fabrication of IPMCs follows the process of impregnation, reduction,

and ion-exchange [7]. Inside the polymer, anions are covalently ﬁxed to polymer chains and bal-

anced by cations that can move freely in the membrane. A mechanical deformation on an IPMC

sensor breaks this charge balance, leading to the redistribution of the cations and accompanying

solvent molecules inside the polymer, as well as the generation of a detectable sensing signal

across the electrodes, which can be the open-circuit voltage or short-circuit current. Recent studies

on characterization, modeling, and modeling of IPMC can be found in [15–22]. Recent appli-

cations of IPMC sensing capability span measurement of displacement [23], shear loading [24],

curvature [25], structural health monitoring [18], and energy harvesting [26–29]. They are also

bio-compatible and amenable to fabrication [7, 8, 10, 11, 30, 31], including 3D-printing [32, 33].

IPMC-based ﬂow applications can be found in [34–38].

2

1.2

IPMC - based Applications

1.2.1 Ionic Polymer-Metal Composite Torsional Sensor

Reported IPMC sensors typically take the shape of beams because thin Naﬁon ﬁlms are often

used as raw material in the fabrication. Such IPMC sensors only respond to mechanical stimuli

acting perpendicular to the beam plane. There have been reports on IPMC actuators or sensors

of tubular [39], cylindrical [40], and columnar [41] shapes, which can bend in all directions. A

tube-shaped IPMC transducer [2] with patterned outer electrodes was examined by Kim’s group

through ﬁnite element simulations. Its sensing response was experimentally investigated under

bending excitation. The buckling effect of IPMC pipes was analyzed by Shen et al. [42]. Our

group previously presented a thin-wall tubular IPMC sensor fabricated with Naﬁon tubing [43].

The sensor had one common inner electrode and four patterned outer electrodes, and its sensing

response under tip-bending excitation was captured with a physics-based model [44]. As discussed

above, IPMC sensors, regardless of their shapes, have been mostly studied under bending stimuli.

We ﬁrst reported the effect of torsion sensing for a tubular IPMC device and proposed a preliminary

model for describing the sensing behavior in [45], where the charge densities at the inner and

outer boundaries were assumed to be proportional to the difference of shear stresses at the two

boundaries. While that model showed some agreement in magnitude frequency response with

empirical measurement, the match in phase response was less than satisfactory. In particular, the

model’s phase response shows appreciable positive offset (error) from the empirical data when

the frequency is above 4 Hz. Furthermore, since the charge density depends on the densities of

both anions and cations, and the (mobile) cation density itself is a state variable that evolves with

dynamics, assuming a prescribed charge density at the boundary is unnatural. In this work, we

3

present an alternative, physics-based modeling approach for the torsional sensing response of an

IPMC tube. Compared with [45], this approach not only adopts a more natural assumption, which

prescribes the anion concentration in terms of the local shear strain state induced only by the

torsion, but also is supported by extensive experimental results that involve transient responses.

In this work the Poisson-Nernst-Planck (PNP) model is adopted to describe the fundamental

physics within the IPMC. In particular, the Nernst-Planck equation is used to describe the ionic

current inside the polymer, due to cation diffusion, electric ﬁeld-induced migration, and convec-

tion. Poisson’s equation is used to describe the electric potential, which affects the cation migration

ﬂux. The external torsional stimulus is coupled to the PNP model through the cation convective

ﬂux term, where the cation velocity is affected by the solvent pressure, which is related to the poly-

mer pressure caused by the applied mechanical stimulus, as adopted in [2]. A key innovation of the

current work is that, we further assume that the anion concentration is perturbed by the local shear

strain states induced by the torsion. This is inspired by the assumption used in [2], which relates

the volumetric strain caused by the bending stimulus to the anion concentration. Based on the pro-

posed model, time-dependent 3D ﬁnite element simulation is conducted for a tubular IPMC sensor

under torsional excitation. Experiments are further conducted to compare the sensor response un-

der torsional load with the simulation results, where a novel artiﬁcial neural network-based method

is used to estimate key parameters of the physical model.

1.2.2 A Bio-inspired Artiﬁcial Lateral Line System

The lateral line system is a ﬂow-sensing organ found in ﬁshes and amphibians. The lateral line is

ﬂow-sensing involved in various biological behaviors, such as schooling [46], predator detection,

prey capture [1], and obstacle avoidance [47]. The lateral line system is comprised of arrays of

4

Figure 1.2: Distribution of a lateral line system [1], (a) A ﬁsh with lateral line systems; (b) The
lateral line system with the superﬁcial and canal neuromasts; (c) Canal neuromasts (CN).

ﬂow sensors, which are mechanoreceptive units called neuromasts. A neuromast consists of a bun-

dle of sensory hair cells enveloped in a gelatinous cupula [48]. There are two types of neuromasts,

superﬁcial neuromasts and canal neuromasts, as shown in Fig. 1.2. The superﬁcial neuromasts

extend from the skin and are directly exposed to the ﬂow, where they tend to respond to the local

ﬂow velocity [49]. The canal neuromasts are found in canals recessed in the skin below the scales

of ﬁsh [50] and they tend to react to the local pressure gradients, as illustrated in Fig. 1.2 (c). The

response of the neuromasts in response to the interaction with the ﬂow motion, in the form of ac-

tion potentials, is transmitted to the central nervous system for further information processing [51].

The lateral line system of ﬁshes has inspired a numerous number of efforts in designing and

developing an engineering equivalent of similar sensing modality to facilitate the navigation, co-

5

ordination, control of underwater robots and vehicles [52], object tracking [53], and dipole source

characterization [37]. Such an artiﬁcial lateral line system offers the potential to introduce a novel

and noiseless ﬂow sensing modality complementary to traditional underwater vision sensors and

sonars. Several research groups have reported hair cell-inspired ﬂow sensors that to varying de-

grees have been motivated by ﬁsh neuromasts, exploiting micro-fabrication techniques [54, 55],

optical transduction [56], and novel sensing materials such as ionic polymer-metal composites

(IPMC) [30, 38, 41, 57]. While the majority of these sensors emulate the superﬁcial neuromasts,

some efforts have focused on canal-type lateral lines [58–60].

Modeling of the lateral line system plays a key role in understanding the dynamic behavior of

the neuromasts and optimizing the design of artiﬁcial lateral lines. Much of the modeling litera-

ture focuses on the computation of ﬂow ﬁelds around the ﬁsh body [61–64]. On the other hand,

analytical or semi-analytical approaches have been employed in understanding the dynamics of

superﬁcial neuromasts [65] and canal neuromasts [66, 67] in response to ﬂow stimuli.

In this work IPMC sensors are exploited to create artiﬁcial lateral line sensors, where both su-

perﬁcial and canal-type artiﬁcial neuromasts are investigated. Additional bio-inspired sensors are

proposed, designed, modeled, and experimentally characterized. A more detailed account of the

contributions follow.

1.2.2.1 Superﬁcial lateral line system

Modeling of the lateral line system plays a crucial role in understanding the dynamic behavior of

the superﬁcial neuromast and then optimizing a lateral line device. McHenry et al. in [65] modeled

the boundary layer created by the ﬂow ﬁeld around the superﬁcial neuromasts and its inﬂuences on

the cupula sensitivity when the stiffness and the size of the cupula changes. Further more, Sharif

6

Figure 1.3: The schematic of a lateral line system, showing a single superﬁcial neuromast and a
hair cell sensor under oscillatory ﬂow.

et al. in [68] reported that the sensitivity of the cupula is signiﬁcantly inﬂuenced by the shape and

stiffness of the cupula. In particular, the sensing performance of a superﬁcial neuromast depends

on mechanical properties of the cupula as well as the cupula morphology. Generally, the shape and

size of the cupula affect both the ﬂuid forces that may be generated by a stimulus and the structural

resistance to these forces [65].

Fig. 1.3 shows the schematic of the lateral line system under consideration, where one su-

perﬁcial neuromast is considered. This conﬁguration provides a reasonable approximation to the

biological superﬁcial neuromast and resembles the setup considered in [65], where the mechanical

sensitivity of the neuromast under an oscillatory ﬂow was analytically derived. A ﬁnite-element

modeling approach is taken in this work for several reasons. First, as a higher-ﬁdelity model, the

ﬁnite-element model is instrumental in exploring the validity of the analytical model in [65]; due

to its analytical but also physical nature, the latter, if validated, could serve as a convenient tool in

the design of artiﬁcial lateral lines. Second, the proposed approach is expected to be useful when

dealing with sensors larger than the scale of biological neuromasts, in which case some assump-

7

tions made in [65] start to fail. Third, the proposed approach enables natural integration with the

physical model of IPMC, thus allowing the analysis of electrical output of the IPMC-based canal

neuromast in response to ﬂow stimuli.

1.2.2.2 Canal-type lateral line system

We model a canal-type lateral line system with an emphasis on the mechanical behavior of the

hemisphere-like canal neuromast. We further consider that an IPMC beam, embedded in the

cupula, serves as an artiﬁcial hair cell sensor that produces an electrical output in response to

the motion of the cupula. The use of IPMC sensors for superﬁcial lateral line systems has been

reported in the past [30, 57, 64, 65], and this work, for the ﬁrst time, investigates its use in canal-

type lateral line systems. We validate the ﬁnite element model experimentally with a custom-made

artiﬁcial canal-type lateral line. The canal is composed of a rigid cylindrical canal, which is ﬁlled

with a viscous ﬂuid. The prototype is comprised of one IPMC ﬂow sensor, embedded in a cupula-

like structure and placed at the middle of the canal, serving as an artiﬁcial hair cell sensor that

produces an electrical output in response to the cupula motion. Experiments are conducted in an

AC ﬂow generated by a dipole source. The magnitudes of the IPMC short-circuit current output

are extracted from the collected data to compare the sensor response under the dipole ﬂow with

the simulation results. A novel parameter identiﬁcation approach from [69] is used to estimate key

parameters of the ﬁnite element model. Fig. 1.4 shows the schematic of the system under consid-

eration, where one canal-type neuromast is considered. This conﬁguration provides a reasonable

approximation to the biological canal neuromast and resembles the setup considered in [66], where

the mechanical sensitivity of the neuromast under an oscillatory ﬂow was analytically derived. A

ﬁnite-element modeling approach is taken in this work for several reasons. First, as a higher-

8

Figure 1.4: The schematic of a canal-type lateral line system schematic, showing a canal neuromast
containing a hair cell-like sensor.

ﬁdelity model, the ﬁnite-element model is instrumental in exploring the validity of the analytical

model in [66]; due to its analytical but also physical nature, the latter, if validated, could serve as a

convenient tool in the design of artiﬁcial lateral lines. Second, the proposed approach is expected

to be useful when dealing with sensors larger than the scale of biological neuromasts, in which

case some assumptions made in [66] start to fail. Third, the proposed approach enables natural

integration with the physical model of IPMC, thus allowing the analysis of electrical output of the

IPMC-based canal neuromast in response to ﬂow stimuli.

1.2.3 A Pressure Gradient Sensor Inspired by the Canal Neuromasts of Fish

It is of interest to develop and implement an engineering counterpart of the biological lateral line

system for underwater applications. The artiﬁcial lateral line system will provide a novel sensing

modality for navigation and control of underwater robots and vehicles [34], and offers a cryptic

complement to existing vision sensing modules such as sonar and camera. There have been a

number of efforts in developing artiﬁcial lateral lines [52, 70]. Inspired by the ﬁsh neuromasts,

some groups have reported hair cell-inspired ﬂow sensors by exploiting micro-fabrication [54],

optical transduction [56], and novel sensing materials such as ionic polymer-metal composites

9

(IPMCs) [30, 38, 41, 57, 71]. While the majority of these sensors emulate the superﬁcial neuro-

masts, some works have focused on emulating canal-type neuromasts [60, 68]. The canal-type

neuromasts-based sensing applications have also been explored, including, for example, determi-

nation of object position and vortex shedding frequency [56], source localization [72], and hydro-

dynamic detection [67, 73].

In this work, we present, to our best knowledge, the ﬁrst pressure difference sensor inspired by

the canal neuromasts of ﬁsh. Such a sensor could be used by underwater robots and vehicles for

object detection, angle of attack measurement, and source localization. Unlike most of the afore-

mentioned artiﬁcial lateral line systems on pressure sensing or object localization, where an array

of sensors were used, the proposed sensor utilizes one sensing element embedded in a cupula-like

structure, which is immersed in a canal (a “semicircular” channel) ﬁlled with a viscous ﬂuid. The

employed sensing element, which is an IPMC sensor, serves as an artiﬁcial hair cell sensor that

produces an electrical output in response to the motion of the cupula. As an illustration, the pres-

sure difference sensor is integrated within a ﬁsh-like body, and the two ends of the semicircular

channel are “pores” like the ears of a ﬁsh. Unlike a ﬁsh canal that has open ends to the surface of

the body, the two pores of the proposed sensor are covered with a thin latex membrane, to prevent

the canal ﬂuid from mixing with the ambient ﬂuid.

Fig. 1.5 shows the schematic of the proposed sensor. Experiments are conducted in an AC

ﬂow generated by a dipole source, when the ﬁsh-like body is at different angles with respect to the

dipole. The magnitudes of the IPMC short-circuit current output are extracted from the collected

data. It is found that the sensor clearly responds to the pressure difference between the pores. To

further understand the sensor behavior, time-dependent 3D ﬁnite-element simulation is conducted,

where both ﬂuid-structure interactions and IPMC physics are accommodated. With experimentally

10

Figure 1.5: The schematic of the proposed sensor, showing a ﬁsh-like structure with two pores on
the front and the artiﬁcial canal neuromast consisting of an IPMC sensor embedded in a cupula-like
structure.

identiﬁed model parameters, the proposed model is able to capture the sensor behavior and shed

light on pore membrane deﬂection and cupula displacement under an oscillatory ﬂow of different

angular displacements. To further demonstrate the use of the proposed sensor in potential robotic

applications, feedback control experiments are conducted, to orient the ﬁsh-like body towards the

dipole source based on the sensor output, starting from an arbitrary initial orientation. In particular,

a sliding discrete Fourier transform (SDFT) algorithm [74, 75] is used

11

Figure 1.6: The schematic of the proposed IPMC ﬂow sensing structure with self-generated vor-
tices.

1.2.4 IPMC Flow Sensor Exploiting Self-Generated Vortices

IPMCs-based underwater sensing applications have also been widely investigated. More specif-

ically, proposed application examples have included tracking of a moving dipole [76], ﬂow sen-

sor [34, 38, 71, 77], a vortex-shedding ﬂowmeter [78], and a turbulent ﬂow sensor [79].

In this work, a novel IPMC ﬂow sensor structure is investigated. The proposed device exploits

the self-generated von Krmn vortices to produce vibration of the sensor. Unlike the system de-

scribed by Di Pasquale et al. [78], where an IPMC sensor was rigidly mounted on a circular ﬂow

pipe wall from one end and a cylindrical bluff body was attached on the free end of the IPMC to

generate vortices, the proposed 3D-printed sensor structure consists of a rigid sphere, which is used

to form the von Krmn vortices, and a soft cylindrical sheath that houses the IPMC ﬂow sensor, as

shown in Fig. 1.6. The response of the IPMC sensor due to vortex-induced sheath vibration is in-

vestigated empirically. In particular, experiments are conducted in a ﬂow channel. The magnitudes

and the frequencies of the free sheath vibration and those of the IPMC short-circuit current output

are extracted from the collected data.

12

Figure 1.7: The schematic of the proposed sensor, showing a circular canal consisting of an IPMC
sensor embedded in cupula-like structure.

1.2.5 Angular Acceleration Sensor Inspired by the Vestibular System

It is of interest to develop and implement an engineering counterpart of the biological vestibular

system for robotic applications. An artiﬁcial vestibular system is of interest in robotics, for ex-

ample, for stabilizing the gaze during the robotic head motion or the body movements [80–83].

Angelaki and Cullen [84] reported a vestibular system to used as an inertial sensor contributing

to both spatial orientation and navigation. Developing an engineering equivalent of the biological

semicircular canals to detect the angular acceleration is not reported yet.

In this work, a novel angular acceleration sensor based on artiﬁcial vestibular sensor is inves-

tigated. Unlike the biological counterpart of the vestibular system, which has three semicircular

canals, the proposed 3D-printed sensor is composed of one rigid circular canal (a “torus” channel

13

), which is ﬁlled with a viscous ﬂuid to emulate the biological equivalent. In this work, we reduce

the three-dimensional sensing ability of the vestibular system to one-dimensional to gain more in-

sight about the sensor performance. An IPMC ﬂow sensor, embedded in a cupula and placed on

the top wall of the canal, serves as an artiﬁcial hair cell sensor that produces an electrical output in

response to the motion of the cupula.

Fig. 1.7 shows the schematic of the system under consideration, where one circular canal with

one cupula is considered. Experiments are conducted with rotational stimuli at different accelera-

tions. The IPMC short-circuit current output signals are collected as results of the the accelerations.

To further understand the behavior, time-dependent 3D-ﬁnite element simulation is conducted for

an artiﬁcial vestibular canal under rotational stimuli.

1.3 Overview of Contributions

The contributions of this research mainly lie in the physics-based modeling of IPMC sensors and

the design and fabrication of several novel sensors based on IPMC. The details are as follows.

First, Poisson-Nernst-Planck (PNP) model is adopted to describe the fundamental physics

within the tubular IPMC. The Nernst-Planck equation is used to describe the ionic current inside

the polymer, due to cation diffusion, electric ﬁeld-induced migration, and convection. Poisson’s

equation is used to describe the electric potential, which affects the cation migration ﬂux. The

external torsional stimulus is coupled to the PNP model through the cation convective ﬂux term,

where the cation velocity is affected by the solvent pressure, which is related to the polymer pres-

sure caused by the applied mechanical stimulus. A key innovation of the current work is that, we

further assume that the anion concentration is perturbed by the local shear strain states induced by

14

the torsion.

Second, while the use of IPMC sensors in the superﬁcial lateral line systems has been reported

in the past, and this work, for the ﬁrst time, investigates its use in canal-type lateral line systems.

We have validate the ﬁnite element model experimentally with a custom-made artiﬁcial canal-type

lateral line. Based on the latter ﬁnite-element model, the role of morphology of in sensitivity of

artiﬁcial superﬁcial lateral lines has investigated.

Third, a novel pressure gradient sensor inspired by the canal neuromasts of the ﬁsh is investi-

gated based on 3D-printed ( “U” channel ) integrated with IPMC ﬂow sensor. Unlike the ﬁsh canal

that has open ends to the surface of the body, the two pores of the sensor are covered with thin

latex membrane, to prevent the canal ﬂuid from mixing with the ambient ﬂuid.

Fourth, in this work, a novel IPMC ﬂow sensor structure is investigated. The proposed device

exploits the self-generated von Krmn vortices to produce vibration of the sensor. The proposed 3D-

printed sensor structure consists of a rigid sphere, which is used to generate the von Krmn vortices,

and a soft cylindrical sheath that houses the IPMC ﬂow sensor. The response of the IPMC sensor

due to vortex-induced sheath vibration is investigated empirically.

Fifth, a novel angular acceleration sensor inspired by the vestibular system is investigated using

circular channel, which is ﬁlled with a viscous ﬂuid to emulate the biological equivalent. An IPMC

ﬂow sensor, embedded in a cupula and placed on the top wall of the canal, serves as an artiﬁcial

hair cell sensor that produces an electrical output in response to the motion of the cupula.

15

Chapter 2

Ionic Polymer-Metal Composite Torsional

Sensor: Physics-based Modeling and

Experimental Validation

We have developed a new physics-based model for a tubular IPMC sensor subjected to a torsional

load. The model is built upon the Poisson-Nernst-Planck (PNP) equations for capturing the move-

ment of cations. A key innovation of this work is the proposal of relating the shear strains to the

local anion concentration. An experimental setup is created for applying twist at one end of the

IPMC tube while keeping the other end ﬁxed. Experiments involving stimuli of different magni-

tudes, loading orientations, and loading/unloading speeds have been conducted, and the proposed

model was shown to be able to capture the trends observed experimentally.

2.1 Physics-based Modeling of the Tubular IPMC Sensor un-

der Torsion

The transport of cations within the IPMC under applied loads is governed by the Nernst-Planck

equation (NP) and the electrical potential is related to the charge density via Poisson’s equation

(P). These two equations, collectively known as the Poisson-Nernst-Planck (PNP) equations, along

16

with appropriate coupling relating the mechanical stimulus to the charge density, provide a phys-

ical model for the IPMC sensor. Much of our model development and ﬁnite element modeling

implementation follows the approach in [2] for the case of an omnidirectional bending sensor;

however, there is a key difference in terms of how the external mechanical stimulus (torsion versus

bending) is incorporated into the model.

2.1.1 PNP Model

For an IPMC sensor subjected to an external mechanical load, the induced ion movement leads to

the redistribution of the charge density. The transport of cations is governed by the Nernst-Planck

equation [40]. The ﬂux vector J of cations consists of terms from diffusion, electromigration, and

convection:

(cid:124) (cid:123)(cid:122) (cid:125)

J = −D∇C+
Di f f usion

−zD

1
RT

(cid:124)

Electromigration

FC+∇φ

(cid:123)(cid:122)

(cid:125)

−D

(cid:124)

C+∆V∇P

(cid:123)(cid:122)

1
RT
Convection

(cid:125)

,

(2.1)

where C+ is the cation concentration, z is the charge number of the cation, D is the diffusion

coefﬁcient, R is the gas constant, T is the absolute temperature, F denotes Faraday’s constant, φ is

the electric potential, ∆V is the molar volumetric change, which represents how much the polymer
volume swells after taking water, and (cid:53)P is the solvent pressure gradient. As treated in [2], the
solvent pressure gradient is considered to be balanced by the gradient of the polymer pressure, (cid:53)p,

(cid:53)P = −(cid:53) p,

(2.2)

where p is the average normal stress of the polymer, resulting from solid mechanics calculation

17

subject to the external load.

From the continuity equation

∂C+
∂t = −(cid:53)·J,

(2.3)

where “(cid:53)·” denotes the divergence, one gets the NP equation:

∂C+
∂t + ∇· (−D∇C+ − z

D
RT

FC+∇φ − D
RT

C+∆V∇P) = 0.

(2.4)

The electric potential inside the polymer is related to the charge density ρ

∇2φ = − ρ
κe

,

(2.5)

where “(cid:53)2” denotes the Laplace operator, and κe is the effective dielectric constant of the polymer.

The charge density is related to the ionic concentrations as follows:

ρ = F(C+ −C−)

(2.6)

where C− is the local anion concentration, which is considered to be related to the local shape

change under the applied torsional excitation, as discussed next.

2.1.2 Mechano-electrical Coupling

The anion concentration C− can be related to the local deformation induced by the mechanical
stimulus. This was ﬁrst done in [2], where the authors relate C− to the local volume change

18

(approximated by the divergence of local displacement (cid:53)· u) under a bending stimulus,

C− = C0(1−(cid:53)· u),

(2.7)

where C0 represents the nominal anion concentration in the absence of deformation, and u =
(u1,u2,u3)T represents the displacement along x, y, and z directions, respectively. For a tube under
pure torsion, (cid:53)· u = 0 , thus there would be no change in C− under (2.7). Since the displacement

under torsion is induced by shear, we propose instead

C− = C0(1− γ)

where γ is the sum of the shear strains [85]:

γ = εxy + εyz + εzx.

(2.8)

(2.9)

2.2 Sensor Fabrication and Experimental Characterization

2.2.1 Fabrication of Tubular IPMC Sensors

The fabrication of tubular IPMC sensors generally follows the traditional impregnation, reduction,

and ion-exchange process [44]. The Naﬁon tubing (TT -110, Perma Pure LLC) was used as the raw

material, which had an inner diameter of 2.4 mm, outer diameter of 2.93 mm, and wall thickness

of 265 µm. It was ﬁrst rinsed with acetone then methanol to clean the tubing and to ensure that

the surfaces of the sensor were free from impurities that might affect the fabrication process. Then

the Naﬁon tubing was boiled in dilute hydrochloric acid (2 wt%) for 30 min to remove impurities,

19

and then boiled in deionized (DI) water for another 30 min to remove the acid and swell the ﬁlm.

After these pre-treatment steps, the Naﬁon tubing was immersed in a platinum complex solution

([Pt(NH3)4]Cl2) for more than 4 hours (usually 4–8 hours) to allow platinum ions to diffuse into

the Naﬁon polymer completely through the ion-exchange process. After a rinse with DI water,
the tubing was immersed in a water bath at 40◦C for 30 min. After the temperature was raised to
60◦C, a sodium borohydride solution (5wt% NaBH4 aq) was added to the water bath as a reducing
agent at a rate of 2 ml every 30 min. Once the platinum deposition was complete, those steps were

repeated, from acid treatment to water-bath reduction, to deposit the platinum for the second time.

The tubing was then boiled in DI water for one hour to release the internal stress. After that, it was

put into a sodium chloride solution to exchange the residual platinum ions with sodium ions. The

tubing was then cut into segments of desired lengths. Finally, a tubular IPMC sensor was formed

by attaching two wire connectors to the inner and outer surfaces of the IPMC, respectively. Fig. 2.1

shows the pictures of a fabricated tubular IPMC sensor.

2.2.2 Experimental Setup

To characterize the sensor behavior under torsional excitation, we impose a pure torsional load at

the tip of the tubular IPMC sensor. The short-circuit current between the inner and outer electrodes

is taken as the sensor output. Fig. 2.2 (a) shows the major elements of the setup, including the

torsion assembly that imposes a torsional load on the IPMC tubular sensor, the conditioning circuit

[86] that ﬁlters and ampliﬁes the sensing output, and the dSPACE system (RTI 1104) for data

acquisition. Fig. 2.2 (b) shows the details of the torsion assembly. The tubular IPMC sensor is

ﬁxed with two drill chucks, one on each end. The chucks securely hold the sensor and ensure no

20

Figure 2.1: Fabricated tubular IPMC sensor.

slip when a torsional load is applied. The top end of the IPMC sensor is ﬁxed on a 3D-printed

plate, which is rigidly connected to a metal frame. The lower chuck is attached to a stepper motor

(SparkFun Electronics - ROB 10846) which is used to generate a programmed angle of twist on

the lower end of the IPMC. The stepper motor is controlled via a microcontroller (Arduino-uno).

2.2.3 Sensor Characterization

The responses of the tubular IPMC sensor are characterized with a sequence of torsional stimuli,

to examine both its transient and steady-state behaviors. In particular, the angle of the stepper
motor ﬁrst ramps up from 0◦ to an angle θ in the clockwise direction, holds for 2 s, and then ramps
back down to 0◦; it then holds for 2 s, ramps up to θ in the counterclockwise direction, holds
for 2 s, and ﬁnally ramps back down to 0◦. Fig. 2.3 shows an example of the motor trajectory,
where θ is 10◦, and the speed of the motor when ramping up and down is 360◦/s. We note that

the chosen sequence of the motor movement allows us to examine a number of sensor behaviors,

21

(a)

(b)

Figure 2.2: (a) Experimental setup involving the torsion assembly, conditioning circuit for the
sensing output, and dSPACE system for data acquisition;(b) Details of the torsion assembly.

22

including both the dynamic behavior during transients and the steady state behavior (when the

torsion angle is held constant for 2 s), the polarity of the sensing current during loading/unloading

of the torsional stimulus, and the polarity of the sensing output when the sensor is twisted in

one direction versus the other. Fig. 2.3 also shows the short-circuit current response from the

sensor under the corresponding motor input. It can be seen that, when the torsion is loaded or

unloaded, the sensor current produces a spike, which then approaches zero at the steady state.

Furthermore, the polarities of the spikes during loading and unloading are opposite, and the polarity

is independent of the loading orientation (clockwise or counterclockwise). These rich behaviors

offer good tests for the proposed model.

In addition, as will be discussed in Section 2.3, the

model will be further tested by examining its ability to predict the sensor responses under different

loading/unloading speeds and magnitudes.

2.3 Parameter Identiﬁcation and Model Validation

2.3.1 Parameter Identiﬁcation

Parameters for the model proposed in Section 2.1 are determined and used in model validation.

The sensor dimensions, including the length, the inner and outer diameters, and the thickness of

the platinum electrode layers, are obtained directly through measurement. In particular, the thick-

ness of the platinum layers is computed using the measured thickness of the polymer tubing before

fabrication and that of the fabricated IPMC tube. For the tubular IPMC sensor used in experiments,

the dimensions are: length 15 mm, inner diameter 2.31 mm, outer diameter 3.02 mm. The physical

constants in the model include the temperature (T ), which is measured directly using a thermome-

ter, density (ρ), which is obtained through measuring the sensor weight and volume, the Faraday

23

Figure 2.3: The applied sequence of motor inputs in loading/unloading the torsion, ﬁrst in one
direction and then in the other, and the corresponding sensing signal. Here the motor speed in
ramping up/down is 360 ◦/s and the twist angle magnitude is 10◦.

24

constant (F), and the gas constant (R). The value of anion concentration C0 was taken from [44].

The electrical conductivity of the electrode (σ) was determined with the measured sensor surface

resistance and the dimensions of the electrode. Table 2.1 lists the aforementioned parameters and

constants.

The remaining parameters include the Young’s modulus Y , diffusion coefﬁcient D, and dielec-

tric constant ε, all of which are obtained through an artiﬁcial neural network-based data ﬁtting

process. The Matlab toolbox (nnstart) is used to prepare a neural network with three inputs, which

represent the parameters to be tuned, and one output, which represents the model ﬁtting error. We

have used a multilayer perceptron (MLP) network that contains one hidden layer with 10 nodes.

The number of hidden layers and nodes are chosen according to [87]. Speciﬁcally, we use the

imposed motor angle trajectory and the corresponding sensing signal in the ﬁrst two seconds of

the experiment shown in Fig. 2.3, for the purpose of parameter identiﬁcation, and these same pa-

rameters will be used in other scenarios (different loading/unloading magnitudes and rates) of the

experiments for model validation. Since the proposed model for the torsion sensor does not have

an analytical input-output relationship expressed in terms of the parameters, ﬁnite element simu-

lation is used to obtain the predicted sensing signal trajectory for the prescribed torsion stimulus,

for any given set of parameters.

The simulation of tubular IPMC sensor model under torsional excitation, as described in Sec-

tion 2.1, is implemented with COMSOL Multiphysics 5.1 ﬁnite element software packages. Four

physics packages are used to implement the sensor model: solid mechanics, transport of diluted

species, general-form PDE to generate the electrical potential within the naﬁon, and electrical cur-

rent physics. The solid mechanics module is used to describe the linear elastic material under

25

torsional excitation. The PNP model, which is used to describe the electrical potential and the

cation concentration inside the Naﬁon during the deformation, is realized through the transport

of diluted species physics and the general-form PDE physics. The implementation of the IPMC

model under torsional stimuli is achieved with two separate computations. The deformation of

the IPMC sensor is calculated ﬁrst, followed by the execution of the PNP model, which uses the

deformation data from the ﬁrst study computation as input. A short-circuit current is collected by

imposing the electrodes with zero potential and integrating the collected current density throughout

the electrode surface.

We follow a tutorial provided by Matlab Inc. [88] to implement the neural network model,

which offers a step-by-step instruction on how to use the command (nnstart). The neural network

model requires a number of input-output data sets to start the training. In addition, the neural

network needs to dedicate some of the input-output sets to test and validate the network after the

training is completed. The average error between the predicted and measured sensing signals is

treated as the output of the neural network for the corresponding input values (i.e., the parameters

used in the simulation). A total of 120 sets of parameters, chosen within feasible ranges of these

parameters, are used in conducting the simulation. Ninety sets of the obtained input-output data are

used to train the neural network, 10 sets are used to test the neural network (cross validation), while

20 sets are used to validate the obtained neural network mode. An overall match of 98% is achieved

between the trained neural network model and the experimental data. The 98% match is used as

stopping criterion to stop the training process which is the highest matching we get in this process.

The established neural network model is then used to serve as a ﬁtness function to the optimization

toolbox (optimtool) to ﬁnd the optimal input vector that minimizes the output, which produces

the optimal parameters (Y,D,ε) for the data ﬁtting. The obtained values for these parameters are

26

Figure 2.4: Testing results: a comparison between the experimental measurement and the simula-
tion model after applying 10◦ twisting angle.

Table 2.1: Model Parameters of the Tubular IPMC Sensor.

F
(C mol−1)
96487

R
(J mol−1K−1)
8.3143

T
(K)

290

z

1

σ
(S m−1)
7000.1

D
(m2 s−1)
3.2× 10−11

C0
(mol m−3)
1056

ε
(F m−1)
5× 10−3

ρ
(kg m−3)
2130

E
(Pa)
3.4× 108

also listed in Table 2.1. Fig. 2.4 shows the comparison between measured signal and the model

prediction based on the identiﬁed parameters. It can be seen that overall the model captures well

the magnitude and transient behavior of the sensing response under the given stimulus.

27

Figure 2.5: Input trajectory: two different stepper motor speeds to reach a speciﬁc angle

2.3.2 Model Validation

The identiﬁed parameters are then used in the simulation of the sensor responses under torsional
stimuli of different magnitudes (10◦, 15◦, 20◦) and loading/unloading rates. In particular, two
loading/unloading speeds, 360◦/s and 180◦/s, are adopted; Fig. 2.5 illustrates the proﬁles of the

two speeds.

Fig. 2.6 (a)-(f) show the comparison between the measured sensor outputs and the model-

predicted sensor outputs under different stimuli. Overall, all ﬁgures show good agreement between

the measurement and model prediction. Given that three of the key model parameters are identiﬁed

using only part of the data under a particular torsional stimulus, the reasonable match across all

cases provides strong support for the validity of the model. Speciﬁcally, the model is able to

capture the magnitude, transients, and polarity of the sensor response. For example, the polarity of

28

(a)

(c)

(e)

(b)

(d)

(f)

Figure 2.6: Comparison between the experimental measurement and model prediction of the sensor
response under different torsional stimuli: (a) Torsion magnitude 10◦, speed 360◦/s; (b) Torsion
magnitude 10◦, speed 180◦/s; (c) Torsion magnitude 15◦, speed 360◦/s; (d) Torsion magnitude
15◦, speed 180◦/s; (e) Torsion magnitude 20◦, speed 360◦/s; (f) Torsion magnitude 20◦, speed
180◦/s.

29

Figure 2.7: The simulated sensing response when the model in [2] is adopted for the stimulus of
magnitude of 10◦ and rate of 360◦/s.

30

the sensing signal is determined only by the loading or unloading trend of the stimulus, instead of

the orientation of the torsional stimulus. The model also predicts correctly that the sensor response

converges to zero at the steady state (for a constant torsion input). For the same loading rate, the

results show that the sensing output magnitude increases with the stimulus magnitude (for example,

see Fig. 2.6 (a), (c), and (e)). For the same stimulus magnitude, a higher loading/unloading rate

results in higher sensing response (for example, see Fig. 2.6 (a) and (b)).

Despite the general good agreement, there are some modest discrepancies between the experi-

mental data and the simulation results, which we attribute mainly to the imperfection in the fabri-

cation of the tubular IPMC sensor and in the experimental setup. This can be seen, for example, in

the experimental curve in Fig. 2.6 (c). The two positive signal spikes, ideally, should be identical;

however, the transient speed of the second spike is appreciably slower than the ﬁrst one, which

can be seen from the increased offset between the simulated curve and the experimental curve for

the second peak. A similar observation can be made for the two negative signal spikes. The latter

could be caused by the rotation asymmetry between clockwise and counterclockwise directions. If

one focuses on the ﬁrst half of each subﬁgure, the agreement between the experimental data and

model prediction is much more consistent.

Finally, to demonstrate the unique utility of the proposed model, we simulate the sensor re-
sponse using the model in [2] for a torsional stimulus of magnitude 10◦ and rate 360◦/s. Recall

that the key difference between the proposed model and the model in [2] is that the latter relates

the volumetric strain to the local anion concentration. From Fig. 2.7, it can be seen that the model

in [2], which was shown to work well for a bending sensor, cannot capture the qualitative behavior

of the tubular IPMC sensor under torsion. In particular, it fails to correctly capture the polarity of

the sensing response as observed in experiments. It also predicts asymmetric positive and negative

31

responses, which are not observed in experiments.

32

Chapter 3

A Bio-inspired Artiﬁcial Superﬁcial Lateral

Line System

Inspired by the superﬁcial neuromasts and the hair cells in the lateral line system of ﬁsh, we

numerically and analytically explore the impact of the size, shape, and the stiffness of a neuromast

on its sensitivity in detecting ﬂow stimuli.

3.1 Modeling of the Superﬁcial Neuromast

3.1.1 Analytical Model

We ﬁrst review the analytical model for the mechanical sensitivity of the cupula structure devel-

oped by MacHenry et al. [65]. In particular, the model relates the morphology of the superﬁcial

neuromasts to the neuromast sensitivity over a range of stimulus frequencies. The model treats

the cupula structure as a long cylinder with a speciﬁc radius and length and calculates the forces

created on the cupula due to the ﬂow. With a setup close to Fig. 1.3, this model is a solution to a

fourth-order governing equation describing the forces acting on the cupula. These solutions pro-

vide predictions of cupular deﬂections as a function of the cupula heights. Unlike the latter model

where they treat the cupula two joined parts of different stiffness, in this work, we treat the cupula-

like structure as a homogeneous part. The inertial force is calculated as the product of acceleration

33

(-ν(z)ω2) and the mass (ρπa2dz) of a beam element

Fm = −ν(z)ω2ρmπa2dz,

(3.1)

where ω is the angular frequency of oscillation (ω=2π f , where f is the stimulus frequency), Fm

is the inertial force, ν is the cupular deﬂection, and ρm is the density of the cupular matrix. The

boundary layer is created due to the ﬂow acceleration and the ﬂow velocity of the boundary layer

is given by:

U(z) = U∞(1− exp(

−z(1 + i)

δ

)),

(3.2)

where U∞ is the stream ﬂow velocity, and δ is the boundary layer thickness. The boundary layer

thickness can be calculated by the following expression:

(cid:115)

δ =

2µ
ρmω ,

where µ is the dynamic viscosity of water and ρm is the density of water.

The deﬂection of the beam can be calculated as:

(cid:34)
1− iωbmδ 4

4EI + iωbmδ 4 exp(

(cid:35)

)

+

(cid:114)iωbm

EI )),

3
∑
j=0

(C j exp( jz 4

−(1 + i)z

δ

ν(z) = −ibwU∞
ωbm

where

(3.3)

(3.4)

bm is the force coefﬁcient for cupular material, and bm can be calculated as:
bm=-4πµk-iπ(ρm+ρw)a2ω + iπ2kµ
L

,

bw is the for coefﬁcient of the ﬂuid, and bw can be calculated as:

34

bw=-4πµk-2iπρwa2ω + iπ2kµ
L

,

k is the viscous drag coefﬁcient,, and k can be calculated as: (k=-

L

L2+(0.25π)2 ),

L is the hydrodynamic force coefﬁcient,, and L can be calculated as:
L=γ+ln( a√
2δ

), where γ is Euler’s constant (γ≈ 0.5772)

ρw is the density of water,
I is the second moment of area(I=π

4 a4),

E is Young’s modulus, and a is the radius of the cupula.

The sensitivity of the neuromast is calculated as the following ratio:

S =

ν(hh)
U∞

,

(3.5)

where hh is the height of interest that we choose to calculate the sensitivity.

3.2 Finite Element Model

3.2.1 Simulation Setup

In this section, we follow the steps in Section 4.2.1 for the simulation setup. The ﬂuid-structure

interaction (FSI) module of COMSOL Multiphysics is used to compute the cupula and the IPMC

sensor displacement under a dipole stimulus. In this section, we assume that the cupula-inspired

IPMC sensor is ﬁxed in a ﬁnite water tank ﬁlled with water. The dipole source is placed within

the tank to generate the periodic ﬂow. To understand the scaling behavior of the canal neuromasts,

two different dimensions are simulated, one at the µm scale and the other at the cm scale. The

µm scale case is closer to the biological scale and is thus relevant to understanding the biological

35

Figure 3.1: The ﬁnite-element modeling of a superﬁcial neuromast in the presence of a dipole
stimulus, where the cupula in the cylindrical shape. The top color bar represents deﬂection of the
IPMC sensor beam while the lower color bar represents the ﬂow velocity around the cupula.

neuromasts and offering meaningful comparison with the analytical modeling results. On the other

hand, the cm scale reﬂects the dimensions of many engineered lateral line devices and is relevant

to practical design of such systems.

The range of dipole frequency use for the µm scale case is 2 to 300 Hz, and that for the cm

scale case is 2 to 24 Hz. These ranges are chosen so that the cupula in each case would produce

sufﬁcient movement and thus sensing signals. The amplitude of the vibration A is set to be much

less than the radius of the sphere [66].

In particular, A is set to be 0.1 µm for the µm scale

cases, and 2 mm for the cm scale cases in this work. Fig. 3.1 and Fig. 3.2 illustrate the simulated

conﬁguration for the superﬁcial lateral line system, where the cupula on the right represents the

cupula (with an IPMC sensor beam embedded) and the sphere on the left represents the dipole

source. Appropriate boundary and initial conditions were used in the simulation. In particular,

the water around the cupula is set to be at rest at time 0. The cupula is fully supported from the

36

Figure 3.2: The ﬁnite-element modeling of a superﬁcial neuromast in the presence of a dipole
stimulus, where the cupula in the cone shape. The top color bar represents deﬂection of the IPMC
sensor beam while the lower color bar represents the ﬂow velocity around the cupula.

bottom, and so is the IPMC beam, which implies that their displacements at the bottom are zero.

The cupula tip is located at the same center line of the dipole. Fig. 3.1 and Fig. 3.2 represent the

ﬂow ﬁeld (mm/s) as well as the displacement of the structure during ﬂuid movement (mm). These

plots represent a slice from the three dimensional canal model. The simulation results in both the

ﬂuid ﬂow proﬁle and the displacement and deformation of the cupula (including the IPMC beam).

Two different geometries of cupula structures are used for the cm scale, one is a cylindrical shape

as in (Fig. 3.1) and the second one is a cone shape as in (Fig. 3.2). Two different aspect ratios are

used in the cylindrical case, the ﬁrst one with a radius of 0.25 cm and length 5 cm, the second one

with a radius of 0.25cm and a length of 2.5 cm. The cone cupula also has two different aspect

ratios, each base and top radius of 0.25 cm and 0.5 cm, respectively and the with two different

lengths (5 cm and 2.5 cm). The distance between the cupula and the dipole source is 2 cm. Similar

setups are used for the µm scale simulation, except all dimensions are scaled down by 1000 times

37

Figure 3.3: Displacement magnitude of the cupula structure with four different shapes as a function
of the dipole frequency, where two Young’s moduli were used 10 KPa (ﬂex) and 0.2 MPa (stiff).

smaller and we do not consider cone shapes. The simulated water tank is a long cylinder closed

at both ends and ﬂat at the bottom with an open boundary from the top. Young’s modulus directly

inﬂuences the sensitivity of the structure, so several different values of Young’s modulus are used

for the cupula structure in the investigation.

3.3 Comparison between Numerical and Analytical Results

As we discussed in 4.2.2, the periodic ﬂuid movement within the water tank produces a periodic

movement of the cupula structure at the same frequency at the steady state. Using fast Fourier

transform (FFT), we can extract the amplitudes of the movement corresponding to different fre-

quencies, as illustrated in Fig. 3.3.

38

Fig. 3.3 shows the amplitude of the cupula displacement as a function of the dipole stimulus

frequency, where four different sizes of cupula (as explained in Section 3.2.1) and two values of

Young’s modulus 10 KPa (ﬂexible) and 0.2 MPa (stiff) are used. In the range of 2 to 24 Hz, it

can be seen that the displacement magnitude of the cupula increases ﬁrst with the frequency of

the dipole until it reaches a maximum at a speciﬁc frequency then drops for the longer cupula

(length = 5 cm). For the cupula with length of 2.5 cm, the amplitude keeps increasing during

that range. These peak frequencies are considered to be related to the resonant frequencies of the

cupula structure in the ﬂuid.

Fig. 3.4 shows the comparison of the simulation results for the two cupula structures at the

cm scale, where the Young’s moduli are set to be 0.2 MPa and 10 KPa for both cupula structures.

From the ﬁgure, the longer cupula structure has a lower peak frequency, as expected. Also, from the

ﬁgure, the softer cupula structure has lower peak frequency. These results are consistent with one’s

expectations, as the resonant frequency of a structure increases with its stiffness and decreases with

its mass (size).

We next present the results on the µm scale cases. As we discussed in Section 4.2.2, the

transition from the cm scale to the µm scale is vital because it will reveal the behavior of the

cupula in biological scales and make connections with the practical engineered lateral lines with

in the cm scale. A cupula structure with radius of 0.25 µm and length of 5 µm is simulated in a

water tank with length of 5 µm. Three different values of Young’s modulus, 80 Pa, 250 Pa, and

500 Pa, are used. Fig. 3.5 shows the sensitivity amplitudes of the cupula structures, where one can

observe that the there is no peak frequency in the cupula response; instead, the cupula shows the

behavior of a low-pass ﬁlter. These results again demonstrate the important roles that dimensions

and stiffness play in the sensor’s sensitivity and appropriate operating frequency range. Overall the

39

Figure 3.4: Comparison between the FE model and the analytical model cm-scale cupula struc-
tures.

40

frequency behavior of the modeled cupula shows good agreement with the behavior of biological

cupula in [65].

41

Figure 3.5: Comparison between the FE model and the analytical model µm-scale cupula struc-
tures.

42

Chapter 4

A Bio-inspired Artiﬁcial Canal-type Lateral

Line System

In this chapter, we investigate the modeling, fabrication and experimental validation of the artiﬁcial

canal-type lateral line system. To emulate the biological counterpart, the canal is ﬁlled with a

viscous ﬂuid. The IPMC sensor physics is coupled to the Fluid-Structure Interaction (FSI) module

for the cupula, allowing the computation of the sensor output in the presence of a dipole ﬂow.

The fabrication process of the IPMC ﬂow sensor and cupula-like structure are described in detail.

Experimental testing in a dipole ﬂow is conducted to explore the sensor performance. Simulation

is conducted to examine the effects of cupula size and stiffness on its displacement under a dipole

stimulus. In particular, the computation results from the ﬁnite-element model are compared with

those predicted by an analytical model to explore the valid regimes of the analytical model. Such

comparisons yield useful insight as to when to use the analytical model for quick exploration of

the design space, and when to resort to the ﬁnite element model for higher-ﬁdelity predictions.

43

4.1 Modeling of the Canal-type Neuromast

4.1.1 Physics-based Modeling of the Canal Neuromast Under Oscillatory

Flow

4.1.1.1 Fluid Structural Interaction (FSI)

The response of a canal neuromast, biological or engineered, is due to the deﬂection of the cupula

structure in the presence of a ﬂow stimulus. To capture the cupula displacement response, a three-

dimensional ﬂuid-structural interaction (FSI) module from COMSOL Multiphysics is considered.

In particular, the model incorporates various material properties and dimensions, including the

canal geometry, cupula shape and size, cupula stiffness, IPMC sensor beam geometry and size, and

ﬂuid density and viscosity. The FSI model uses the incompressible Navier-Stokes equation to de-

scribe the ﬂuid ﬂow and the Hooke’s law to capture the linear elastic material behavior. As detailed

in the next subsection, Poison-Nernst-Plank (PNP) equations are used to model the IPMC sensor

response under a mechanical stimulus, which is generated by the ﬂow-induced capula movement.

4.1.1.2 Modeling of the IPMC Sensor Under Bending Excitation

The modeling of an IPMC sensor under bending excitation starts from the Nernst-Plank equation

(NP) that governs the transport of cations within the IPMC sensor. The electrical potential gener-

ated inside the IPMC is governed by the Poisson’s equation (P). Collectively, these equations form

the PNP system, which, along with suitable coupling with the mechanical stimulus to the charge

density, provides a physical model for the IPMC sensor. The ﬂux vector J of cations consists of

contributions from diffusion, electromigration, and convection:

44

(cid:124) (cid:123)(cid:122) (cid:125)

J = −D∇C+
Di f f usion

−zD

1
RT

(cid:124)

Electromigration

FC+∇φ

(cid:123)(cid:122)

(cid:125)

−D

(cid:124)

C+∆V∇P

(cid:123)(cid:122)

1
RT
Convection

(cid:125)

,

(4.1)

where C+ is the cation concentration, z is the charge number of the cation, D is the diffusion

coefﬁcient, R is the gas constant, T is the absolute temperature, F denotes Faraday’s constant, φ

is the electric potential, ∆V is the molar volume, which represents how much the polymer volume

swells after taking water, and P is the solvent pressure gradient. As treated in [40], the solvent
pressure gradient is considered to be balanced by the gradient of the polymer pressure, (cid:53)p,

(cid:53)P = −(cid:53) p,

(4.2)

where (cid:53)P is the average normal stress of the polymer, resulting from solid mechanics calculation

subject to the external load.

From the continuity equation

∂C+
∂t = −(cid:53)·J,

(4.3)

where “(cid:53)·” denotes the divergence, one gets the NP equation:

∂C+
∂t + ∇· (−D∇C+ − z

D
RT

FC+∇φ − D
RT

C+∆V∇P) = 0.

(4.4)

The electric potential inside the polymer is related to the charge density ρ

(4.5)

∇2φ = − ρ
κe

,

45

where “(cid:53)2” denotes the Laplace operator, and κe is the effective dielectric constant of the polymer.

The charge density is related to the ionic concentrations as follows:

ρ = F(C+ −C−)

(4.6)

where C− is the local anion concentration, which is considered to be related to the local shape

change under the applied bending excitation, as discussed next.

The anion concentration C− can be related to the local deformation induced by the mechanical
stimulus. This was ﬁrst done in [40], where the authors relate C− to the local volume change
approximated by the divergence of local displacement (cid:53)· u,

C− = C0(1−(cid:53)· u),

(4.7)

where C0 represents the nominal anion concentration in the absence of deformation, u = (ux,uy,uz)T
represents the displacement along x, y, and z directions, respectively, and (cid:53)· u is the sum of the

normal strains [89]:

(cid:53)· u = εxx + εyy + εzz.

(4.8)

We solved equations (1)-(8) are simultaneously in COMSOL Multiphysics 5.2a ﬁnite element

software to implement the PNP model and the deformation effects. Four module packages are

used to simulate the sensor model: ﬂuid-structural interaction (FSI), transport of diluted species,

general-form PDE to generate the electrical potential within the naﬁon, and electrical current

physics. The solid mechanics part in the FSI module is used to describe the linear elastic materials

under periodic ﬂow excitation. The PNP model, which is used to describe the electrical poten-

46

tial and the cation concentration inside the Naﬁon during the deformation, is realized through the

transport of diluted species physics and the general-form PDE physics. The implementation of the

IPMC model under consideration is achieved with two separate computations. The deformation of

the IPMC sensor is calculated ﬁrst, followed by the execution of the PNP model, which uses the

deformation data from the ﬁrst study computation as input. A short-circuit current is collected by

imposing the electrodes with zero potential and integrating the collected current density throughout

the electrode surface.

4.1.2 Analytical Modeling of Cupula Displacement

We review the analytical model for the mechanical sensitivity of the cupula structure under a

dipole stimulus which was presented by Van Netten [66]. A dipole source is a vibrating sphere

in the ﬂuid, and it has been used extensively in the investigation of biological and artiﬁcial lateral

lines [90] [37]. With a setup close to Fig. 1.4, the analytical model is a solution to the Navier-

Stokes equation for an incompressible oscillatory ﬂow, for a small amplitude of vibration A for the
uniform ﬂow ﬁeld. Let the ﬂuid displacement be, x = Asin(ωt), where A (cid:28) a with a being the

cupula radius, and ω is the angular frequency. The general form of the governing equation is as

follows

ρ

∂ v
∂t + ∇p− µ∇2v = 0,

∇· v = 0,

(4.9)

(4.10)

where ρ is the ﬂuid density, p is the pressure, v is the ﬂuid velocity, and µ is the dynamic viscosity

of the ﬂuid. The ﬂuid force on the cupula is obtained by integrating the pressure and the shear

stress in the direction of the movement of the sphere, which is in the horizontal direction. The ﬂuid

47

force, which is essential to the deformation of the cupula, is given by

Ff luid = −6πaµAω[(

a

δ + 1)cos(ωt)− a
δ (

2a
9δ + 1)sin(ωt)]

(4.11)

where δ is the boundary layer thickness, ω = 2π f , where f is the stimulus frequency.

To calculate the displacement of the cupula, the latter is modeled as a rigid hemisphere slid-

ing over the sensory epithelium via an elastic coupling with a sliding stiffness S. Let D(t) =

D0 exp(iωt) denote the displacement of the ﬂuid inside the canal, and X(t) = X0 exp(iωt) be the

resulting cupula displacement. It is shown in [66] that X0 is given by

X0 =

√
2(i− 1)(
f
)
ft
√
2(i− 1)(

i(

f
ft
Pc + i(

) + 1
2
f
) + 1
ft
2

)2

3
2 − 1
f
2(
ft
3
2 − 1
f
3 (
ft

)

)2

f
ft

D0,

(4.12)

where f is the stimulus frequency, ft = µ

2πρa2 , and Pc =

Saρ
6πµ2 .

Through the comparison with the ﬁnite-element model, we will explore the validity and limi-

tations of this analytical model, which will offer insight into the choice of models for lateral line

design and analysis.

4.2 Finite Element Model

4.2.1 Simulation Setup

The ﬂuid-structure interaction (FSI) module of COMSOL 5.2 Multiphysics is used to compute the

cupula displacement under a dipole stimulus. The canal is assumed to be ﬁlled with a ﬂuid that

has a viscosity ﬁve times of that of water, which is close to the viscosity of ﬂuid within ﬁsh canals.

48

Figure 4.1: Finite-element modeling of a canal neuromast in the presence of a dipole stimulus. The
left color bar represents the ﬂow velocity within the canal. The upper right color bar represents
deﬂection of the IPMC sensor beam while the lower right color bar represents the deﬂection of the
cupula-like structure.

Emulating the setup in [66], a dipole source is placed within the canal to generate the periodic

ﬂow. To understand the scaling behavior of the canal neuromasts, two different dimensions are

simulated, one at the mm scale and the other at the cm scale. The mm scale case is closer to the

biological scale and the scale considered in analytical modeling, and is thus relevant to understand-

ing the biological neuromasts and offering meaningful comparison with the analytical modeling

results. On the other hand, the cm scale reﬂects the dimensions of many engineered lateral line

devices and is relevant to practical design of such systems.

The range of dipole frequency used for the mm scale case is 60 to 1000 Hz, and that for the cm

scale case is 6 to 30 Hz. These ranges are chosen so that the cupula in each case would produce

sufﬁcient movement and thus sensing signals. The amplitude of the vibration A is set to be much

less than the radius of the sphere [66]. In particular, A is set to be 3 µm for the mm scale cases,

and 30 µm for the cm scale cases in this work. Fig. 4.1 illustrates the simulated conﬁguration for

49

the canal-type lateral line system, where the hemisphere on the left represents the cupula (with an

IPMC sensor beam embedded) and the sphere on the right represents the dipole source. Appro-

priate boundary and initial conditions are used in the simulation. In particular, the viscous ﬂuid

ﬁlling the canal was set to be at rest at time 0. The cupula is fully supported from the bottom, and

so is the IPMC beam, which implies that their displacements at the bottom are zero. The cupula

is located at the same center line of the dipole. Fig. 4.1 represents the ﬂow ﬁeld (mm/s) as well as

the displacement of the structure during ﬂuid movement. The plot is a slice from the three dimen-

sional canal model. The simulation resulted in both the ﬂuid ﬂow proﬁle and the displacement and

deformation of the cupula (including the IPMC beam). Two different sizes of cupula structures are

used for the mm scale, one with a radius of 0.35mm and the other with a radius of 0.7 mm. The

shape of the cupula consists of a hemisphere sitting on a short cylinder. As a result, the heights

of the cupula structures at mm scale are 0.4 mm and 0.8 mm, respectively. The distance between

the cupula and the dipole source is 2 mm. Similar setups were used for the cm scale simulation,

except all dimensions are 10 times of those in the mm scale case. The simulated canal is a long

cylinder closed at both ends and ﬂat at the bottom. For the mm scale simulation, the canal has a

radius of 2 mm and length of 15 mm. Because the shape of the canal plays an important role in

the ﬂow proﬁle [59], we choose the canal in this way to ensure that the periodic ﬂow generated by

the sphere moves easily to deﬂect the cupula-like structure, and to ﬁt the cupula which has a ﬂat

bottom. Young’s modulus directly inﬂuences the sensitivity of the structure, so several different

values of Young’s modulus are used for the cupula structure in the investigation.

50

Figure 4.2: An example of cupula displacement trajectory for a 280 Hz dipole stimulus, where the
radius of the cupula was 0.7 mm and the Young’s modulus was 2000 Pa.

4.2.2 Simulation Results: Cupula Displacement

The periodic ﬂuid movement inside the canal produces a periodic movement of the cupula structure

at the same frequency at the steady state. Fig. 4.2 shows an example of the cupula displacement

response in the presence of a dipole source that vibrates at 280Hz, where the cupula with radius 0.7

mm is used. From the ﬁgure, the displacement (still on track to the steady state) is almost periodic.

Using fast Fourier transform (FFT), we can extract the amplitudes of the movement corresponding

to different frequencies, as illustrated in Fig. 4.3.

Fig. 4.4 shows the amplitude of the cupula displacement as a function of the dipole stimulus

frequency, where the cupula radius is 0.7 mm and its Young’s modulus is 300 Pa. It can be seen

that the displacement increases ﬁrst with the frequency of the dipole until it reaches a maximum at

51

Time (s)00.010.020.030.040.050.060.070.080.090.1Cupula displacement (nm)-1.5-1-0.500.511.5Figure 4.3: Exacted amplitude of cupula movement, where the radius of the cupula was 0.7 mm
and the Young’s modulus was 2000 Pa.

52

Frequency (Hz)01002003004005006007008009001000Absolute magnitude (nm)00.10.20.30.40.50.60.70.80.9Figure 4.4: Displacement magnitude of the cupula structure with radius 0.7 mm as a function of
the dipole frequency, where the Young’s modulus was 300 Pa.

53

Frequency (Hz)050100150200250300350400Disp. magnitude (nm)01234567Figure 4.5: The comparison with radius 0.7 mm as a function of the dipole frequency, where the
Young’s modulus was 2000 Pa for both.

54

Frequency (Hz)1002003004005006007008009001000Disp. magnitude (nm)00.20.40.60.811.21.4Big cupulaSmall cupulaFigure 4.6: The comparison of the displacement responses between the two mm scale cupula
structures, where the Young’s modulus was set to be 5000 Pa for both.

55

Frequency (Hz)1002003004005006007008009001000Disp. magnitude (nm)00.20.40.60.811.21.4Big cupulaSmall cupulaFigure 4.7: Comparison of the displacement responses of cupula structures (radius of 0.7 cm) with
different Young’s moduli (300 Pa and 600 Pa).

56

about 120 Hz. The amplitude then drops with frequency until it reaches another peak (lower than

the ﬁrst one) at about 230 Hz. These peak frequencies are considered to be related to the resonant

frequencies of the cupula structure in the ﬂuid. Overall the frequency behavior of the modeled

cupula shows good agreement with the behavior of biological cupula in [67].

Fig. 4.5 shows the comparison of the simulation results for the two cupula structures at the mm

scale, where the Young’s modulus is set to be 2000 Pa for both cupula structures. From the ﬁgure,

the larger cupula structure has a lower peak frequency, as expected. Fig. 4.6 shows the frequency

responses of the two cupula structures but with a higher Young’s modulus (5000 Pa). It can be

seen that overall the peak frequencies for both structures have increased comparing to the case

with lower Young’s modulus (2000 Pa). These results are consistent with one’s expectations, as

the resonant frequency of a structure increases with its stiffness and decreases with its mass (size).

We next present the results on the cm scale cases. The transition from the mm scale to the cm

scale is crucial because of its relevance to practical engineered lateral lines. A cupula structure

with radius of 0.7 cm is simulated in a canal with length of 15 cm and radius of 2 cm. Two

different values of Young’s modulus, 300 Pa and 600 Pa, are used. Fig. 4.7 shows the displacement

amplitudes of the cupula structures, where one can observe that the peak frequencies are much

lower than those for the mm scale capula structures, and that the softer cupula has a lower peak

frequency. These results again demonstrate the important roles of dimensions and stiffness play in

the sensor’s sensitivity and operating frequency range.

57

Figure 4.8: Comparison between the FE model and the analytical model for capula radius of 0.7
mm and Young’s modulus of 2000 Pa. The sliding stiffness in the analytical model = 2.6 N/m.

4.2.3 Comparison between Numerical and Analytical Results

As stated before, one purpose of this work is to use the numerical model to validate the analytical

model in [66]. The analytical model has a few parameters that need to be identiﬁed. Some param-

eters are readily known from the simulation setting, examples of which include the ﬂuid viscosity

and the canal diameter. The sliding stiffness of the cupula, however, needs to be calculated. To

do this, we use the ﬁnite element model to apply a range of constant loads to the cupula and then

calculate the corresponding displacement. The slope of the obtained displacement-load curve is

taken as the required sliding stiffness in each case of cupula size and stiffness.

To present the results, we have normalized the cupula displacement in the ﬁnite element model

(FE) and the analytical model by the ﬂuid velocity to get the sensitivity A (in the unit of ms),

58

Frequency (Hz)01002003004005006007008009001000Sensitivity A0123FE. modelMath. modelFrequency (Hz)01002003004005006007008009001000Sensitivity B00.511.52FE. modelMath. modelFigure 4.9: Comparison between the FE model and the analytical model for capula radius of 0.35
mm and Young’s modulus of 2000 Pa. The sliding stiffness in the analytical model = 1.2 N/m.

59

Frequency (Hz)01002003004005006007008009001000Sensitivity A0123FE. modelMath. modelFrequency (Hz)01002003004005006007008009001000Sensitivity B00.511.52FE. modelMath. modelFigure 4.10: Comparison between the FE model and the analytical model for capula radius of 0.7
mm and Young’s modulus of 5000 Pa. The sliding stiffness in the analytical model = 5.4 N/m.

60

Frequency (Hz)01002003004005006007008009001000Sensitivity A0123FE. modelMath. modelFrequency (Hz)01002003004005006007008009001000Sensitivity B00.511.52FE. modelMath. modelFigure 4.11: Comparison between the FE model and the analytical model for capula radius of 0.35
mm and Young’s modulus of 5000 Pa. The sliding stiffness in the analytical model = 1.9 N/m.

61

Frequency (Hz)01002003004005006007008009001000Sensitivity A0123FE. modelMath. modelFrequency (Hz)01002003004005006007008009001000Sensitivity B00.511.52FE. modelMath. modelFigure 4.12: Comparison between the FE model and the analytical model for capula radius of 0.7
cm and Young’s modulus of 300 Pa. The sliding stiffness in the analytical model = 1.52 N/m.

62

Frequency (Hz)51015202530Sensitivity A020406080FE. modelMath. modelFrequency (Hz)51015202530Sensitivity B00.10.20.30.40.5FE. modelMath. modelFigure 4.13: Comparison between the FE model and the analytical model for capula radius of 0.7
cm and Young’s modulus of 600 Pa. The sliding stiffness in the analytical model = 3.6 N/m.

63

Frequency (Hz)51015202530Sensitivity A020406080FE. modelMath. modelFrequency (Hz)51015202530Sensitivity B00.10.20.30.40.5FE. modelMath. modeland by ﬂuid acceleration to obtain the sensitivity B (in the unit of nm· s2(mm)−1), to examine the

match between the FE results and the analytical model in the millimeter and centimeter dimensions

scales. Figs. 4.8 - 4.11 show the comparisons for the mm scale cases, while Figs. 4.12 and 4.13

show the results for the cm scale cases. In all these comparisons, for the numerical model, the

ﬂuid displacement amplitude is obtained by averaging the dipole-generated ﬂow ﬁeld close to the

cupula. The detailed information on each comparison (cupula size and Young’s modulus) can be

found in the ﬁgure captions. Overall it can be seen that the FE model has good agreement with

the analytical model for the mm scale cases, both in terms of the value of the peak frequency and

in terms of speciﬁc values of sensitivity. The slight discrepancies between the simulated and ana-

lytical results can be attributed to some ideal assumptions made in deriving the analytical model,

such as the uniform ﬂow ﬁeld (while the dipole-generated ﬂow is not spatially uniform). On the

other hand, in the comparisons for the cm scale cases, even though the peak frequencies still match

well, the discrepancies in sensitivity become much bigger, which points to the limitation of the

analytical model when the cupula is scaled up.

4.2.4 IPMC Flow Sensor Output

The IPMC sensor is embedded inside the cupula, and thus the deformation of the cupula imposes

a mechanical stimulus on the IPMC, which in turn produces an electrical signal. The simulation

of beam IPMC ﬂow sensor model under bending load excitation, as described in Section 4.1, is

implemented with COMSOL Multiphysics 5.2 ﬁnite element software packages. As we stated in

Section 4.1.1.2, four physics packages are used to implement the sensor model: ﬂuid structural-

interaction, transport of diluted species, general-form PDE to generate the electrical potential

within the naﬁon, and electrical current physics. The FSI module is used to describe the linear

64

(a)

(b)

(c)

Figure 4.14: Simulation results on the IPMC sensor beam embedded in the cupula: (a) Sensor
beam displacement; (b) Electrical potential distribution within the Naﬁon polymer; (c) Electrical
charge density distribution in the vicinity of the IPMC electrodes.

elastic material under oscillatory ﬂow. The PNP model, which is used to describe the electrical po-

tential and the cation concentration inside the Naﬁon during the deformation, is realized through

the transport of diluted species physics and the general-form PDE physics. The implementation of

the IPMC model under oscillatory stimuli is achieved with two separate computations. The defor-

mation of the IPMC sensor is calculated ﬁrst, followed by the execution of the PNP model, which

uses the deformation data from the ﬁrst study computation as input. A short-circuit current, which

is the sensor output, is collected by imposing the electrodes with zero potential and integrating the

collected current density throughout the electrode surface. Fig. 4.14 shows a snapshot of displace-

ment, electric potential, and charge distribution within the IPMC when the cupula is subjected to a

dipole stimulus of 18 Hz. Here the cupula has a radius of 0.7 cm with Young’s modulus of 600 Pa,

and the IPMC beam is 7 mm long, 1.2 mm wide, and 0.15 mm thick.

65

4.3 Fabrication of Artiﬁcial Canal Neuromast

The fabrication of the cupula neuromasts is done by poring an Ecoﬂex00-30 (A), Ecoﬂex-30 (B),

and a silicone oil into a 3D-printed mold. The custom-design is created using SolidWorks software.

The prototype is shaped as a smooth hemisphere to mimic a cupula-like structure (Fig. 1.2 (c)).

The prototype is formed with a cap which is used to protect the mixture and to create a place to

insert the IPMC ﬂow sensor. Fig. 4.15 (a) shows the SolidWorks design of the canal-type cupula-

like structure. The diameter of the cupula is 0.7 cm and the height is 0.8 cm. Once the design is

ﬁnalized in SolidWorks, the mold parts are printed with a 3D printer (Objet Connex350, Stratasys

Ltd.), as shown in Fig. 4.15 (b). An ultrasonic cleaning process is conducted to make sure that the

mold is free of any impurities caused by the printing process.

The liquid Ecoﬂex A and B are initially mixed with the Silicon oil in the ratio of 3:1:2 and
injected into the mold. After that, the mold is placed over a hot plate under 70◦C for 15 min-

utes in order to achieve a ﬂexible structure. The IPMC fabrication process follows the traditional

impregnation-reduction ion-exchange process [7, 45, 91]. Following the IPMC fabrication, an ad-

ditional step of encapsulation is conducted with a parylene coating of 20 µm, as can be seen in
Fig. 4.15 (c), followed by a water drive-in process under 70◦C for three days [92]. Finally, the

IPMC sensor is inserted into the cupula structure (in particular, the slot) through the slit at the

bottom of the cupula-like structure. Fig. 4.15 (d) shows the fabricated cupula-type with the IPMC

sensor embedded in the center of the structure. In this paper, one type of cupula-like structure is

studied with ﬁxed dimensions and stiffness. Both of which can be modiﬁed for the future work

by changing the mold design to implement different cupula-type dimensions, and by adjusting the

ratio of the raw materials and/or changing the baking temperature respectively to have a variety

values of Young’s Modulus.

66

(a)

(b)

(c)

(d)

Figure 4.15: Fabrication of cupula-like structure: (a) design schematic of the cupula-like structure;
(b) 3D-printed mold parts; (c) fabricated IPMC ﬂow sensor (1 cm long, 1 mm wide); (d) cupula-
like structure-inspired IPMC ﬂow sensor.

67

4.4 Characterizations of Artiﬁcial Canal Neuromast in a Dipole

Flow

A periodic ﬂow, generated by a vibrating sphere (a dipole source), is one of the most common

methods to stimulate a lateral line system or its engineering counterpart. In this work we have

conducted experiments to examine the proposed canal-type lateral line under a dipole ﬂow stimulus

in a still water tank.

4.4.1 Experimental Setup

Experiments are conducted by using a small plastic tube measuring 15cm in length and 2cm in

radius, as shown in Fig. 4.16 to emulate the canal lateral line in the ﬁshes. A mini-shaker (Type

4810, Br¨uel & Kjær) was mounted on an aluminum frame above the tube, generating vibration

stimulus (back and forth) on the horizontal plane in the range of 2 to 20 Hz at a ﬁxed amplitude of

the electrical input to the mini-shaker. The dipole source used is a metallic sphere with diameter of

19.4 mm and excited by the mini-shaker. The sphere is placed deep enough below the oil surface.

The cupula-inspired IPMC sensor is attached to a thin 3D-printed stick and extended to the same

depth as the dipole source, as shown in Fig. 4.16. The cupula-inspired IPMC sensor is placed

ﬁrst with a distance of 2cm from the dipole source center. A laser displacement sensor (OADM

20I6441/S14F, Baumer Electric) is mounted above the tube to measure the vibration displacement

of the mini-shaker as the input of the sensor. The mounting frame for the laser sensor is isolated

from the frame where the mini-shaker is ﬁxed. An ampliﬁcation circuit [86] is used to measure

the short-circuit current generated by the IPMC sensor. Control signal generation, sensing data

acquisition, and processing are all performed through a dSPACE system.

68

(a)

(b)

Figure 4.16: Experimental setup: (a) the canal assembly, mini shaker to apply a vibrating motion,
laser sensor to measure the mini-shaker displacement; (b) Details of the canal assembly.

69

4.4.2 Results and Discussion

Experiments are conducted where the IPMC tip bending direction is parallel to the dipole source

vibration direction. The canal is ﬁlled with silicone oil to emulate the biologic counterpart. The

frequency of the dipole source was set to vibrate with a range of frequencies from 2 to 20 Hz. These

experiments included two different locations for the the cupula-like structure. First, the dipole is set

to vibrate at 2 cm from the cupula-like structure. For the second location, the dipole is set to vibrate

at 3cm from the cupula-like structure. The dipole vibration produces periodic ﬂow within the canal

and the ﬂow movement in turn stimulates the IPMC-embedded canal neuromast, resulting in an

IPMC sensing output at the same frequency as the dipole source. We use fast Fourier transform

(FFT) to extract the magnitude of the IPMC sensing signal, which is the short circuit current, and

the dipole displacement corresponding to the dipole frequencies. Fig. 4.18, shows the comparison

of the IPMC sensing signals at different frequencies for the two dipole locations. From the ﬁgure,

it can be seen that the IPMC sensing output increases with the frequency of the dipole within the

range of frequencies from 2 to 16 Hz. We observe that the IPMC sensing signal at frequencies

above 18 Hz has lower magnitude. We attribute that to the dipole displacement, where we set the

amplitude of the mini-shaker input voltage to be ﬁxed but not the vibration amplitude.

4.5 Parameter Identiﬁcation and Model Validation

4.5.1 Parameter Identiﬁcation

Parameters for the model proposed in Section 4.1 are determined and used in model validation.

The sensor dimensions (including the length and the thickness) and the thickness of the platinum

electrode layers, are obtained directly through measurement. In particular, the thickness of the plat-

70

inum layers is computed using the measured thickness of the polymer membrane before fabrication

and that of the fabricated IPMC beam. For the IPMC sensor used in experiments, the dimensions

are:

length 10 mm and thickness 0.068 mm. The physical constants in the model include the

temperature (T ), which is measured directly using a thermometer, density (ρ), which is obtained

through measuring the sensor weight and volume, the Faraday constant (F), and the gas constant

(R). The value of anion concentration C0 and the Young’s modulus of the IPMC ﬂow sensor are

taken from [93]. The Young modulus of the cupula-like structure is obtained experimentally as

follows. We subject the cupula to a displacement and measure the load and the deformation. A

high-precision load cell device (Transducer Techniques, GSO 10g) is used to measure the applied

load and a laser displacement sensor (OADM 20I6441/S14F, Baumer Electric) is used to measure

the resulting displacement. Fig. 4.17 shows the measured stress-strain relationship to obtain the

Young’s modulus of the cupula. The electrical conductivity of the electrode (σ) is determined with

the measured sensor surface resistance and the dimensions of the electrode. Table 4.1 lists the

aforementioned parameters and constants.

The remaining parameters include the diffusion coefﬁcient D and dielectric constant ε, both of

which are obtained through an artiﬁcial neural network-based data ﬁtting process [69]. The Matlab

toolbox (nnstart) is used to prepare a neural network with two inputs, which represent the parame-

ters to be tuned, and one output, which represents the model ﬁtting error. The network contains one

hidden layer with 10 nodes. The number of hidden layers and nodes are chosen according to [87].

Speciﬁcally, we use the collected IPMC output magnitude when the dipole at 1 cm from the cupula

as shown in Fig. 4.18, for the purpose of parameter identiﬁcation, and these same parameters are

used in the other scenario (different dipole location) for model validation. The ﬁnite element sim-

ulation is used to obtain the predicted sensing signal magnitude for the prescribed dipole stimulus,

71

Figure 4.17: Measured stress-strain relationship curve for identifying the Young modulus of the
artiﬁcial canal neuromast.

72

for any given set of parameters.

As stated in [69], we follow a tutorial provided by Matlab Inc. [88] to implement the neural

network model, which offers a step-by-step instruction on how to use the command (nnstart). The

average error between the predicted and measured sensing signals is treated as the output of the

neural network for the corresponding input values (i.e., the parameters used in the simulation).

A total of 25 sets of parameters, chosen within feasible ranges of these parameters, are used in

conducting the simulation. Twenty sets of the obtained input-output data are used to train the

neural network, while the remaining sets are used to test the obtained neural network model. The

established neural network model is then used to to serve as a ﬁtness function to the optimization

toolbox (optimtool) to ﬁnd the optimum input vector that minimizes the output, which produces

the optimal parameters (D,ε) for the data ﬁtting. The obtained values for these parameters are

also listed in Table 4.1. Fig. 4.18 shows the comparison between measured signal and the model

prediction based on the identiﬁed parameters. It can be seen that overall the model captures well

the magnitude of the sensing signal under the given stimulus.

4.5.2 Model Validation

The identiﬁed parameters are then used in the simulation of the sensor sensing signal under a dipole

ﬂow with different location of the dipole (3 cm away from the cupula). In particular, the same set

of frequencies are used to run the simulation by using the identiﬁed parameters.

Fig. 4.18 is also show the the comparison between the measured sensing signals and the model-

predicted sensing signals for the new distance. Overall, the ﬁgure shows a good agreement between

the measurement and model prediction. Given that two of the key model parameters are identiﬁed

using only part of the data under a dipole stimulus, the reasonable match across all the data points

73

Table 4.1: Model Parameters of Canal-type Neuromasts.

F
(C mol−1)
96487

D
(m2 s−1)
1.8× 10−12
ρ IPMC
(kg m−3)
8571.4

R
(J mol−1K−1)
8.3143

T
(K)

290

z

1

C0
(mol m−3)
1085

ρ Cupula
(kg m−3)
2431.5357

ε
(F m−1)
2× 10−3
E IPMC
(Pa)
5.116× 108

σ
(S m−1)
2200

E Cupula
(Pa)

9633

provides strong support for the validity of the model. Speciﬁcally, the model is able to capture the

magnitude of the sensor sensing signals.

Despite the general good agreement, there are some modest discrepancies between the experi-

mental data and the simulation results, which we attribute mainly to imperfection in fabrication of

the IPMC ﬂow sensor and in the experimental setup.

74

Figure 4.18: Comparison between the experimental and the simulation sensing signal for two
distances.

75

Chapter 5

A Pressure Gradient Sensor Inspired by the

Canal Neuromasts of Fish

In this chapter, we present, to our best knowledge, the ﬁrst pressure difference sensor inspired

by the canal neuromasts of ﬁsh. Such a sensor could be used by underwater robots and vehicles

for object detection, angle of attack measurement, and source localization. Unlike most of the

aforementioned artiﬁcial lateral line systems on pressure sensing or object localization, where an

array of sensors were used, the proposed sensor utilizes one sensing element embedded in a cupula-

like structure, which is immersed in a canal (a “semicircular” channel) ﬁlled with a viscous ﬂuid.

The employed sensing element, which is an IPMC sensor, serves as an artiﬁcial hair cell sensor

that produces an electrical output in response to the motion of the cupula. As an illustration, the

pressure difference sensor is integrated within a ﬁsh-like body, and the two ends of the semicircular

channel are “pores” like the ears of a ﬁsh. Unlike a ﬁsh canal that has open ends to the surface of

the body, the two pores of the proposed sensor are covered with a thin latex membrane, to prevent

the canal ﬂuid from mixing with the ambient ﬂuid.

76

5.1 System Development

The ﬁsh-like structure was produced with a multi-material 3D printer (Objet Connex 350, Strata-

sys) using a hard material (VeroWhite), and it consisted of two parts, as shown in Fig. 5.1. The

front part had a semicircular canal (inner diameter 3 cm), to house the cupula (see Fig. 5.2 (b)),

and the two pores (diameter 2 cm) at both ends of the canal would be covered by two membranes.

The membrane was made of natural latex rubber (thickness 0.1 mm). The cupula structure was

3D-printed with the same multi-material printer (Objet Connex 350, Stratasys), using the soft ma-

terial. The cupula structure, as shown in Fig. 5.2 (b), was printed as one piece and comprised of

two parts: a cylinder (length 1.5 cm, radius 0.3 cm) is on top of another cylinder (length 0.5 cm,

radius 0.13 cm) with a slot (length 1.7 cm, cross-section of 0.2 mm by 0.2 cm) passing through

the two cylinders for housing the IPMC sensor. The IPMC fabrication process followed the tradi-

tional impregnation-reduction ion-exchange process [7, 44]. Following the IPMC fabrication, an

additional step of encapsulation was conducted with a parylene coating of 20 µm, followed by a
water drive-in process under 70◦C for three days [92]. Finally, the IPMC sensor was inserted into

the cupula structure (in particular, the slot) through the slit at the bottom of the smaller cylinder.

5.2 Experimental Characterization

5.2.1 Experimental Setup

The rhythmic movement of the body appendages or the ﬁns can be emulated by a vibrating sphere

known as a dipole source. A dipole is often can be used as a stimulus in the study of a lateral line

system or its engineering counterpart. In this paper, we have conducted experiments to examine

the proposed sensor under an AC ﬂow stimulus generated by a dipole source in a still water tank.

77

Figure 5.1: 3D-printed ﬁsh-like structure with two pores to be covered with natural latex rubber
membranes.

(a)

(b)

Figure 5.2: Fabrication of the proposed sensor: (a) fabricated IPMC ﬂow sensor (1.5 cm long, 2
mm wide); (b) 3D-printed cupula-structure with the IPMC sensor inserted.

78

Fig. 1.5 shows a schematic diagram of the proposed sensor and the experimental setup, while

Fig. 5.3 shows a picture of the major elements that have been used in the experimental setup.
Experiments were conducted in a water tank measuring 6× 2× 2 ft3. A mini-shaker (Type 4810,

Br¨uel & Kjær) was mounted on an aluminum frame above the tank, generating vibration (back

and forth) on the horizontal plane in a range of 2 to 30 Hz at a ﬁxed amplitude of electrical input

to the mini-shaker. The dipole source used was a metallic sphere with a diameter of 25 mm and

excited by the mini-shaker. The ﬁsh-like structure was ﬁxed to a metal rod via a 3D-printed con-

nector. The 3D-printed connector securely held the ﬁsh-like body and the metal rod to ensure no

slip when a rotational movement was applied. The top end of the metal rod was ﬁxed on a metal

connector, which was rigidly attached to a stepper motor (STM23S-2AE, Applied Motion) used

to generate a rotation of the ﬁsh-like structure. The stepper motor was controlled via a microcon-

troller (Arduino-uno). The dipole source and the ﬁsh-like structure were completely submerged

underwater at a depth of about 20 cm. The separation between the dipole source and the ﬁsh-like

structure was about 10 mm when the ﬁsh-like structure was perfectly oriented towards the dipole.

A laser displacement sensor (OADM 20I6441/S14F, Baumer Electric) was mounted above the wa-

ter to measure the vibration displacement of the mini-shaker, which was used later in the data

processing (see Fig. 5.5). The mounting frame for the laser sensor was completely isolated from

the frame where the mini-shaker was ﬁxed. The IPMC output was ampliﬁed with a two-tier am-

pliﬁcation circuit [86] before the acquisition and processing by a lab PC equipped with a dSPACE

system(dSPACE, DS 1104).

79

Figure 5.3: Picture of the experimental setup.

5.2.2 Experimental Results and Discussion

Experiments were ﬁrst conducted for the case where the dipole source was placed at a ﬁxed point

while the ﬁsh-like structure was rotated at different angles relative to the dipole source, as illus-

trated in Fig. 1.5. The sensor was ﬁlled with silicone oil which provides better performance than

water as suggested by our earlier work [94]. The frequency of the dipole source was set at 10 Hz.

Conceivably, the pressure difference between the two pores would be dependent on the relative

dipole location; in particular, the difference is expected to be largest when the dipole is facing one

of the membranes and smallest when the dipole is at the midpoint between the pores. Through the

pressure difference, the periodic movement of the dipole ﬂow induces the ﬂow movement within

the canal and thus the motion of the IPMC-embedded cupula structure, resulting in an IPMC cur-

rent output at the same frequency as the dipole.

80

We used fast Fourier transform (FFT) to extract the amplitude of the IPMC sensor output cor-

responding to different angles, shown in Fig. 5.4. Experiments were conducted 5 times at each

angle, and the mean and standard deviation of these measurements are plotted in Fig. 5.4. From

the ﬁgure, it is clear that as either pore approached the dipole source, the sensor output increased.
When the dipole was at the midpoint (angle 0◦) between the two pores, the IPMC sensor gener-

ated the lowest signal, indicating that the pore membranes were vibrating in phase. These results

support that the sensor is able to capture the pressure difference between the two pores. The slight

asymmetry between the left and right halves of the ﬁgure is attributed to the positioning errors for

the dipole in the experiments.

To further characterize the dynamic behavior of the sensor in detecting the pressure differences,

we next conducted experiments where the body was placed at several different angles relative to

the dipole source while the dipole vibrated at a range of frequencies. Three angles were chosen to
obtain the a frequency response (0◦, 30◦, and 45◦) with a range from 2 to 30 Hz. Each experiment

was repeated 5 times to compute the average and the standard deviation.

Fig. 5.6 shows the comparison of the sensitivity of the pressure sensor at different frequen-

cies for the three angles. The sensitivity was taken by normalizing the magnitude of IPMC sensor

output over the ﬂow acceleration as characterized by the dipole acceleration (Fig. 5.5). From the

ﬁgure, it can be seen that the sensitivity of the sensor decreased with the frequency of the dipole
within the entire range of frequencies tested. The sensitivity of the sensor in the case of 45◦ was
higher than the case of 30◦, which was higher than that in the case of 0◦. These results further

support that this sensor is able to capture the pressure difference at different angular positions.

81

Figure 5.4: Experimental measurements of the sensor output where the ﬁsh-like structure is at
different angles relative to a dipole source.

82

Figure 5.5: The dipole displacement and the acceleration in the frequency range 2 to 30 Hz.

5.3 Finite Element Model and Simulation

5.3.1 Finite Element Modeling

The response of a canal neuromast, biological or engineered, is due to the cupula deﬂection in

response to a ﬂow ﬁeld, which is in turn due to a pressure difference between the canal pores. Finite

element modeling is essential to the understanding of the sensor behavior and ultimately serving as

a tool for design optimization. The modeling of the proposed pressure difference sensor under an

oscillatory ﬂow was implemented using COMSOL Multiphysics ﬁnite element software packages.

The geometry and dimensions of the simulated ﬁsh-like structure, the cupula-like structure, and

hair cell (IPMC sensor) were exactly the same as to those of the experimental prototype.

The modeling was done in two steps. In the ﬁrst step a three-dimensional ﬂuid-structure inter-

83

Figure 5.6: Comparison of the sensor frequency response at different angles relative to the dipole
source.

84

Figure 5.7: The ﬁnite-element modeling of a ﬁsh-like pressure difference sensor in the presence
of a dipole source. The upper color bar represents the ﬂow velocity within and around the sensor
while the lower color bar represents the deﬂection of the membrane and the cupula-inspired IPMC
ﬂow sensor.

85

action (FSI) module was used to understand the cupula structure and membrane deﬂection under

a dipole stimulus. The second step was to model the IPMC sensor physics and predict its output

under bending.

5.3.1.1 Fluid-structure interaction (FSI)

In the ﬁrst step of the simulation, FSI physics package was used to model the ﬂuid-structure inter-

action between the sensor, dipole, and the surrounding water. The canal of the ﬁsh-like structure

was ﬁlled with a ﬂuid that had ﬁve times the viscosity of water, which was close to the viscosity

of the biological counterpart. A dipole source was placed outside the canal to create a pressure

difference across the pores (see Fig. 5.7). Similar to the experimental setting as shown in Fig. 5.3,

in the simulation setup the ﬁsh-like structure could be oriented at different angles relative to the

dipole source as seen in Fig. 5.9.

The dipole frequency was set to be 10 Hz and the amplitude of the dipole vibration was set to

be 2.5 mm. Fig. 5.7 shows a snapshot of the simulated conﬁguration, where the sphere represents

the dipole source. The cylinder in the front part of the ﬁsh-like structure represents the cupula

containing the IPMC sensor. Flexible membranes were attached to the pores. Appropriate initial

and boundary conditions were used in the simulation. The water outside the ﬁsh-like structure and

the canal-ﬁlling ﬂuid were set to be at rest at the initial time. The membranes were fully attached to

the boundaries of the canal pores. The cupula structure was ﬁxed from the bottom, which implies

that the displacement at the cupula base was zero. The snapshot in Fig. 5.7 shows both the ﬂow

ﬁeld and the displacement of the cupula and membranes. Note that the plot was a slice from the

three-dimensional model.

86

5.3.1.2

IPMC

The modeling of IPMC sensor under oscillatory ﬂow was also achieved by using COMSOL Mul-

tiphysics ﬁnite element software packages. Four physics packages were used to implement the

sensor model, ﬂuid-structure interaction (FSI), transport of diluted species, general-form PDE to

generate the electrical potential within the ion-exchange membrane (Naﬁon), and electrical cur-

rent physics. The FSI module was used to describe the ﬂow ﬁeld and the linear elastic material

under bending excitation due to the oscillatory ﬂow inside the canal. The Poisson-Nernst-Plank

equation (PNP), which describes the cation concentration and electrical potential dynamics was re-

alized through the transport of diluted species physics and the general-form PDE physics modules.

The implementation of the IPMC model under bending stimuli was achieved with two separate

computations. The deformation of the IPMC sensor due to the dipole ﬂow was calculated ﬁrst

(see 5.3.1.1), followed by the execution of the PNP model, which used the deformation data from

the ﬁrst computation as input. A short-circuit current was collected by imposing the electrodes

with zero potential and integrating the collected current density throughout the electrode surface.

5.3.2 Parameter Identiﬁcation

The parameters used in simulation were obtained based on the experimental setup. The dimensions

of the IPMC sensor and the cupula-like structure, including the length, the diameter, the thickness,

and the thickness of the platinum electrode layers, were obtained directly through measurement.

In particular, the thickness of the platinum layers was computed using the measured thickness of

87

Figure 5.8: Experimentally obtained stress-strain curve of the cupula structure for estimating
Young’s modulus.

the polymer membrane before fabrication and that of the fabricated IPMC beam. The physical

constants in the IPMC model include the temperature (T ), which was measured directly using a

thermometer, density (ρ), which was obtained through measuring the sensor weight and volume,

the Faraday constant (F), and the gas constant (R). The value of anion concentration C0 and the

Young’s modulus of the IPMC ﬂow sensor were taken from [93]. The Young’s modulus of the

cupula-like structure was obtained based on experimental data on the stress/strain relationship col-

lected through a tensile test (see Fig. 5.8). The electrical conductivity of the electrode (σ) was

determined with the measured sensor surface resistance and the dimensions of the electrode. Ta-

ble 2.1 lists the aforementioned parameters and constants.

The remaining parameters include the diffusion coefﬁcient D and dielectric constant ε, both

88

of which were obtained through an artiﬁcial neural network-based data ﬁtting process [?]. The

Matlab toolbox (nnstart) was used to prepare a neural network with two inputs, which represented

the parameters to be tuned, and one output, which represented the model ﬁtting error. The network

contains one hidden layer with 10 nodes. The number of hidden layers and nodes were chosen

according to [87]. Speciﬁcally, we used the collected IPMC output magnitude in the case of single

frequency (10 Hz) and when the ﬁsh-like structure was orientated at different angles relative to

the single dipole (data in Fig. 5.4), for the purpose of parameter identiﬁcation. The ﬁnite element

simulation was used to obtain the predicted sensing signal magnitude for the prescribed dipole

stimulus, for any given set of parameters. The average error between the simulation and measured

sensing signals was treated as the output of the neural network for the corresponding input values

(i.e., the parameters used in the simulation). A total of 30 sets of parameters, chosen within fea-

sible ranges of these parameters, were used in conducting the simulation. Twenty four sets of the

obtained input-output data were used to train the neural network, while the remaining sets were

used to test the obtained neural network model. The obtained values for these parameters are also

listed in Table 5.1.

5.3.3 Simulation Results

The identiﬁed parameters were then used in the simulation of the sensor response. Simulations was

ﬁrst conducted for the case where the ﬁsh-like structure was oriented at different angles relative to

the dipole source, the snapshots of which are shown in Fig. 5.9. Each sub-ﬁgure in Fig. 5.9 also

shows the deﬂections of the pore membranes and the cupula-like structure, where the top color

bar represents the membranes deﬂection (mm) and the lower color bar represents the cupula dis-
placement (mm). In Fig. 5.9 selected six different angles (0◦, 30◦, 45◦, 60◦, 75◦, 90◦) out of 19

89

Table 5.1: Model Parameters of the Pressure Difference Sensor.

F
(C mol−1)
96487

D
(m2 s−1)
1× 10−14
ρ IPMC
(kg m−3)
8571.4

R
(J mol−1K−1)
8.3143

T
(K)

290

z

1

C0
(mol m−3)
1050

ρ Cupula
(kg m−3)
1000

ε
(F m−1)
31× 10−3
E IPMC
(Pa)
5.116× 108

σ
(S m−1)
2200

E Cupula
(Pa)
0.162× 106

different angles (0 to 90 with step of 5◦) used in the simulation study. As seen from the ﬁgure,
when the dipole source is located at the midpoint between the two pores (0◦), both membranes are

ﬂuctuating symmetrically, suggesting minimal pressure difference between the pores and minimal

ﬂow of the viscous ﬂuid in the canal, which in turn leads to minimal displacement of the cupula.

Fig. 5.10 further shows the tip displacement amplitude of the cupula structure and the mem-

brane displacement,as a function of the orientation of the ﬁsh-like structure with respect to the

dipole source. It can be noted that magnitudes of both displacements show strong dependency

on the orientation of the ﬁsh-like body relative to the dipole, with the maximum values occur-

ring around 45c and a trend consistent with the experimentally observed sensor output (shown in

Fig. 5.4).

Fig. 5.11 shows the comparison between the measured sensing signal magnitude and the simu-

lation sensing signal amplitude, under (10 Hz) dipole stimulation. Overall, the ﬁgure shows a good

agreement between the measurement and simulation. Given that two of the key model parameters

were identiﬁed using only part of the data under a dipole stimulus, the reasonable match across

90

all the data points provides strong support for the validity of the model. Despite the general good

agreement, there are some modest discrepancies between the experimental data and the simula-

tion results, which we attribute mainly to the imperfection in fabrication of the membrane and the

IPMC ﬂow sensor, and in the experimental setup.

5.4 Orientation Control of Fish-like Body with Sensor Feed-

back

5.4.1 Sliding Discrete Fourier Transform (SDFT) Algorithm

In this section the utility of the proposed sensor is illustrated with feedback control of the orienta-

tion of the ﬁsh-like body using measurement from the pressure difference sensor. Discrete Fourier

transform (DFT) can be used to extract the signal magnitudes of the sensor output at different fre-

quencies. However, when the ﬁsh-like body rotates, the magnitude of the sensor output evolves

with time. The sliding discrete Fourier transform (SDFT) algorithm [74, 75] performs joint time-

frequency analysis and is a suitable method for computing a speciﬁc spectral bin based on a sliding

window of n-time samples.

For a window of N samples, {x[n−N −1], .....,x[n]}, we can evaluate the kth spectral bin using

DFT: for 0 ≤ k ≤ N − 1

Xk[n] =

N−1
∑
m=0

x[n− m + 1 + k]e− j2πkm/N

(5.1)

Since we are interested in a single frequency f0 for a dipole stimulus, it sufﬁces to consider

a single frequency bin k = [

f0N
Fs ], where [.] denoted rounding to the nearest integer and Fs is the

91

(a)

(c)

(e)

(b)

(d)

(f)

Figure 5.9: Snapshots of simulation showing the membrane and the cupula displacement (units
in mm) when the ﬁsh-like structure is oriented with different angles relative to the dipole stim-
ulus, where the upper color bar represents the membrane displacement and the bottom color bar
represents the cupula displacement: (a) 0◦; (b) 30◦; (c) 45◦ (d) 60◦; (e) 75◦ (f) 90◦.

92

Figure 5.10: Computed magnitudes for the displacement of the membrane and for the tip displace-
ment of the cupula, respectively.

93

Figure 5.11: Comparison between the experimental and the simulation sensing signal.

sampling frequency to obtain the sensor signals. The SDFT algorithm, can be used to efﬁciently

evaluate Xk recursively as the time index n advances:

Xk[n] = e− jω0Xk[n− 1] + x[n]− x[n− N]

(5.2)

where ω0 = 2πkm
N . The resulting sequence from (5.2) is complex, for which the algorithm needs
to compute the magnitude. The algorithm monitors | Xk[.] |, which deﬁnes the power density at f0.

5.4.2 Feedback Controller

The proposed algorithm aims to orient the ﬁsh-like structure towards the dipole source (see Fig 5.9

(a)), starting from an arbitrary initial orientation. In particular, it uses the magnitude of the IPMC

sensing signal to guide the rotation of the ﬁsh-like body. In the experiments the ﬁsh-like body

94

was initialized at an arbitrary orientation within the range [−45◦,45◦], and the goal was to drive
it towards 0◦, namely, orienting towards the dipole, based on the measurement of the pressure

difference sensor. Since the sensor output is a convex function of the orientation angle with the
global minimum located at 0◦ (see Fig. 5.4), a greedy search algorithm was adopted. In particular,
at each time instant, the stepper motor will move one step (corresponding to 0.9◦ ), but the rotation

direction depends on whether the previous action has led to a decrease or increase of the sensor

output. Speciﬁcally,

Un+1 = sign(Xk(n)− Xk(n− 1))Un

(5.3)

where Un+1 is the next control for the stepper motor, while Un is the current control at time n.
Xk(n) is the current magnitude of the IPMC sensing signal, while Xk(n− 1) is the sensing signal
magnitude at the previous time step.

Fig. 5.12 shows the evolution of the sensor output magnitude during one experimental run,
when the ﬁsh-like body started at 45◦. It can be seen that, with the feedback from the pressure
difference sensor, the body was rotated to 0◦ in less than 0.5 second, where the sensor output

dropped to the level lower than 0.1 nA.

95

Figure 5.12: Magnitude trajectory of the IPMC sensor under the feedback control, activated at
about t = 1.3 seconds.

96

Chapter 6

IPMC Flow Sensor Exploiting

Self-Generated Vortices

In this chapter, we propose a novel IPMC-based ﬂow sensing structure that exploits self-generated

von Krmn vortices. A 3D-printed soft material sheath is fabricated to house the IPMC ﬂow sensor.

A key innovation of this work is the proposal of combining the direct mechanosensory property of

the IPMC with the structural design of the sensor. Experimental testing in a laminar ﬂow setting is

conducted, and the collected data on mechanical vibration and IPMC sensor output are analyzed

to reveal the dependence of both signal magnitudes and frequency contents on the ﬂow speed.

Speciﬁcally, it is found that the average magnitude of the IPMC current output could serve as a

sensitive representation of the ﬂow speed.

6.1 Sensor Fabrication

6.1.1 IPMC Flow Sensor Fabrication

The IPMC fabrication process follows the traditional impregnation-reduction ion-exchange process

[7]. The Naﬁon ﬁlm with a thickness of 254 microns (Naﬁon PFSA N 1110, DuPont) is ﬁrst boiled

in dilute hydrochloric acid (2 wt%) for 30 min to remove ions and impurities, and then boiled in

deionized (DI) water for another 30 min to remove the acid and swell the ﬁlm. After these pre-

97

treatment steps, the Naﬁon ﬁlm is immersed in a platinum complex solution ([Pt(NH3)4]Cl2) for

more than 4 h (usually overnight) to allow platinum ions to diffuse into the Naﬁon ﬁlm completely

through the ion-exchange process. After a rinse with DI water, the ﬁlm is immersed in a water bath
at 40 ◦C. After the temperature is raised up to 60 ◦C gradually, a sodium borohydride solution

(5 wt% NaBH4 aq) is added to the water bath as a reducing agent at a rate of 2 ml every 30

min. Once the platinum deposition is complete, those steps are repeated, from acid treatment to

water-bath reduction, to deposit the platinum for the second time. The ﬁlm is then cut into beam-

shaped samples with the length of 20 mm and the width of 3 mm. Finally, an IPMC sensor is

formed by soldering two electrical wire connectors to the IPMC platinum electrodes as shown in

Fig. 6.1(a). To further ensure the sensing consistency of the IPMC sensor, an additional step of
parylene encapsulation (20 µm) is conducted, followed by a water drive-in process under 70◦C for

three days [92].

6.1.2 Sensor Structure Fabrication

The rest of the sensor structure is 3D-printed with a multi-material printer (Objet Connex 350,

Stratasys), using the soft TangoBlack material. The sensor structure, as illustrated in Fig. 6.1 (b),

is printed as one piece and comprised of three parts, a cylindrical sheath (length 40 mm, outer

diameter 3 mm), a solid sphere (diameter 10 mm) with a slot passing through the cylinder for

housing the sensor for vortex-generation, and a solid shaft (length 30 mm, diameter 5 mm) for

mounting. The IPMC sensor is inserted into the ﬂow structure (in particular, the sheath) through

the slit (length 1.5 mm, width 0.3 mm, and depth 20 mm) at the back of the sphere, as shown in

Fig. 6.1 (c).

98

(a)

(b)

(c)

Figure 6.1: Fabrication of the IPMC ﬂow-sensing structure with self-generated vortices: (a) a
parylene-encapsulated IPMC sensor; (b) design schematic of the ﬂow-sensing structure; (c) 3D-
printed structure with a sphere, a sheath, and a mounting shaft.

99

6.2 Experimental Results on Flow Sensing

6.2.1 Experimental Setup

A uniform ﬂow ﬁeld is generated in a swim tunnel (Loligo Systems) measuring 146× 68× 35 cm3,
with an enclosed test section of 65× 20× 20 cm3. The ﬂow velocity in the working section of

this ﬂow tank is controlled through adjusting the rotating speed of the motor, which is used to

circulate the water in the tunnel. The sensor is mounted on the top, so that the sheath is placed

15 mm underwater and parallel to the stream ﬂow direction. The sheath is oriented towards the

downstream direction. Placing the sensor this way makes the sphere work as an obstacle in water,

through which von Krmn vortices are created. These vortices in turn could induce vibrations of the

cylindrical sheath, which in turn would stimulate the embedded IPMC beam. A laser displacement

sensor (OADM 20I6441/S14F, Baumer Electric) is mounted outside the ﬂow tank to measure the

vibration displacement of the free end of the sheath in the horizontal plane (lateral displacement

only). The mounting frame for the laser sensor is isolated from the ﬂow tank to ensure that the

displacement measurement be free from any motion disturbance caused by the tank motor. An

ampliﬁcation circuit and a dSPACE system are used to measure the short-circuit current generated

by the IPMC sensor, and to collect and process the data, respectively.

6.2.2 Experimental Results and Discussion

Experiments are conducted for ﬂow speeds ranging from 17.5 to 87 cm/s. Fig. 6.2 shows the

measured sheath tip displacement and the corresponding IPMC sensor output (short-circuit current)

when the ﬂow speed is at 35 cm/s. From the ﬁgure, it is clear that both signals are oscillatory but

not periodic. To gain additional insight into the frequency components of the signals, fast Fourier

100

transform is conducted on the signals and Fig. 6.3 shows the the spectral content of each signal.

It is interesting to note that the mechanical displacement displays a low-pass behavior while the

IPMC current output displays a band-pass behavior, which is due to the additional transduction

physics of IPMC.

Fig. 6.4 and Fig. 6.5 show the measured data, sheath tip displacement and IPMC current out-

put, and their spectral contents, respectively, when the ﬂow speed is at 70 cm/s. It can be seen

that while the sensor responses at 70 cm/s are qualitatively similar to those at 35 cm/s (oscillatory

and irregular), the magnitudes of both signals at the higher speed are higher, and the frequency

components at 70 cm/s also shift higher. This is, to some extent, consistent with the expectation

that the vortex-shedding frequency increases with the ﬂow speed, although the collected signals

encompassed a band of frequencies instead of a single frequency. To capture the sensor response

quantitatively, we computed the average amplitude and average frequency of each signal, at dif-

ferent ﬂow speeds, as shown in Fig. 6.6 and Fig. 6.7. Here the average amplitude is calculated by

simply taking the mean of amplitudes at all frequencies, and the average frequency is calculated

by amplitude-weighted mean of the frequencies. From these ﬁgures, it is evident that both average

amplitude and average frequency are highly correlated with the ﬂow speed. In particular, from the

perspective of ﬂow sensing, the average amplitude of the IPMC sensor output is able to provide a

highly sensitive indication of the underlying ﬂow speed.

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Figure 6.2: Experimental measurements of the sensor tip displacement and current output, in re-
sponse to sheath laminar ﬂow of 35 cm/s: (a) measured sheath tip displacement; (b) measured
short-circuit current of the IPMC ﬂow sensor.

102

Figure 6.3: Experimental measurements of the sensor tip displacement and current output, in re-
sponse to sheath laminar ﬂow of 35 cm/s: (a) spectral content of the sheath tip displacement; (b)
spectral content of the IPMC current output.

103

Figure 6.4: Experimental measurements of the sensor tip displacement and current output, in re-
sponse to sheath laminar ﬂow of 70 cm/s: (a) measured sheath tip displacement; (b) measured
short-circuit current of the IPMC ﬂow sensor.

104

Figure 6.5: Experimental measurements of the sensor tip displacement and current output, in re-
sponse to sheath laminar ﬂow of 70 cm/s: (a) spectral content of the sheath tip displacement; (b)
spectral content of the IPMC current output.

105

Figure 6.6: Average amplitude of the sheath displacement and the IPMC sensing signal.

106

Figure 6.7: Average frequency of the sheath displacement and the IPMC sensing signal.

107

Chapter 7

Angular Acceleration Sensor Inspired by

the Vestibular System

In this chapter, a novel angular acceleration sensor inspired by the vestibular system is investigated.

Unlike the biological vestibular system, which has three semicircular canals, the proposed 3D-

printed sensor is composed of one rigid circular canal, which is ﬁlled with a viscous ﬂuid to emulate

the biological equivalent. In this model, we reduce the three-dimensional sensing ability of the

vestibular system to one-dimensional to gain more insight about the sensor performance. An IPMC

ﬂow sensor, embedded in a cupula and placed on the top wall of the canal, serves as an artiﬁcial

hair cell sensor that produces an electrical output in response to the motion of the cupula.

Fig. 1.7 shows the schematic of the system under consideration, where one circular canal with

one cupula is considered. Experiments are conducted with rotational stimuli at different accelera-

tions. The IPMC short-circuit current output signals are collected as results of the the accelerations.

It is found the sensor clearly responds to different angular acceleration at constant angular velocity.

To further understand the behavior, time-dependent 3D-ﬁnite element simulation is conducted for

an artiﬁcial vestibular canal under different rotational stimuli.

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7.1 The Approach

7.1.1 Sensor fabrication

The artiﬁcial vestibular circular canal structure is produced with a 3D printer (Form2, Formlabs),

using the clear hard Resin material. The vestibular canal structure, as illustrated in Fig. 7.1 (a), is a

one-piece structure comprised of two parts: a circular canal (outer diameter 10 cm, inner diameter

3 cm), a circular canal (radius 1 cm), to house the cupula (see Fig. 7.1 (b)), and to be ﬁlled with

a viscous ﬂuid as shown in Fig. 7.1 (a). The cupula structure is 3D-printed with a multi-material

printer (Objet Connex 350, Stratasys), using the soft TangoBlack material. The cupula structure,

as illustrated in Fig. 7.1 (d), is printed as one piece and comprised of two parts: a cylinder (length

1 cm, radius 0.3 cm) is on top of another cylinder (length 0.3 cm, radius 0.13 cm) with a slot

(length 1.3 cm, cross-section of 0.2 mm by 0.15 cm) passing through the two cylinders for housing

the IPMC sensor. The IPMC fabrication process follows the traditional impregnation-reduction

ion-exchange process [7, 44]. Following the IPMC fabrication, an additional step of encapsulation
is conducted with a parylene coating of 20 µm, followed by a water drive-in process under 70◦C

for three days [92]. Finally, the IPMC sensor is inserted into the cupula structure (in particular, the

slot) through the slit at the bottom of the smaller cylinder.

7.1.2 Experimental Setup

To characterize the proposed device under rotational excitation, we impose a pure angular accel-

eration excitation to the vestibular system device. Fig. 7.2 shows the components of the setup,

including the rotational assembly that imposes a rotational stimulus on the device, the ampliﬁca-

tion circuit that ampliﬁes and ﬁlters the sensing output, and the data acquisition system (dSPASE

109

(a)

(b)

(c)

Figure 7.1: Fabrication of the proposed sensor: (a) 3D-printed vestibular system circular canal
device; (c) fabricated IPMC ﬂow sensor (1 cm long, 1 mm wide); (d) 3D-printed cupula-structure
with the IPMC sensor inserted.

110

(a)

Figure 7.2: Experimental setup involving a details of the rotational assembly.

RTI 1104). The sensor device is coupled to a stepper motor (Applied motion- STM23S) through a

metal coupler. The stepper motor is used to generate a programmed rotation of the sensor device.

The stepper motor has a built-in shaft-encoder to better control the stepper motor trajectory.

7.1.3 Sensor Characterization

The responses of the angular acceleration sensor are characterized with a sequence of angular ve-

locity stimuli with different angular accelerations. In particular, the angular velocity of the stepper

motor ﬁrst ramps up from 0 rad/s to a constant angular velocity ω to generate a constant angular

acceleration a of the device, stays constant for 10 s, and then decelerates to 0 rad/s with decelera-

tion of magnitude a. Fig. 7.3 shows an example of the stepper motor trajectory, where the constant

angular velocity is 31 rad/s and the angular acceleration/deceleration is 62 rad/s2. We note that the

chosen sequence of the motor movement allows one to examine a number of sensor behaviors, in-

111

(a)

Figure 7.3: The applied sequence of the stepper motor inputs in acceleration/deceleration and the
corresponding sensing signal from the IPMC. Here the constant angular velocity is 31 rad/s and
the acceleration/deceleration is 62 rad/s2.

cluding the transient and the steady state behavior (acceleration/deceleration and constant angular

velocity), the IPMC sensor polarity during the acceleration/deceleration of the stimulus, and the

sensing signal when the device is in the steady state.

Fig. 7.3 shows the short-circuit current output from the IPMC sensor under the correspond-

ing input. From ﬁg. 7.3, one can see that, during the acceleration, the sensor output produces

two spikes: the ﬁst spike happens when the acceleration starts and the second spike takes place

when the motor reaches the constant angular velocity. The sensor has similar behavior during the

deceleration but with opposite sensing polarity. Furthermore, when the motor is rotating with a

steady-state angular velocity, the sensor produces oscillatory signals, which can be attributed to

the shaking of the motor or the device during the rotational movement.

112

To further characterize the sensor behavior in detecting the angular acceleration, we have con-

ducted additional experiments with a set of angular acceleration/deceleration values, which are

62 rad/s2, 125 rad/s2, 188 rad/s2, 251 rad/s2, and 314 rad/s2. These experiments included three

scenarios. In the ﬁrst scenario, the device is ﬁlled with silicone oil and its viscosity is about 5 times

the viscosity of water. In the second scenario, the device is ﬁlled with water. In the third scenario,

the device is free from liquid.

Fig. 7.4 and Fig. 7.5 show the sensing signal responses from the sensor under the corresponding

motor trajectories. From the two ﬁgures, when the device is ﬁlled with silicon oil, no matter what

is the value of the angular acceleration, it can be seen that the magnitude of the generated sensing

signal increased with the angular acceleration. Compared with the case with silicone oil, the case

with water shows signiﬁcantly lower sensor output. This is because the viscosity of the ﬂuid

impacts the drag on the sensor. The device without liquid shows no sensing signals. Comparing

the sensing results with different ﬂuids ﬁlled, one can see that the sensitivity with silicone oil ﬁlled

is over twice of that with water.

Fig. 7.6 shows the experimental results under sinusoidal rotational stimulus. At each stimulus

frequency, a response of the IPMC sensor is collected. Fast Fourier transform is used to extract the

amplitudes of the IPMC sensor output at each testing. From the ﬁgure, one can tell that the IPMC

sensor output increase with the angular acceleration.

7.1.4 Finite Element Simulation

7.1.4.1 Fluid Structural Interaction (FSI)

The response of a superﬁcial neuromast, biological or engineered, is due to the movement or de-

ﬂection of the cupula-like structure in the presence of a ﬂow stimulus. To capture these deﬂections,

113

(a)

(b)

(c)

(d)

(e)

(g)

(h)

(f)

(i)

Figure 7.4: Experimental measurements of the sensor response under different acceleration stimuli
and one angular velocity which is 31 rad/s: (a) Angular acceleration 62 rad/s2 with viscous ﬂuid;
(b) Angular acceleration is 62 rad/s2 with water; (c) Angular acceleration is 62 rad/s2 with air;
(d) Angular acceleration 125 rad/s2 with viscous ﬂuid; (e) Angular acceleration is 125 rad/s2
with water; (f) Angular acceleration is 125 rad/s2 with air;(g) Angular acceleration 188 rad/s2
with viscous ﬂuid; (h) Angular acceleration is 188 rad/s2 with water; (i) Angular acceleration is
188 rad/s2 with air.

114

(a)

(b)

(c)

(d)

(e)

(f)

Figure 7.5: Experimental measurements of the sensor response under different acceleration stimuli
and one angular velocity which is 31 rad/s: (a) Angular acceleration 251 rad/s2 with viscous ﬂuid;
(b) Angular acceleration is 251 rad/s2 with water; (c) Angular acceleration is 251 rad/s2 with air;
(d) Angular acceleration 314 rad/s2 with viscous ﬂuid; (e) Angular acceleration is 314 rad/s2 with
water; (f) Angular acceleration is 314 rad/s2 with air.

115

Figure 7.6: Frequency response of the IPMC sensor output under sinusoidal stimuli with different
angular accelerations.

116

a 3D-ﬂuid-structural interaction (FSI) module from COMSOL Multiphysics is considered. In par-

ticular, the model incorporates various material properties and dimensions, including the cupula

geometry, cupula shape and size, cupula stiffness, IPMC sensor beam geometry and size. The FSI

model uses the incompressible Navier-Stokes equation to describe the ﬂuid ﬂow and the Hooke’s

law to capture the linear elastic material behavior. As detailed in the next subsection, Poison-

Nernst-Plank (PNP) equations are used to model the IPMC sensor response under a mechanical

stimulus, which is generated by the ﬂow-induced capula movement.

7.1.5 Modeling and Simulation Setup

In this section, the modeling of the angular acceleration sensor is modeled. The simulation setup of

this sensor is done through COMSOL Multiphysics. A three-dimensional ﬂuid-structure interac-

tion (FSI) module from COMSOL Multiphysics is used to conduct simulation and help understand

the the viscous ﬂuid movement and the cupula structure displacement when the proposed sensor is

subject to a rotational movement stimulus. The geometry and dimensions of the simulated angular

acceleration device are close to those of the experimental prototype. The device has an outer radius

of 5 cm, an inner radius of 3 cm, and a circular canal of 1 cm in radius. The cupula structure is

comprised of two cylinders, one sitting on the other. The ﬁrst one has a radius of 0.3 cm and height

of 1 cm and the second one has a radius of 0.13 cm and height of 0.5 cm.

Fig. 7.7 shows the simulated conﬁguration for the angular acceleration device, where the cir-

cular canal represents the circular canal that is ﬁlled with viscous ﬂuid. The ﬂexible cupula is

attached from the top of the circular canal and integrated with an IPMC sensor structure. The ﬂuid

ﬁlling the canal is set to be at rest at the initial time. The device is imposed with an angular velocity

with different angular acceleration rates. The angular velocity trajectories are close to those in the

117

Figure 7.7: The schematic of the proposed sensor, showing a circular canal consisting of an IPMC
sensor embedded in cupula-like structure.

118

Figure 7.8: The schematic of the proposed sensor, showing a circular canal consisting of an IPMC
sensor embedded in cupula-like structure.

experiments. Fig. 7.8 presents a the trajectory of the angular velocity with different rates of angular

accelerations.

7.1.6 Simulation Results

The angular movement of the circular canal creates an angular movement of the ﬂuid inside the

canal, which in turn provides a stimulus to the cupula structure. Fig. 7.9 shows the IPMC tip

displacement responses when the canal is subjected to one angular velocity and different rates of

accelerations. From the ﬁgure, it can be seen that the IPMC has a clear displacement when there

is a change in the angular velocity which means that there is a constant angular acceleration. The

cupula-inspired IPMC sensor does not show a displacement when the angular acceleration is zero.

From that, the ﬂuid-ﬁlled the canal acts as a rigid body in the constant angular velocity, leading

119

Figure 7.9: The input trajectory to the circular canal with the correspondence sensor displacements.

Figure 7.10: The IPMC sensor tip displacement and the IPMC sensor output (short circuit current).

120

to the whole body (canal, cupula-inspired IPMC sensor, and the ﬂuid) rotating as a single object,

which in turn lead to no displacement of the cupula. Fig. 7.10 further shows the tip displacement

amplitude of the IPMC structure and the corresponding IPMC sensing signal.

7.2 Comparison between Experimental Measurements and Sim-

ulation Results

It can be noted that the displacement magnitude of the IPMC tip shows a behavior that is consistent

with the IPMC sensor output observed in experiments (Fig. 7.4 and Fig. 7.5), which suggests

that ﬁnite-element simulation could be used as an instrumental tool for further understanding and

optimization of the canal sensor device. Fig. 7.11 shows the comparison between the measured

sensor outputs and the ﬁnite-element model (FEM) sensor outputs under one angular velocity

with different angular acceleration stimuli. Overall, the ﬁgure shows good agreement between the

measurement and FEM. We used the Young’s modulus of the cupula and diffusion constant of

the IPMC sensor to ﬁt the model. Speciﬁcally, the FEM is able to capture the magnitude and the

polarity of the sensor response. For example, the polarity of the sensing signal is determined only

by the acceleration or deceleration trend of the stimulus.

121

(a)

(b)

(c)

Figure 7.11: Comparison between the FE model and the experimental measurements of the sen-
sor response under different acceleration stimuli and one angular velocity which is 16 rad/s: (a)
Angular acceleration 15.6 rad/s2 with viscous ﬂuid; (b) Angular acceleration is 31.2 rad/s2 with
viscous ﬂuid; (c) Angular acceleration is 40.3 rad/s2 with viscous ﬂuid.

122

Chapter 8

Conclusions and Future Work

8.1 Conclusion

We reported a new physics-based model for a tubular IPMC sensor subjected to a torsional load.

The model was built upon the Poisson-Nernst-Planck (PNP) equations for capturing the movement

of cations. A key innovation of this work was the proposal of relating the shear strains to the local

anion concentration. An experimental setup was created for applying twist at one end of the IPMC

tube while keeping the other end ﬁxed. Experiments involving stimuli of different magnitudes,

loading orientations, and loading/unloading speeds were conducted, and the proposed model was

shown to be able to capture the trends observed experimentally.

Inspired by the lateral line system of the ﬁsh, we explored the sensitivity of the IPMC-based

artiﬁcial superﬁcial and canal neuromasts based on their dimensions, shapes, and cupula stiffness.

For the canal-type lateral line system, modeling, fabrication, and experimental testing of were

investigated. Instead of water, the canal was ﬁlled with a viscous ﬂuid to emulate the biological

canals. The IPMC sensor physics was coupled to the FSI module for the cupula, allowing the

computation of the sensor output in the presence of a dipole ﬂow. The fabrication process of

the IPMC ﬂow sensor and cupula-like structure were described in detail. Experimental testing in a

dipole ﬂow was conducted to explore the canal performance. Simulation was conducted to examine

the effects of cupula size and stiffness on its displacement under a dipole stimulus. In particular,

123

the computation results from the ﬁnite-element model were compared with those predicted by an

analytical model to explore the valid regimes of the analytical model. Such comparisons yielded

useful insight as to when to use the analytical model for quick exploration of the design space, and

when to resort to the ﬁnite element model for higher-ﬁdelity predictions. By using the later ﬁnite

element model, we have modeled the superﬁcial lateral line and compared the simulation results

with an analytical model to have connection with the engineering counterpart.

we presented the fabrication, experimental testing, and simulation of a ﬁsh canal lateral line-

inspired pressure difference sensor and illustrated its use in underwater applications via a feedback

control experiment. The sensor consisted of a 3D-printed rigid semicircular channel and a 3D-

printed soft cupula, which housed an IPMC sensor that served as a hair cell. Experimental testing

in a dipole ﬂow was conducted to explore performance of the sensor, and the collected data on

the IPMC sensor output was analyzed. The experimental results conﬁrmed that the sensor was

able to effectively capture the pressure difference between the pores. Finite-element simulation,

with parameters identiﬁed using experimental data, was conducted to capture the ﬂuid-structure

interactions within the proposed sensor. It was found that the simulated displacement of the cupula

structure demonstrated similar behavior as observed in the experimental sensor output, when the

sensor was oriented at different angles relative to the dipole source. A sliding discrete Fourier

transform (SDFT) algorithm was used to effectively compute the IPMC sensor magnitude, which

enabled real-time feedback control of the orientation of the ﬁsh-like body.

We presented a new IPMC-based ﬂow sensing structure that exploits self-generated von Krmn

vortices. A 3D-printed soft material sheath was fabricated to house the IPMC ﬂow sensor. A key

innovation of this work was the proposal of combining the direct mechanosensory property of the

IPMC with the structural design of the sensor. Experimental testing in a laminar ﬂow setting was

124

conducted, and the collected data on mechanical vibration and IPMC sensor output were analyzed

to reveal the dependence of both signal magnitudes and frequency contents on the ﬂow speed.

Speciﬁcally, it is found that the average magnitude of the IPMC current output could serve as a

sensitive representation of the ﬂow speed.

Finally, we reported the fabrication, experimental characterization and the simulation of a novel

angular accelerometer inspired by the vestibular system. The sensor consist of a 3D-printed rigid

torus canal and a 3D-printed soft cupula, which housing an IPMC sensor that served as a hair

cell. Experimental characterization with a rotational movement stimuli was conducted to explore

the performance of the angular sensor, and the collected data on the IPMC sensor was recorded.

The experimental results conﬁrmed that the sensor was able to capture the angular acceleration of

the rigid body, and provided evidence that the ﬂuid-ﬁlled the canal play a key role in the sensor

performance. Finite-element simulations were conducted to capture the ﬂuid structure interaction

between the cupula-inspired IPMC sensor and the ﬂuid-ﬁlled the canal and to gain more insights

about the behavior of the angular acceleration device.

8.2 Future Work

First, in the study of the artiﬁcial lateral line system, further simulation results will be collected to

conduct non-dimensionalized analysis on the sensitivity. Experiments will be designed to charac-

terize the sensing response of the IPMC ﬂow sensor for both types (superﬁcial and canal) of lateral

lines.

Second, in the study of the bio-inspired pressure gradient sensor, a ﬁnite-element simulation

can be conducted, where IPMC physics is explicitly incorporated. Model parameters can obtained

from experimental data, so that the model captures the physical device with high ﬁdelity. Such

125

a model will be used to optimize the geometry and materials of different parts of the device (the

U-channel, cupula, etc) as well as the viscosity of the canal ﬂuid.

Third, for the ﬂow sensor using self-generated vortices’s, a ﬁnite-element modeling capturing

the ﬂuid-structure interactions and the IPMC physics will also be instrumental to further under-

stand the experimentally observed phenomena. Such a model can also be used to optimize the

geometry and material properties of the ﬂow sensor structure. Real-time algorithms for processing

the IPMC output can be developed to predict the ﬂow speed.

126

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