Swimming microrobots for biomedical applications

(1)

Swimming microrobots for biomedical

applications

HANNALI MILLAN FLORES

Department of Information Engineering

University of Pisa

This thesis is submitted for the degree of

Master of Science in Biomedical Engineering

(2)

(3)

I would like to dedicate this thesis to my be beloved husband Alejandro, thank you for holding my hand all the time.

(4)

(5)

Acknowledgements

I express my sincere gratitude to my supervisors, Dr. Ben Parslew who supported me throughout my thesis, tactfully correcting my conceptual errors, and providing guidance, and to Dr. Arianna Menciassi for her unconditional assistance.

I would like to thank the National Council for Higher Education (CNBES) for funding my studies and provided support to successfully overcome most difficulties of studying abroad. In addition, I thank the The State of Mexico Council for Science and Technology (COMECYT) for supporting this thesis work.

I am especially grateful to Guido Malloggi and his family. Le ragazze, Chiara, Cristina, Maria, Alba and Silvia, for their kindly student advise and guidance. To my family for cheering me up in the tough times. I express my sincere thankfulness to my husband Alejandro for his infinite patient and love.

(6)

(7)

Abstract

State-of-the-art miniaturisation technologies are now boosting the development of endoge-nous medical tools to micro-scales. Amongst these ongoing research efforts, endowing micro-tools with effective locomotion would represent a major breakthrough, specially swim-ming microrobots through the bloodstream since they would have access to any part of the body. However many challenges have to be overcome to enable the swimming micro-robot concept, for example the full characterisation of the fluidic medium and its dynamic behaviour at micro-scale is needed.

The aim of this investigation is to formulate an experimental protocol for the best performance of a swimming microrobot. The first part of this thesis presents a brief review of existing swimming microrobots concepts and their characteristics of motion. Second section presents computer simulations for kinetic and kinematic estimations for the microrobot configuration at issue. The final section presents the simulation results showing that it is plausible to obtain net displacement from a simple reciprocating microrobot with one degree of freedom in non-newtonian fluids at low Reynolds number.

(8)

(9)

Introduction

In medicine, one of the most popular techniques used to explore inside of human body is Endoscopy. The first endoscopic techniques appear in 1860s, however the most remarkable results have been seen in recent years. The introduction of robotic systems in the medical field has enabled the ability to steer and control traditional flexible endoscopes efficaciously, reducing patient discomfort and hospital stay. In addition, miniaturised technologies have broadened the means and ways to explore the human body. Such miniaturised devices in the form of capsules, have found application in wireless endoscopy and drug delivery. In general, the capsule is a small pill-like case containing a minute camera that the patient swallows reducing invasiveness. Once in the patient interior, collects data of the gastrointestinal tract and transmit it to a remote unit control.

State-of-the-art miniaturisation technologies are now boosting the development of en-dogenous medical tools to micro-scales. Amongst these ongoing research efforts, endowing micro-tools with effective locomotion would represent a major breakthrough, specially swim-ming microrobots through the bloodstream since they would have access to any part of the body. However many challenges have to be overcome to enable the swimming micro-robot concept, for example the full characterisation of the fluidic medium and its dynamic behaviour at the micro-scale is needed. This investigation sets out to assess the dynamic interaction of potential body fluids with a suitable micro-locomotion mechanism, to identify theoretical mechanism performances.

(10)

(11)

xii Table of contents 2.1.3 Shear rate on a blood vessel . . . 33 2.2 Simulation approach . . . 35 3 Discussion and Results 41 3.1 The milimodel swimming microrobot in non-newtonian fluid . . . 41 3.2 The micromodel swimming microrobot in Non-Newtonian Fluid . . . 46 3.3 The micromodel swimming microrobot in newtonian fluid . . . 49

References 53

(13)

List of figures

1.1 Shear Stress . . . 5

1.2 Non-Newtonian Fluids Shear Stress and Viscosity . . . 8

1.3 Blood vessels . . . 11 1.4 Blood cells . . . 11 1.5 Human Eye . . . 12 1.6 HV structure. . . 13 1.7 Illustration of a ciliate. . . 15 1.8 Cilia propulsion. . . 16

1.9 Cilia Multiple Actuation . . . 17

1.10 Vibrio Cholerae Bacterium . . . 17

1.11 Human spermatozoa . . . 18

1.12 Cilium and Flagellum Beating . . . 18

1.13 Flagellum Bacterial Inner Structure . . . 19

1.14 Bacterial Flagella Arrangements . . . 20

1.15 Generic Capsule . . . 21

1.16 Ellipsoid microrobot . . . 23

1.17 Differently coated shaped microrobots . . . 24

1.18 Retraction Instrument . . . 25

(14)

xiv List of figures

1.20 Magnetic Propulsion . . . 27

2.1 Drag Force Interaction . . . 30

2.2 Drag force-velocity relationship. . . 31

2.3 Drag coefficient as function of the Re number. . . 32

2.4 Effective viscosity versus shear rate. . . 33

2.5 Shear Rate Profile . . . 34

2.6 Two-link Simulink Reference System . . . 35

2.7 Effective body vectors diagram. . . 36

2.8 Two-link Simulink Diagram . . . 37

2.9 PID simulink diagram. . . 38

2.10 Sawtooth function approximation using Fourier series. . . 39

3.1 Angle between links in the milimodel. . . 42

3.2 Displacement of the milimodel . . . 43

3.3 Summary of simulation results for the milimodel in non-newtonian fluid. . . 45

3.4 Displacement of the micromodel . . . 47

3.5 Summary of simulation results for the micromodel in non-newtonian fluid. . 48

3.6 Displacement of the milimodel . . . 49

(15)

List of tables

(16)

(17)

Nomenclature

Greek Symbols η Dynamic viscosity µ Prefix 10−6m ν Kinematic viscosity ρ Density τ sheer stress Subscripts

crit Critical state

Acronyms / Abbreviations ALU Arithmetic Logic Unit BEM Boundary Element Method CD Contact Dynamics

CFD Computational Fluid Dynamics CK Carman - Kozeny

(18)

xviii Nomenclature DEM Discrete Element Method

DKT Draft Kiss Tumble

DNS Direct Numerical Simulation EFG Element-Free Galerkin FEM Finite Element Method FLOP Floating Point Operations FPU Floating Point Unit FVM Finite Volume Method GPU Graphics Processing Unit LBM Lattice Boltzmann Method LES Large Eddy Simulation MPM Material Point Method MRT Multi-Relaxation Time

PCI Peripheral Component Interconnect PFEM Particle Finite Element Method PIC Particle-in-cell

PPC Particles per cell

RVE Representative Elemental Volume SH Savage Hutter

(19)

Nomenclature xix SM Streaming Multiprocessors

USF Update Stress First USL Update Stress Last

(20)

(21)

Chapter 1 Swimming microrobots

Aiming the reduction of invasiveness in medical procedures and to enable unprecedented access to the human body, current investigations find inspiration in micro-life to find far-reaching solutions. The study of microorganisms help to envisage minute robots capable of exploring the human body. This apparent science fiction paradigm, is realisable with current technological achievements. Two major breakthroughs have paved the way to the realisability and viability of micro robots. Firstly, the invention of the microscope in 1595, and subsequently the invention of the integrated circuits in 1949. The microscope showed us the micro world, and the integrated circuits provide the means to work on it [5].

The current dimensions of minute robots range from the order of centimetre (10−2m), to nanometre (10−9m). Thus, a micro-robot can be defined robot in the order of a micrometre (10−6m), however many definitions exists. One definition states that a micro-robot is a miniaturised robotic system that make use of micro technologies [5]. Another definition is that a micro-robot is a miniature robot, chiefly mobile, with characteristic dimensions of less than 1 mm [4]. A microrobot consists of structural components, sensors, and actuators whose characteristic size is of less than 1 mm. These elements permit the microrobot to perform complicated tasks as well as sense and interact with the environment [25].

(22)

2 Swimming microrobots Based on this concepts, the new field of Microrobotics is stablished. Microrobotics aim not only in scaling down traditional robots, but to develop a new intuition that differs from the traditional one [1]. For example, in microrobots, bulk forces such as inertial forces and buoyancy are negligible or comparable to surface area and perimeter-related forces such as surface tension, adhesion, viscous forces, friction, and drag [28]. Inferring that microrobots for human body exploration have to swim through fluids, is possible to extend its definition to a swimming microrobot for biomedical application as a self-driven device with neutral buoyancy [15].

Several swimming microrobot concepts have been proposed for biomedical applications such as those navigating in viscous fluidic environments to release drugs, or assist in diagnosis. Locomotion designs in these concepts are chiefly inspired by those observed in nature, which are evolved for optimum propulsion generation at low Reynolds numbers [20].

1.1 Physics and dynamics at microscale

Predominant typical physical forces in macroscale differ to those found in microscale. For example surface interactions gain relevance as the analysed system scales down whereas other body characteristics, such as weight, become negligible. For this reason, swimming microorganisms have developed hardly familiar ways to locomote on their environment.

Hydrodynamics of a swimming body is characterised by the Reynolds number (Re). The Reynolds number is defined as the ratio of inertial forces to viscous forces into a flowing fluid. In swimming microbodies is commonly found low Reynolds numbers, which is typically termed low Reynolds number regime. Thus the Reynolds number is given by Eq. 1.1

Re= inertial f orces

(23)

1.1 Physics and dynamics at microscale 3 where

Inertial f orces: F_inertial = ma =v tρ l

3 _(1.2)

Viscous f orces: F_viscous= v tη l 2 _(1.3) yielding Re= ρ vl µ = vl ν (1.4)

where η is the dynamic viscosity, ρ is the fluid density, ν is the kinematic viscosity, v is velocity, and l a characteristic length. Whenever the viscous forces dominate over inertial forces Re < 1 and is to this as low Reynolds regime.

Using equation 1.4 to assess the movement of a Escherichia coli Bacterium swimming at 10 µm s−1in water which characteristic viscosity is around 10−3Pa s and length around 1 − 10µm, the Reynolds number corresponds to 10−5− 10−4. Some ciliates as the Parame-cium move at the characteristic velocity of 1 mm s−1, and have a characteristic length of 100µm yielding a Reynolds number of Re = 0.1 [11].

Another way to explain the phenomenon of micro swimming is through the Navier-Stokes equations given by ∇ · v=0 and equation 1.5. These equations completely define a fluid flow.

− ∇p + η∇2v | {z } Viscous term = ρ∂ v ∂ t + ρ(v · ∇)v| {z } Inertial term (1.5) Assuming an incompressible fluid, no-slip boundary, and constant η, these equations can be combined yielding a simplified equation that can be suitably nondimensionalised by the flow speed v and a characteristic length l as shown in equation 1.6

− ∇p + ∇2v = ρ vl η |{z} Re dv dt (1.6)

(24)

4 Swimming microrobots In the left side of the equation, the dimensionless coefficient Re is derived from the ration of the inertial and the viscous terms that under the fluid conditions mentioned above gives equation 1.7.

Re= ρ (v · ∇)v η ∇2v ∼

ρ vl

η (1.7)

At low Re, the left side of equation 1.6 may become negligible up to an extreme limit wherein equation 1.8 is simplified to the Stoke’s equation in equation 1.8

− ∇p + ∇2v = 0 (1.8) For this reason, the fluid flow around a body at low Reynolds number is defined as creeping flow or Stokes’ flow [2]. At low Re transition to turbulence barely exists, and fast and slow movements are indistinct as time becomes a negligible ingredient1. An important consequence of these conclusions is that a body moving at low Reynolds number and transitioning between two reciprocating configurations, will cause null effective movement. Extrapolating this effect to a micro swimmer, sequential symmetric reciprocating movements on an incompressible newtonian fluid, the resulting displacement of the swimmer will be zero, the so-called Purcell’s scallop theorem. In Purcell’s own words, "Fast, or slow, it exactly retraces its trajectory, and it’s back where it started" [23]. A result of this postulate is that if a microbody has only one degree of freedom it cannot go any where, it is necessary at least two degrees of freedom to do it so. It is important to notice that the scallop theorem is not supported in non-newtonian fluids [24].

(25)

1.2 Biofluids Dynamics 5

1.2 Biofluids Dynamics

The human body is mainly composed of water around 65 % [26]. All cells are immersed in a water-based extracellular fluid, and their intracellular composition is water-base too. Fundamental transportation mechanisms take place through flow streams, such as the blood circulation, and others use the fluids to move through. To study these biological mechanisms, fluid mechanics principles are applied. This section presents mathematical concepts about fluid characteristics assisting the analysis of biological fluids.

A fluid is a quantity of matter that deforms when a continuous stress tangential to the surface of a fluid element is applied as shown in figure 1.1. Under the action of this shear stress the fluid element will move. The shear stress is defined as in equation 1.9

τ = F

A (1.9)

(26)

6 Swimming microrobots One of the most important properties of a fluid is its viscosity. Viscosity is the resistance of a fluid to be deformed by shear stress, a phenomenon interpreted as the internal particles friction of a moving fluid. In order to relate viscosity to shear stress, consider the geometry configuration presented in figure 1.1. Assume that a force F is applied at constant velocity v, the velocity gradient (γ) or shear rate defined as:

γ = ∂ v ∂ y [s

−1_]

(1.10) The relationship between shear stress and shear strain rate of a fluid is

τ ∝ ∂ θ

∂ t (1.11)

Acknowledging that the relationship between shear stress rate and velocity gradient is given by equation 1.12

∂ θ ∂ t =

∂ v

∂ y (1.12)

it is possible rewrite the shear stress as: τ = η∂ θ

∂ t = η ∂ v

∂ y (1.13)

where η is the dynamic viscosity coefficient with units [ Pa s ], or equivalently [kg_/_{m s}_]

in equation 1.14.

η = τ

γ (1.14)

Another important concept is the kinematic viscosity (ν), which relates the dynamic viscosity and fluid density as presented in equation 1.15.

(27)

1.2 Biofluids Dynamics 7 ν =η ρ m2 s (1.15) A fluid can be classified according to its dynamic viscosity as ideal fluid (η = 0) or nonviscous, newtonian (η = constant) and non-newtonian (variable η) [16]. A newtonian fluid has a linear relation between shear stress and shear rate, i.e. its dynamic viscosity is constant under any share rate e.g. water or blood plasma. A non-newtonian fluid has variable dynamic viscosity, that is the dynamic viscosity is dependent on shear rate or shear rate history. Some important examples of non-newtonian fluids found in the human body are the blood and the vitreous humour.

The behaviour of the non-newtonian fluids can be summarised in three categories. The first category encompasses time independent non-newtonian fluids, wherein the shear rate is a function of the shear stress at a point at a specific time. Examples of this first category are the Bingham, pseudoplastic and dilatant shown in figure 1.2. In the second category are included the time-dependent non-newtonian fluids wherein their viscosity is determined by the duration of the shear stress applied. A third group is characterised by viscoelastic non-newtonian fluids, that is, typically viscous but present slight elastic behaviour after deformation. Some examples of viscoelastic fluids are the sputum and the vitreous humour [16].

A dilatant or shear thickening fluid has larger viscosity at higher shear rate, in contrast to the behaviour of a pseudoplastic or shear thinning fluid wherein lager viscosity is presented at low shear rates. Some examples of pseudoplastic fluids are the saliva, blood and synovial fluid. In a viscoplasic fluid, the shear stress in the fluid has to exceed the yield stress in order to deform it or to make it flow. In a Bingham fluid, exists a threshold shear stress value required to produce deformation or induce flow [26].

Non-newtonian fluids follow non-linear relationships that are typically represented by power laws. A suitable equation form for newtonian, non-newtonian, pseudoplastic and dilatant fluids is presented in equation 1.16.

(28)

8 Swimming microrobots

Fig. 1.2 Non-Newtonian fluids shear stress-shear rate and viscosity-share rate. Image credit: Ostadfar [16].

τ = kγn (1.16) where k is a consistency index and n is the power law constant. In order to ensure that τ has the same sign that γ, the equation can be rewritten in the form

τ = η γ (1.17) with η it the apparent o effective viscosity given by

η = k|γn−1| (1.18) Thus for pseudoplastic fluids n < 1 so that the apparent viscosity decreases with the shear rate; for newtonian fluids n = 1 recovering a straight line equation; for dilatant fluids n > 1, expressing that the apparent viscosity increases with the shear rate. On the other hand, the equation representing a Bingham fluid is

(29)

1.2 Biofluids Dynamics 9 τ = η γ + τ0 τ ≥ τ0 (1.19)

with

γ = 0 τ ≤ τ0 (1.20)

In this case the shear stress has to surpass a threshold value or yield stress τ0to cause

flow or deformation. After the shear stress threshold is reached, its relationship with the shear rate is linear [14].

(30)

1.3 Biofluids characteristics

The fluids within the human body may contain air, O2, CO2, water, solutions, suspensions,

serum, lymph and blood. Biofluid composition is an important design parameter in micro-robots because it greatly defines the overall interaction with the robot. In this section is presented an overview of the biofluids where swimming microrobots find potential applica-tion.

Blood

Blood is a suspension of cells in aqueous solution of electrolytes, it delivers nutrients and oxygen to every cell and take away their waste byproducts, and has an average density of 1050 kg/m3[9]. In addition, blood regulate the body’s functioning, maintain homeostasis, supply immunological functions and body repairing mechanisms, and serves as heat trans-port mechanism to optimise body temperature regulation. Blood presents a shear thinning behaviour and circulate throughout the body using blood vessels. The driving force in the cardiovascular system is by far, the hearth beating. Figure 1.3 illustrates various types of blood vessels and their main physical characteristics. The main components of the blood are cells of various types and plasma as describe below.

The cells constituting the blood are erythrocytes, leukocytes and thrombocytes, illustrated in figure 1.4. The erythrocytes, so-called red cells, are present in number density of 5 × 106mm−3, and contain the blood’s haemoglobin and distribute oxygen. An erythrocyte is a biconcave disc of 8.1 µm with thickness 1 − 2.7 µm, and its main function is to transport haemoglobin. The leucocytes, or white cells, are present in number density 5 − 8 × 103mm−3, and are responsible of fighting disease and infections in the body. Thrombocytes, or platelets, are found in number density 250 − 500 × 103mm−3, and present an average diameter of 2.5 µm. Thrombocytes are responsible of blood clotting. Thrombocytes and leukocytes have a negligible effect on the flow properties of blood.

(31)

1.3 Biofluids characteristics 11

Fig. 1.3 Blood vessels and their main physical characteristics.

(32)

12 Swimming microrobots Blood plasma is the liquid component of blood in which blood cells are suspended and constitutes around 55% of the total blood’s volume. Its major component is water, and contain proteins, glucose, clotting factors, hormones, as well as gasses like carbon dioxide. It has an average density of 1020 kg/m3 [9] and present non-newtonian behaviour with dynamic viscosity of ∼ 1.32 Pa s [33].

Vitreous Humor

The human eye is the organ that provides vision input. Its main characteristic as sensorial organ is that it reacts to light and pressure. The eye ball has a sphere-like shape that can be analytically subdivided in two main parts, the anterior part and the posterior part. The anterior part encompasses the lens, iris and cornea. The posterior part encompasses the vitreous humour, retina, choroid and the sclera. The posterior part is bigger than the anterior part, with a typical diameter of more than 24 mm. The vitreous humour (VH) is a non vascularised clear gel-like fluid, enclosed by the lens and the retina as shown in figure 1.5. The vitreous humour presents non-newtonian behaviour in two observed different phases, i.e. liquid and gel phases.

(33)

1.3 Biofluids characteristics 13 Table 1.1 Vitreous humour scaffold composition.

Element Composition [ µg/cm3] Collagen 40-120 Hyaluronic acid (HA) 100-400

The VH is a blend water in 90 %, salts in 9 %, and 0.1 % of fine collagen fibrils and hyaluronic acid, these last two forming a scaffold structure illustrated in figure 1.6. Table 1.1 reports the density of the elements of the scaffold structure.

Fig. 1.6 HV Structure. Image courtesy of Andreia F. Silva [3].

The gelatinous characteristic of the vitreous humour is the result of long arrangements of collagen fibrils and HA molecules that stabilise water molecules and proteoglycans. The fibre patterns increase in density away from the centre, forming two distinguishable bodies, the anterior and posterior hyaloid membranes. The VH in the human eye has a volume of 4 ml and density of 1005.3 − 1008.9 kg/m3. The VH average density is 1005 kg/m3 and dynamic viscosity of ∼ 1.06 × 10−3Pa s [9]. Some studies have revealed that the viscosity of HV exhibits shear thinning with a power-law behaviour of τ ∼ γ−1 [3]. In addition, the VH presents viscoelastic behaviour, due to the presence of HA and collagen. The spatial distribution of collagen fibres and HA molecules is not uniform, causing uneven properties distribution on the VH. Ageing cause changes in the structure of the VH, resulting in liquefaction. That is, the transformation from formed gel to a phase-separated fluid occurs.

(34)

14 Swimming microrobots Liquefaction reduces the VH viscoelasticity, causing the appearance of diseases such as retinal detachment and retinal tears.

(35)

1.4 Swimming Microorganism 15

1.4 Swimming Microorganism

Propulsion and locomotion in swimming microrobots has been inspired by the swimming microlife that inhabits at low Reynolds number regime. Some microorganisms termed motile, have developed ways to control its displacement prompted by the fundamental needs of feeding, mating, surviving, etc. Along their evolution, microorganisms have developed diverse techniques of self-propulsion and self-locomotion, that is, they are able to navigate without external forces acting on their bodies, making them a highly adaptable form of life. Research is focused on understanding the movement solutions developed by bacteria as their swimming motion is governed by viscous forces rather than inertial forces, the type of scenario found in swimming microrobots. Relevant to microrobots are the swimming mechanisms developed by ciliates and flagellates described below.

1.4.1 Ciliates

Ciliates are a group of unicellular eukaryotic organisms, the protozoa, characterised by the presence of multiple active hair-like organelles named cilia, illustrated in figure 1.7 . Cilia serve multiple purposes such as for navigating, dragging, hooking up, feeding and sensing. All these behaviours are triggered by signal processes.

(36)

16 Swimming microrobots Ciliates live in water, with characteristic lengths between 10µm to 4 mm. A ciliate moves by metachronal wave motion, a kind of wavy motion created by the sequential action of the cilia. These movements resemble a travelling wave that furnish propulsive waves travelling through the surface of the bacteria [17]. The metachronal wave motion may present two different forms as: sympletic metachrony, that is the effective stroke moving in the same direction as the wave crests, and antipletic metachrony, the effective stroke moving in the opposite direction with respect to the wave crests.

The cilium movement has two characteristic phases. During the first phase, the cilium is maintained perpendicular to the flow generating a high drag power stroke causing advance motion. In a second phase, the cilium is kept parallel to the flow generating a low recovery stroke [2]. An illustration showing the way cilium generates propulsion in the bacteria body is presented in figure 1.8.

Fig. 1.8 Cilia propulsion: a) a single cilium motion b) visualisation of the antipletic metachronal wave [17].

Ciliates moved by multiple cilium classifies as the largest and fastest group of microswim-mers in nature. In microrobots, the simultaneous activation of multiple actuators to reproduce cilia motion illustrated in figure 1.9, is at present unachievable. However, several investiga-tions have implemented the principle of propulsion of a cilia, resulting in feasible designs.

(37)

1.4 Swimming Microorganism 17

Fig. 1.9 Idealisation of a multiple actuation on ciliates [18].

1.4.2 Flagellates

A flagellate is a unicellular organism, with size 5 − 20 µm characterised by one o more tail-like appendages called flagella. A flagellum is a whip-tail-like organelle, used for propulsion and locomotion through a fluid where the microorganism lives. Examples flagellate organisms are the prokaryotes, e.g. vibrio cholera in figure 1.10, and eukaryotes, mammalian sperm cell in figure 1.11.

Fig. 1.10 Vibrio Cholerae Bacterium. Image courtesy of Pope [22].

An eukaryotic flagellum could be seen as a larger cilium, in fact, historically they have been distinguished according their length and the number that the cell has on its surface, for example eukaryotes have eight flagella at most. Both, the cilium and flagellum have the same ultrastructure, however their motion differ. Eukaryotic flagella deform its shape to create a paddling motion, i.e. beating in a planar wave form, or circular translating movements [2]. On the other hand, cilia motion is more complex as observed from the figure 1.12.

(38)

Fig. 1.11 Human spermatozoa. Image courtesy of De Blas et al. [7].

(39)

1.4 Swimming Microorganism 19 In another example, prokaryotic (bacterial) flagellum is a helical, 20 nm thick, hollow appendage. it moves in a helical way, as a result of a molecular motor that spin the flagellum base, in a corkscrew fashion [2]. The flagella rotation is continuous resulting in a non reciprocal motion. The flagellum spin is stabilised by a counter-spin made by the bacterial body. However it doesn’t add propulsion to the bacterium. The system of the flagellum is compose of a basal body, embedded in the plasma membrane that has two protein-base rings one over the other, a rod, that connects the basal body to a hook, the hook is the interface between the cell to the flagellum, figure 1.13. When an exchange of protons occurs in the basal body, one ring rotes relative to the other making to rotate the rod, consequently the hook. How the flagella is attached to the hook, it results in a step rotation, the rotation can be clock-wise or counter clock-wise.

(40)

20 Swimming microrobots Some bacteria have more than one flagellum, that bundle during swimming [2]. In figure 1.14 is show the different arrangements for bacterial flagella.

Fig. 1.14 Bacterial flagella arrangement: a)monotrichous, b)lophotrichous, c)amphitrichous, d)peritrichous [32].

(41)

1.5 Microrobots state of the art 21

1.5 Microrobots state of the art

Since the time the first microcontroller was released in 1971 researchers have envisioned different medical applications, however it was until the 80’s when medicine boosted to the idea of miniaturisation in a myriad of possible applications, from the introduction of minimal invasive surgery procedures to targeted therapy and drug delivery.

One of the first miniaturised technologies and the most successful is the video endoscope capsule in gastroenterology. The endoscope capsule is a type of video-telemetry capsule that is sufficiently small to be swallowed (11 × 30 mm) and has no external wires, fibre-optic bundles nor cables. By using lens of short focal length, images are obtained as the optical window of the capsule go ahead through the gut wall, waiving air inflation of the gut lumen. The capsule endoscope is moved by peristalsis through the gastrointestinal tract (GIT) and does not require a pushing force to propel it through the bowel. In figure 1.15 is shown an example of endoscope capsule. During the travel through the GIT, the capsule is turned on in specific zones of interest saving power.

Fig. 1.15 Structure of a generic capsule: 1-optical dome; 2-lens holder; 3-short focal length lens; 4-LEDs; 5-CMOS image sensor; 6-batteries; 7-ASIC RF; 8-antenna

The video images are transmitted using radio-telemetry to a portable recorder attached to the patient’s body which allow image capture. The patient is not required to be confined to a hospital environment during the examination and is free to continue his or her daily

(42)

22 Swimming microrobots routine [10]. At the end of the examination the images are retrieved from the data recorder to a work station for detailed examination [13]. This technique of examination has been useful in the premature diagnosis of diseases on the oesophagus, small bowel and colon. The first capsule endoscopy system was manufactured by Given Imaging in 2001 [12]; since then, many companies are focusing on this wireless capsule endoscopy. Olympus, IntroMedic, and Jinshan have released their own commercial products of wireless capsule endoscopy.

Some of the challenges found in this technique include: Energy constrains: Due to the reduced space in the capsule the number of batteries is restricted, setting the functionalities of imaging acquisition, wireless transmission and locomotion to a limited application. Local-isation: It is necessary to know the precise position of the capsule to achieve far-reaching functionalities like active locomotion and drug delivery.

Recently, microrobots application has gain attention in ophthalmology for robotic assisted surgery and drug delivery. Ophthalmic surgeries are procedures requiring high level of precision, such that the surgeon must be greatly experienced due to the small forces applied into delicate tissue eye, which are below of the human force perception threshold. In this field, a microrobot provided with minute needles, minute pumps, as well as force and chemical sensors could manage specialised tasks as required in eye surgery. Thus reducing the invasiveness compared to conventional ocular surgery. For example, the use of microrobots may be advantageous in ailments like detached retinas, neovascularisation or abnormal lump tissue, where currently a large portion of vitreous humour is removed to create a workspace. Besides that an optical microscope could be used to track the microrobot motility, reducing further the invasiveness [30].

Addressing this area of opportunity, The Institute of Robotics and Intelligent Systems at the ETH (Swiss Federal Institute of Technology, Zurich) has fabricated a microrobot prototype using hybrid MEMS, to explore magnetic driving and wireless operation. The

(43)

1.5 Microrobots state of the art 23 winged ellipsoid prototype in figure 1.16 was built with ferromagnetic materials using a hybrid MEMS/electroplating manufacturing technique.

Fig. 1.16 Prototype of magnetic microrobot. Image courtesy of Troccaz and Bogue [30]. The driving system where the prototype is placed fuses two couples of coaxial field-generators. A couple is implemented in the form of two coils in Helmholtz configuration, to generate a steady magnetic field at the centre of the coils, and a couple in Maxwell configuration to generate a steady gradient field. By regulating the current feeding in the coils, is possible to manipulate the torque and force in the microrobot prototype.An additional engine controls the position of the coils. Reported results [30] show that it was possible to guide the microrobot along channels of water.

Experiments like this have lead the development of new designs of swimming microrobots. Some of these designs are discussed below. A set of three microrobots in figure 1.17 are proposed for ophthalmologic applications. One of them has the shape of a hollow cylinder with outer diameter of 285 µm and inner diameter of 125 µm, with length of 1800 µm. In

(44)

24 Swimming microrobots addition, a needle for puncture, and a microrobot for drug delivery fabricated using a non toxic polypyrrole (a type of organic polymer formed by the polymerisation of pyrrole) or inert metallic coatings (e.g. gold) [31] are proposed. These microrobots are introduced into the vitreous cavity by a tiny incision in the zone of the sclera. The microrobots are then driven wirelessly to the area of interest where the surgeon have to execute a specific task [31].

Fig. 1.17 Differently coated shaped microrobots: a)gold-coated for drug delivery b)microneedle for punctura c)Polypyrrole-coated for drug delivery [8].

The hollow cylindrical microrobots in figure 1.17a,c are designed as drug containers. Driving the microrobot to the location of interest, the drug is delivered in a more contained region reducing its impact on surrounding tissues. The robot way path design from its insertion into the eye to the area of interest is assisted by 3D computational algorithms. Once the microrobot is inside the eye, is monitored using a camera and computer visualisation algorithms to gather information to feed a close-loop controller. The control system regulates the driving magnetic fields and gradients steering the micro robot througth its designed path. On the other hand, magnetic guided microrobots supplied with microneedles (Figure 1.17b) could be used to puncture blood vessels to treat neovascularization.

This prototype is characterised by high precision in the introduction of the microrobot and in realtime force feedback when the punctures are carried on. Once the procedures are finished, the employed microrobot is removed with a bespoke magnetic instrument, figure 1.18. This magnetic instrument is a magnetic wire, placed in a 23G medical needle, it attracts the microrobot bringing back into the needle, and clearing away from the eye.

(45)

Fig. 1.18 A tailored retraction instrument for removal of a microrobot. Image courtesy of Franziska Ullrich and Nelson [8].

Recently, a swimming microrobot driven by a light-induced peristaltic motion have been developed by the Max Planck Institute for Intelligent Systems in Stuttgart. This microrobot is simple actuated, conversely to the previous example. This model follows a ciliate-like design made with materials incorporating properties of liquid crystals and elastic rubbers. The material has a rod cylinder shape of 1 mm in length and 200 − 300 µm in diameter and reacts to green light. This design [18] aims is to be a type of universal swimmer, driving freely within a liquid without the need of predefined paths or external forces.

Fig. 1.19 Triggered motion of a soft swimming microrobot. Image courtesy of Palagi et al. [18].

The swimming microrobot advances on when an arrange of active light field is applied. The body of the microrobot is a compound of liquid crystal molecules and coloured molecules that warm up when lighted up. The temperature change induces flexure on the liquid crystal molecules causing protuberances on the material geometry. In an actively illuminated field,

(46)

26 Swimming microrobots the protuberances run along the model in a peristalsis-like effect, thus moving the model forward. In figure 1.19 is shown a diagram of the movement. The material used in that prototype have rapid response to illumination, instantly changing its shape accordingly and returning to its geometric base form state when light is turned off. This form of actuation has shown a speed around 2.2 µm/s and reached a displacement distance of 110 µm in experiments [18].

1.5.1 Propulsion and Locomotion

The most common power source used in microrobots is the battery although it represents a major size limitation. Other types of power source have shown high performance like radio frequency power, optical power, and energy scavenging techniques [5].

At present, it is possible to scale down mechanical and electrical systems by MEMS and VLSI techniques, enabling the exploration of electrochemical energy storage out of reach before the development of such techniques. Another benefited area from the MEMS and VLSI techniques is the manufacturing of micro actuators and micro propulsion systems. A major current technique [2] is using magnetic fields to transfer energy and propulsion to the microrobot from the exterior. Propulsion is achieved by magnetic fields and gradients that produce translational forces into the microrobot, or by oscillating magnetic fields to produce motion. In figure 1.20 are shown two types of swimming microrobots using magnetic fields for propulsion.

The development of an extremely miniaturised motor has been reported by Monash University. It consists of a piezoelectric motor that mimics the biological mechanism of the Escherichia coli. The motor has the dimensions of about a grain of sand and use a flagella to propel. The motor uses ultrasonic frequencies to make resound a microstructure inside the rotor, and when it is compressed towards the rotor, unroll and the rotor twist letting the robot going forward in a screw-like motion. [30]

(47)

Fig. 1.20 Magnetic Propulsion a)microrobot and b)microrobot with helical propeller pulled via magnetic field gradients. Image courtesy of Abbott et al. [2].

Locomotion at low Reynolds regime is possible using non reciprocal actuation in newto-nian fluids. Microorganism rule out time-reversal actuation by rotating or beating flagella, or undulating cilia. The idea of using helically shaped micropropellers with rigid asymmetric structures is that the structure and mirrored image are not superimposable. In this way, unidi-rectional and nonreciprocal rotations would produce forward advancement. Strictly speaking, it is not propulsion, it is a form of enhanced diffusivity. Other swimming microrobot concepts have been constructed using supermagnetic beads to build up a chain-like structure being actuated by magnetic fields gradients [24].

A biological swimming microrobot has been proposed by the University of Montreal in cooperation with the Canadian École Polytechnique of Montreal. It is called the molecular motor and uses a magnetotactic bacteria, that is a bacteria that naturally contain nanoparticles of iron oxide termed magnetosomes causing them to move in response to the magnetic characteristics of their environment. This robot concept combines a MEMS device, mi-croelectronics and microcoils, and the magnetotactic bacteria. The microcoils produce the magnetic flux required to orient the bacteria [30].

(48)

28 Swimming microrobots Recently, a size-reduced electromagnetic system has been proposed for magnetic micro-robot control, the OctoMag. This system is able to control microdivices in three dimension and its workspace is about 800 mm3. The system is capable of reaching the posterior part of the human eye. This system is composed of eight electromagnets disposed in hemispher-ical configuration, wherein the rotation of the microrobot is carried out by controlling the orientation of the applied tridimensional magnetic field, and force control by field gradient management [31].

After this brief introduction to the current state-of-the-art in microrobots technology, it is clear that the mechanism of swimming at microscale differ as much from macroscale. Microorganism have developed novel systems of actuation to overcome the unfavourable of its surrender. All the efforts that researches have done to mimic this behaviour is seeing a bright future. However, there is a fairly lack of understanding about how to improve the performance of these swimming microrobots. The next chapter describes the numerical simulation protocol followed to study the performance of a two-link swimming microrobot in biological fluids.

(49)

Chapter 2 Two-Link Swimming Microrobots

Simulations

The most studied movement solutions in newtonian fluids at low Reynolds numbers, exclude those employing reciprocating motion due to the impossibility to obtain net movement as summarised by the Purcell’s scallop theorem. However, little is known about reciprocating motion in non-newtonian fluids at low Reynolds numbers, where the scallop theorem in no longer valid. Due to the non-newtonian nature of common biofluids and the convenient simplicity of reciprocating motion in microrobots, this chapter presents a design approach for the computational analysis of this scheme. The study focus on the numeric analysis of a 2D two-link swimming microrobot under the action of reciprocating motions, whose design is detailed below.

2.1 Theoretical Background

This section presents mathematical models applicable to the two-link model. In addition, are stablished the assumptions and simplifications needed to delimit the scope of the simulation, in a trade-off between computational adequacy and representativeness of the model.

(50)

30 Two-Link Swimming Microrobots Simulations

2.1.1 Drag Force

Drag force relates is an experimental quantity that relates five factors, namely drag force F_d, medium density ρ, reference area A, the drag coefficient Cd, relative speed v. The drag

coefficient captures the complexity of the fluid-surface interaction into a non dimensional quantity. The value of Cd is sometimes simplified to fixed values although the nature of Cd is

variable as function of the Reynolds number. If the interaction with the fluid is high, then the value of Cd increases, whereas in reduced interaction conditions it may be reduced as

illustrated in figure 2.1. The remaining factors in the drag force formula in equation 2.1, involve the fluid properties (ρ), the scale of the C_d interaction through A, and the relative velocity between the reference area and the fluid.

F_d= 1 2ρ v

2_C

dA (2.1)

(51)

2.1 Theoretical Background 31 The magnitude of the drag force is a strong function of relative velocity, squared velocity, and its direction is defined by the counter reaction of the relative velocity to which the incident flow impinges on the surface, see figure 2.2.

Fig. 2.2 Drag force-velocity relationship.

The value of Cd depends on the fluid motion and its interaction with the body properties

as shape and surface condition. In specific circumstances where the fluid is prone to remain trapped or attached to the surfaces during the relative motion, the overall interaction can be approximated as that of a sphere. In practice, the interaction of fluids and microrobots presents that phenomenon enabling the assumption of a simplified spherical geometry. Therefore, in this study is used the analytic Cdfunction of the Reynolds number representing a sphere as

reported by Plötner et al. [21]. C_d= 24 Re+ 6 1 +√Re+ 0.4 0 ≤ Re ≤ 2 × 10 5 (2.2) The plot of equation 2.2 is presented in figure 2.3. Note that at Re below unity, CD is

proportional to Re−1. Let’s consider a Re < 1 and combine the equation 2.1, 2.2 and 1.4, we will see that the drag force scales proportionally to the characteristical length of the body in study.

(52)

32 Two-Link Swimming Microrobots Simulations 10−5 10−4 10−3 10−2 10−1 100 101 102 103 104 105 100 102 104 106 Re Cd

Fig. 2.3 Drag coefficient as function of the Re number.

2.1.2 Non Newtonian Viscosity Model

For the simulation are considered the thinning non-newtonian properties of blood, using the power law function as discussed in chapter 1. In order to model the shear thinning properties of blood, a constitutive equation defining the relationship between viscosity and shear rate is required. Experimental data reported by Neofytou and Tsangaris, and Yilmaz et al. [34] shows that the values of parameter in equation 1.18 are given by k = 14.67 mPasn and n = 0.7755. These parameters are obtained by model fitting on experimental data. The equation relates the time-independent effective viscosity to the shear rate in the form presented equation 2.3.

η = 14.67 × 10−3|γ−0.2245| (2.3) It is worth mentioning that he behaviour of blood apparent viscosity shows three charac-teristic regions. A region encompasses the conditions of low shear rate, and constant viscosity. In a middle region the apparent viscosity decreases with increasing γ, and an extreme region where high values of γ produce constant η. The equation 2.3 is valid describing the middle region and is chosen for application in this investigation because it captures the standard

(53)

2.1 Theoretical Background 33 observed non-newtonian viscosity of blood and its shear thinning behaviour. Figure 2.4 shows the apparent dynamic viscosity of the blood shear thinning behaviour using the power law mentioned above.

10−4 10−3 10−2 10−1 100 101 0.1 0.06 0.02 γ η

Fig. 2.4 Effective viscosity η versus shear rate γ according to the power law.

2.1.3 Shear rate on a blood vessel

It is discussed in the previous chapter that the shear rate is a characteristic of the fluids in the presence of a differential velocity between adjacent parallel layers. This idea is captured in the fundamental concept of an infinitesimal fluid element that presents deformation as a result of the action of a shear force acting on it. Under the assumption of no-slip condition at the boundary, that is the point where the fluid meets the surface must have zero velocity, the bulk flow velocity presents a velocity profile fulfilling the boundary condition. These can be written in equation 2.4, as a velocity gradient function of distance from the surface.

γ = ∂ v

∂ r (2.4)

Applying this concepts to a blood vessel assuming it as a rigid and cylindrical tube with diameter d, and that the blood shows constant viscosity, and laminar flow, the Poiseuille’s

(54)

34 Two-Link Swimming Microrobots Simulations law can be used to obtain an approximated analytical function for the shear rate in equation 2.5.

γ = 8v

d (2.5)

Under these conditions a parabolic velocity profile is set as shown in figure 2.5. If the velocity is incremented and the vessel diameter is kept constant, the shear rate is reduced and vice versa.

Fig. 2.5 Velocities profiles in cylindrical tubes [19]

Recapping these equations, the drag coefficient in equation 2.2 is governed by the Reynolds regime, that in turn is defined by the non-newtonian characteristics of the fluid modelled in equation 2.3. The relationship between the Reynolds number and η is given by equation 2.6, wherein η is expected to vary with the velocity profile as shown in equation 2.5. The aforementioned models provide a rough approximation of the interaction fluid-microrobot swimming in a non-newtonian fluid. The mixed effect of low Reynolds number and the properties of a non-newtonian fluid, modifies the effective drag force experienced in a swimming microrobot actuated with reciprocating laws. The analysis of the dynamics of a swimming microrobot under this scenario is suitably addressed with numerical simulations as detailed in the following section.

Re= ρ vl

(55)

2.2 Simulation approach 35

2.2 Simulation approach

A two-link microrobot model is constructed in Simulink Matlab®

using two rigid bodies connected by a hinge at one of their extremes as shown in figure 2.6. The microrobot model is restricted to move freely in planar motion (x − y plane) as dictated by its movement and the interaction with the fluid.

Fig. 2.6 Two-link Simulink Reference System

Two different scales are used for the microrobot. In one of them, the model size is 4 mm × 4 mm × 10 mm in each link, referred to as the milimodel. A second model is the scaled version of the milimodel by a factor of 1/10, referred to as the micromodel. The material properties chosen for the model correspond to those of Titanium (Ti). Although the inertial properties of the model are expected to be negligible in comparison to the surface interaction, this material is selected in compliance to the typical biocompatibility requirement in a real device.

The drag force is expected to be distributed along the links geometry in an initial rigid body kinetics approach. The effective drag force on each link is assumed actuating on its centre of mass with direction antiparallel to the effective velocity ⃗v. As the microrobot

(56)

36 Two-Link Swimming Microrobots Simulations model is allowed to move in planar motion, the velocity vector of each link may differ, in particular if the microrobot’s links are moving with respect to each other, i.e. the angle between them is changing with time. If the microrobot is moving and the links are rotating about its connecting hinge, the vectorial sum of velocities allow the identification of the link’s centre of mass velocity. Thus the effective link velocity has two components with respect to its body reference frame, a component parallel to the surface vector and a component perpendicular to the surface vector. The component of interest for drag force estimation, is the velocity projected on the parallel direction ⃗v1,2, because it can be interpreted as the

effective flow bulk velocity seen by the link. These concepts are illustrated in figure 2.7

Fig. 2.7 Effective body vectors diagram.

To include reciprocating motion of the links in the model, a periodic input signal is used. The time-dependent periodic signal serves a control law to establish the angle of aperture between the two links. In order to approximate the conditions encountered in a real device, a Proportional?Integral?Derivative controller is used to furnish a suitable torque level to ensure the reciprocating link’s motion according to the interacting fluid characteristics. The block diagram of the microrobot model enclosing the aforementioned conditions is presented in figure 2.8. The model of the PID controller is presented in figure 2.10.

(57)

(58)

38 Two-Link Swimming Microrobots Simulations

Fig. 2.9 PID Simulink diagram for swimming two-link microrobot.

Two different reciprocating link motions are used in the simulations. In both cases the angle of aperture is maintained within the range 0 − 90◦, but with differing angular velocity profiles. The input reference periodic functions used to control the links angle of aperture, are a sawtooth function and a sine function. The sawtooth function is characterised by uniformly varying angle of aperture, i.e. 0 → 90, followed by sudden closing motion 90 → 0. On the other hand, the sine function opens and closes smoothly in a time symmetric curve. In both cases the motion is repeated periodically.

A technical issue is presented in the sawtooth function as may be expected from its discontinuous behaviour. The sudden closing movement, although advantageous under specific circumstances to the swimming microrobot, is a situation difficult to handle in a numerical environment. The numerical integration in the simulation may present singularities or an excessively large transient response in the controller. To overcome this issue, a Fourier series approximating the sawtooth function is employed. In this investigation the first ten successive partial Fourier series are used as they give a good approximation of the sawtooth function as shown in figure 2.10.

(59)

(60)

(61)

Chapter 3 Discussion and Results

3.1 The milimodel swimming microrobot in non-newtonian

fluid

The milimodel swimming microrobot (4 mm × 4 mm × 10 mm in each link) is tested in a non-newtonian thinning fluid. In this case the properties of blood are used in the model and two different types of actuation. The first type of actuation consists of asymmetric open and close angle between the two links (θ ) as show in figure 3.1 in the sawtooth wave. The sawtooth wave has an opening and a closing rate of 0.2532 rad s−1and 4.3011 rad s−1 respectively. The second type of actuation uses a symmetric open-close motion, modelled with a sine wave at frequency 2/3π. Both types of actuation are thus reciprocating and the links meet with the same period, although show different angular velocity profiles.

In figure 3.2 is shown the displacement of the milimodel in both actuation instances. The milimodel shows a net displacement forwards with characteristic speed of approximately 3.3 mm/s. On the other hand, symmetric actuation (sine wave) resulted in negligible dis-placement. From these results, the role of inertial forces is still dominant at the scale of the milimodel as the impulse input from the sawtooth function increases the linear momentum in

(62)

42 Discussion and Results

Fig. 3.1 Angle between links in the milimodel. Both curves have the same period but show different angular velocity profiles.

(63)

3.1 The milimodel swimming microrobot in non-newtonian fluid 43 the model. The average Reynolds number is this case confirms this explanation with a value of 4.05, whereas the average Reynolds number for the symmetric case is 1.69 with higher influence of viscous forces.

Fig. 3.2 Displacement of the milimodel

Figure 3.3 presents a summary of plots from the simulation of the milimodel in non-newtonian fluid. In figure 3.3a and 3.3b are shown the Reynolds number against drag coefficient for link one and link two respectively. At this point it is worth mentioning that the summary figure reports data for the two links because although the links are controlled simultaneously small differences such as inherent blocks latency may lead to tinny asymme-tries in the actuation causing a barely noticeable rotation trend. In this case however, both links show clear mirrored characteristics indicating negligible rotation in the milimodel with respect to the inertial reference frame.

(64)

44 Discussion and Results Continuing with the analysis of the figure, the range of values presented in both plots are near the knee point in Figure 2.3 with low values of Re in the symmetric case. Lower values of Re produce grater values of Cd as discussed in Chapter 1. This in turn increment

the drag force in the in a proportional way. Figure 3.3c and 3.3d shows the drag force in both links with respect to the velocity vector, for this reason the drag force is reported in negative values i.e. link velocity and drag force are antiparallel. Both plots are nearly-reflected with the exception of few values near the extreme left in the velocity axis. This asymmetry would cause the rotation of the milimodel in a long-term simulation. In the last row, figure 3.3e and figure 3.3f, show the characteristic curve of a pseudoplastic or thinning fluid the behaviour of a non newtonian fluid (the logarithmic scale in the γ axis is used to amplify this effect visually).

(65)

3.1 The milimodel swimming microrobot in non-newtonian fluid 45

(a) (b)

(c) (d)

(e) (f)

(66)

3.2 The micromodel swimming microrobot in Non-Newtonian

Fluid

The micromodel, the scaled version of the milimodel at 1/10, is tested in non-newtonian fluid. The fluid properties of blood are used. The average Reynolds number in the asymmetric and symmetric cases are 0.020 and 0.0036 respectively. At these values viscous forces dominate the dynamics of the movement and the impulsive effect of the sawtooth function becomes less relevant. This conclusion is inferred from the comparable displacement with that of the sinusoidal function in figure 3.4. Low Reynolds numbers in this experiment, produce grater values of C_d than in the milimodel, figure 3.5a and figure 3.5b. This still ensures a marginal advantage in the asymmetric model because, even though the drag force is proportionally higher, exists nearly equivalent force acting in opposite direction. The force imbalance is arguably the source of higher displacement in the sawtooth function. With the reduction of the Reynolds number, the time dependence of the movement is greatly reduced, see equation 1.6 in Chapter 1. Thus, the fast or slow movements of the links have a less important role in the overall displacement of the micromodel.

Figures 3.5c−3.5d show the drag force that in this case despite the reduced scale and link velocity, is remarkably comparable to the that of the milimodel. As discussed above, this is the effect of the increased value of Cd as Re becomes smaller. Figures 3.5e−3.5f

show a displacement to the right in the shear rate domain in comparison to the milimodel, approximately two orders of magnitude.

(67)

3.2 The micromodel swimming microrobot in Non-Newtonian Fluid 47

(68)

(a) (b)

(c) (d)

(e) (f)

(69)

3.3 The micromodel swimming microrobot in newtonian fluid 49

3.3 The micromodel swimming microrobot in newtonian

fluid

The micromodel with characteristic low Reynolds number is tested in a newtonian fluid as a figure of merit. In this case the properties of water are used. The same sawtooth and sinusoidal functions are implemented for the sake of comparison to the previous analyses. In figure 3.6 is shown the displacement of the micromodel for both motion regimes. The curves presented in the figure are nearly equivalent with low net displacement of the microrobot.

Fig. 3.6 Displacement of the milimodel

Figures 3.7a−3.7b show higher values of Reynolds number with average of 0.50 in comparison to the average of 0.02 reported in the non-newtonian fluid for the same robot scale. The most remarkable difference is this set of summary plots with respect to the

(70)

50 Discussion and Results non-newtonian fluid, is observed in the plots of dynamic viscosity versus shear rate in figures 3.7e−3.7f. In this case is observed a constant value, levelled at the dynamic viscosity of the newtonian fluid, namely water 8.90 × 10−4Pa s.

The scallop theorem applies in reciprocating swimmers at Re << 1 in newtonian fluids. With the strict exception of a Reynolds number much lower than one, the model clearly approaches the scallop theorem by showing reduced displacement with its mean value of

¯

Re= 0.5. This result supports the validity of the designed numerical models and the results herein presented.

(71)

3.3 The micromodel swimming microrobot in newtonian fluid 51

(a) (b)

(c) (d)

(e) (f)

(72)

Conclusions

Swimming microrobots employing reciprocating motion in non-newtonian and newtonian fluids is analysed. The microrobot design consists of two rigid body links connected to each other via a two dimensional hinge. The angle between both links is managed with a PID controller following a stablished periodic function. The controller periodic input function is modelled with a sawtooth function and a sine function. The functions have distinct angular velocity profiles. The sawtooth function furnish periodic characteristic impulses whereas the sinusoidal function presents soft periodic motion. Both motion profiles are tested in two scales of robot models, the milimodel and the micromodel. Subsequently, a newtonian fluid is simulated in the smaller swimming microrobot model as a figure of merit.

Computational numerical simulations show the inertial prevalence in the milimodel swimming in non-newtonian fluid. The effect of the input functions is clearly different on the model. Conversely, the micromodel swimming in non-newtonian fluid evinces a reduced effect of the impulsive sawtooth function in adding momentum to the model. In both cases, the sawtooth function and the sinusoidal function are closely comparable in the net displacement produced in the model. The simulation on the micromodel in newtonian fluid present low Reynolds number, that in near-compliance to the scallop theorem, produce minimal displacement with near-undifferentiated displacements amongst the input functions.

The simulation results presented in this investigation show that it is plausible to obtain net displacement from a simple reciprocating microrobot in non-newtonian fluids. In addition to the manufacturing advantage of a simple microrobot with a one degree of freedom, the prevalence of non-newtonian biofluids emphasise on the suitability of this design for future use in biomedical applications.

(73)

References

[1] Jake J Abbott, Zoltan Nagy, Felix Beyeler, and B Nelson. Robotics in the small. IEEE Robotics & Automation Magazine, 14(2):92–103, 2007.

[2] Jake J Abbott, Kathrin E Peyer, Lixin X Dong, and Bradley J Nelson. How should microrobots swim? In Robotics Research, pages 157–167. Springer, 2010.

[3] Mónica S. N. Oliveira Andreia F. Silva, Manuel A. Alves. Rheological behaviour of vitreous humor. Springerlink, 2016.

[4] Robotic Technology Center. Robotpark, 2017. URL http://www.robotpark.com/ academy/all-types-of-robots/micro-robots-microbotics/.

[5] Royson Donate D’Souza, Shubham Sharma, and Allister Jacob. Microrobotics: Trends and technologies. American journal of Engineering Research (AJER), 5(5):32–39, 2016.

[6] Olgac Ergeneman, Jake J Abbott, Gorkem Dogangil, and Bradley J Nelson. Functional-izing intraocular microrobots with surface coatings. pages 232–237, 2008.

[7] De Blas et al. Embrylogy, 2017. URL http://journals.plos.org/plosone/article?id=10. 1371/journal.pone.0006095.

[8] George Chatzipirpiridis Salvador Pané Franziska Ullrich, Stefano Fusco and Bradley J. Nelson. Recent progress in magnetically actuated microrobotics for ophthalmic thera-pies. European Ophthalmic Review, 2014.

[9] Baumgartner C Neufeld E Gosselin MC Payne D Klingenböck A Kuster N Hasgall PA, Di Gennaro F. It’is database for thermal and electromagnetic parameters of biological tissues,”, September 01st 2015. URL www.itis.ethz.ch/database.

[10] Gavriel Iddan, Gavriel Meron, Arkady Glukhovsky, and Paul Swain. Wireless capsule endoscopy. Nature, 405(6785):417, 2000.

[11] Eric Lauga and Thomas R Powers. The hydrodynamics of swimming microorganisms. Reports on Progress in Physics, 72(9):096601, 2009.

[12] Zhaoshen Li, Zhuan Liao, and Mark McAlindon. Handbook of capsule endoscopy. Springer, 2014.

[13] Lin Lin, Mahdi Rasouli, Andy Prima Kencana, Su Lim Tan, Kai Juan Wong, Khek Yu Ho, and Soo Jay Phee. Capsule endoscopy—a mechatronics perspective. Frontiers of Mechanical Engineering, 6(1):33–39, 2011.

(74)

54 References [14] Jagannath Mazumdar. Biofluid mechanics. World Scientific, 2015.

[15] Jonathan Mestel. Biofluids lecture 2: Introduction to animal locomotion. Technical report, Imperial College London, 2017.

[16] Ali Ostadfar. Biofluid Mechanics: Principles and Applications. Academic Press, 2016. [17] Stefano Palagi, Edwin WH Jager, Barbara Mazzolai, and Lucia Beccai. Propulsion

of swimming microrobots inspired by metachronal waves in ciliates: from biology to material specifications. Bioinspiration & biomimetics, 8(4):046004, 2013. [18] Stefano Palagi, Andrew G Mark, Shang Yik Reigh, Kai Melde, Tian Qiu, Hao Zeng,

Camilla Parmeggiani, Daniele Martella, Alberto Sanchez-Castillo, Nadia Kapernaum, et al. Structured light enables biomimetic swimming and versatile locomotion of photoresponsive soft microrobots. Nature materials, 2016.

[19] Theodoros G Papaioannou and Christodoulos Stefanadis. Vascular wall shear stress: basic principles and methods. Hellenic J Cardiol, 46(1):9–15, 2005.

[20] Kathrin E Peyer, Li Zhang, and Bradley J Nelson. Bio-inspired magnetic swimming microrobots for biomedical applications. Nanoscale, 5(4):1259–1272, 2013.

[21] P Plötner, K Harada, N Sugita, and M Mitsuishi. Theoretical analysis of magnetically propelled microrobots in the cardiovascular system. pages 870–873, 2014.

[22] Leodotia Pope. Microbewiki. URL https://microbewiki.kenyon.edu/index.php/Vibrio_ cholerae.

[23] Edward M Purcell. Life at low reynolds number. American journal of physics, 45(1): 3–11, 1977.

[24] Tian Qiu, Tung-Chun Lee, Andrew G Mark, Konstantin I Morozov, Raphael Münster, Otto Mierka, Stefan Turek, Alexander M Leshansky, and Peer Fischer. Swimming by reciprocal motion at low reynolds number. Nature communications, 5, 2014.

[25] Jacob Rosen, Blake Hannaford, and Richard M Satava. Surgical robotics: systems applications and visions. Springer Science & Business Media, 2011.

[26] David Rubenstein, Wei Yin, and Mary D Frame. Biofluid mechanics: an introduction to fluid mechanics, macrocirculation, and microcirculation. Academic Press, 2015. [27] Ryokuryonu. The secrets in biology, 2017. URL http://biologicalsecrets.blogspot.co.

uk/2013/07/characteristics-of-ciliate.html.

[28] Metin Sitti, Hakan Ceylan, Wenqi Hu, Joshua Giltinan, Mehmet Turan, Sehyuk Yim, and Eric Diller. Biomedical applications of untethered mobile milli/microrobots. Pro-ceedings of the IEEE, 103(2):205–224, 2015.

[29] Stanford Children’s Hospital. Stanford children’s hospital, 2017 2017. URL http: //www.stanfordchildrens.org/en/topic/default?id=what-are-red-blood-cells-160-34. [30] Jocelyne Troccaz and Robert Bogue. The development of medical microrobots: a

(75)

References 55 [31] Franziska Ullrich, Christos Bergeles, Juho Pokki, Olgac Ergeneman, Sandro Erni, George Chatzipirpiridis, Salvador Pané, Carsten Framme, and Bradley J Nelson. Mobil-ity experiments with microrobots for minimally invasive intraocular surgerymicrorobot experiments for intraocular surgery. Investigative ophthalmology & visual science, 54(4):2853–2863, 2013.

[32] Wikipedia. Wikipedia, 2017. URL https://en.wikipedia.org/wiki/Main_Page.

[33] JP Woodcock. Physical properties of blood and their influence on blood-flow measure-ment. Reports on Progress in Physics, 39(1):65, 1976.

[34] Fuat Yilmaz, Mehmet Yasar Gundogdu, et al. A critical review on blood flow in large arteries; relevance to blood rheology, viscosity models, and physiologic conditions. Korea-Australia Rheology Journal, 20(4):197–211, 2008.

(76)

(77)

Appendix A

Simulink

Simulink® _{is a graphical programming platform for modelling, simulating and analysing}

multi-domain dynamic systems. Its interface is composed of a graphical block diagramming tool and predefined blocks libraries. It supports system level design, simulation, automatic code generation and a continuous test and verification of embedded systems.

Simulink, developed by Mathworks Inc., it is integrated with Matlab®_{, enabling}

incor-porate Matlab algorithms into models and export simulation results to the workspace of Matlab.Some of the its key features comprise graphical editor for building and managing hierarchical block diagrams, systems modelling for continuos and discrete time, scopes and data displays for viewing simulations results even when the simulation runs and Legacy Code Tool for importing C and C++ code into models.

Its tool for model-base design enables to examine more realistic non linear models by adding variables that describe real-world phenomena. Simulink also offer a variety of examples that describe real-world phenomena. Its graphical user interface of Simulink is easy to operate and offer a vast block library of math operations, sources, sinks, etc, it is possible to create a block to specific needs.

Once a model is created, it can be simulated for analysis of its dynamic behaviour selecting a mathematical integration method, either from Simulink menu configurations or by