Bead manipulation to enable electrically controlled wire braiding
Bead Manipulation to Enable Electrically Controlled Wire Braiding
NSTITLITE MASSACHUSETTS OF rECHNOLOLGY
by
JUN 2 4 2015
Alexxis Isaac and Makai Cartman
LIBRARIES
Submitted to the Department of Mechanical Engineering in partial fulfillment of the requirements for the degree of Bachelor of Science in Mechanical Engineering at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY June 2015 Massachusetts Institute of Technology 2015. All rights reserved.
Signature redacted Signature redacted .
Author'.
Department of Mechanical Engineering May 14, 2015
Signature redacted .. .. ... ..
.
Certified by ..................
Cullen R. Buie
Assistant Professor of Mechanical Engineering Thesis Supervisor
Signature redacted Accepted by ......................................................... Anette Hosoi Undergraduate Officer, Professor of Mechanical Engineering
2
Bead Manipulation to Enable Electrically Controlled Wire Braiding by Alexxis Isaac and Makai Cartman Submitted to the Department of Mechanical Engineering on May 14, 2015, in partial fulfillment of the requirements for the degree of Bachelor of Science in Mechanical Engineering
Abstract Litz wire bundles are highly effective at enhancing the current carrying capacity and limiting the losses of electronic devices up to MHz frequencies due to the pattern in which the individual wires are braided in the bundle. However, the technology to fabricate Litz wire bundles at higher radio frequencies has not been developed due to current manufacturing limitations. Litz wire bundles developed to accommodate higher radio frequencies would have a tremendous impact for electronic devices because these bundles would allow for inductors to be manufactured with increased quality factors from the current range of less than 10 to a possible range of up to 1000 at frequencies of 1-10GHz. This would allow for less spectral crowding, jamming, improved power handling, and more efficient systems. In this thesis, through collaboration with The Charles Stark Draper Laboratory, dielectrophoretic and driven fluid flow bead manipulation methods were explored for the purpose of demonstrating the plausibility of controlled litz wire braiding at a nano-to-micro scale. Results from this thesis show that both dielectrophoresis and driven fluid flow are viable methods for bead manipulation and should be further developed to enable fabrication of "NanoLitz" wires. Thesis Supervisor: Cullen R. Buie Title: Assistant Professor of Mechanical Engineering
3
4
Acknowledgments We would like to thank our advisor, Prof. Cullen R. Buie, for his support in our completion of this thesis - especially at a time when we needed him most. We have both been lucky enough to have you as a professor during our time here at MIT and we appreciate the time that you took out of your schedule then and now to accommodate for our needs. We are also especially grateful to our mentor, Amy Duwel, for being a constant source of advice for us, both academically and personally, over the time that we have been blessed enough to know her. You have done so much for us since we first interned at The Charles Stark Draper Laboratory with you and we are so thankful for all of your generosity. Lastly, we would like to acknowledge Alisha Schor for all of her support in our understanding of the material and fabrication of the demo. You created an open space for us where we felt comfortable approaching you with questions and we are very grateful for the time that you sacrificed to help us reach our goal.
5
6
Contents
1
Introduction 1.1
Nano-Litz Wire Bundles
1.2
Goals
1.3
Requirements
1.4 2
. . . . . . . . . . . . . . . . . . . . . . . . . . .
13
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
15
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
16
1.3.1
Wire Stiffness . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
17
1.3.2
Viscous Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
18
1.3.3
Electric Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
Thesis Layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
Dielectrophoretic Bead Manipulation 2.1
2.2
2.3
Physics of Dielectrophoresis
2.4
23
. . . . . . . . . . . . . . . . . . . . . . . . . 23
2.1.1
Dielectrophoretic Force
2.1.2
Positive DEP vs. Negative DEP . . . . . . . . . . . . . . . . . . . 24
. . . . . . . . . . . . . . . . . . . . . . . 24
Channel Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2.2.1
Spoke Electrode Configuration . . . . . . . . . . . . . . . . . . . . 26
2.2.2
Point Electrode Configuration
Force and Dynamic Model . . . . . . . . . . . . . . . . . . . . . . 29
Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 2.4.1
DEP for Nano-wire Braiding . . . . . . . . . . . . . . . . . . . . . 30 33
Bead Manipulation via Fluid Flow 3.1
. . . . . . . . . . . . . . . . . . . . 27
Numerical Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.3.1
3
13
Fluid Flow Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 7
3.2
3.3
3.4
Platform Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 3.2.1
Initial Platform Prototype
3.2.2
Gate System
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.2.3
Final Design
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 3.3.1
Platform Fabrication . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.3.2
Experimentation
. . . . . . . . . . . . . . . . . . . . . . . . . . . 39
Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 3.4.1
4
. . . . . . . . . . . . . . . . . . . . . . 34
Driven Flow for Nano-Wire Braiding
Conclusions and Future Work 4.1
4.2
. . . . . . . . . . . . . . . . 41 43
Summary of Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 4.1.1
DEP Manipulation . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.1.2
Driven Flow Manipulation . . . . . . . . . . . . . . . . . . . . . . 43
Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
A CAD of Platform Design
45
B Valve Arduino Code
53
8
List of Figures 1-1
Example of a litz bundle comprised of nine wire strands (image excerpted 14
1-2 Overall setup concept - independent of proposed platform geometries. . .
16
.
.
from [5]). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Cantilevered beam undergoing a small deflection (image excerpted from [10]).
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
.
1-3
1-4
Cross-section of an open rectangular channel (image excerpted from [6]).
1-5
CD
18
versus Reynolds number for a smooth, spherical sphere (image ex.
cerpted from [3]). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-6
17
19
Force diagram illustrating the relationship between overall force and the .
viscous and bending forces. . . . . . . . . . . . . . . . . . . . . . . . . .
20
2-1
Particle polarity for pDEP vs. nDEP (image excerpted from [14]).
. . . 25
2-2
Spoke electrode geometry integrated into a six-channel system.....
. . . 26
2-3
Point electrode geometry integrated into a six-channel system.....
27
2-4
Point electrode geometry integrated into a six-channel system (image ex. .
cerpted from [9]). . . . . . . . . . . . . . . . . . . . . . . . . . . .
28
Machined version of the initial prototype.
. . . . . . . . . . . . . .
. . . 35
3-2
Schematic representation of the balloon gating system. . . . . . . .
. . . 36
3-3
Final platform design. . . . . . . . . . . . . . . . . . . . . . . . . .
. . . 36
3-4
Final channel geometry. . . . . . . . . . . . . . . . . . . . . . . . .
. . . 37
3-5
Each type of acrylic part used and the overall platform assembly. . .
. . . 38
3-6
Schematic of the electrical circuit. . . . . . . . . . . . . . . . . . .
. . . 39
3-7
Balloon gating system integrated into the platform channels. . . . .
. . . 40
.
.
.
.
.
.
.
3-1
9
3-8
In-lab experimental setup.
. . . . . . . . . . . . . . . . . . . . . . . . . . 41
3-9
Soft lithography layering process. (image excerpted from [15]).
A-1
Solidworks drawing of the top wall, where the braid wires are joined.
. . . . . . 42 . . . 46
A-2 Solidworks drawing of the side walls, which hold up the overall structure and the top w all. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 A-3 Solidworks drawing of the outer ring of the structure. . . . . . . . . . . . . 48 A-4 Solidworks drawing of the outer ring of the structure. . . . . . . . . . . . . 49 A-5 Solidworks drawing of the platform sections. A-6 Solidworks drawing of the base plate. A-7 Image of the overall structure.
. . . . . . . . . . . . . . . . 50
. . . . . . . . . . . . . . . . . . . . 51
. . . . . . . . . . . . . . . . . . . . . . . . 52
B-1 Arduino code for gate release to enable braiding.
10
. . . . . . . . . . . . . . 54
List of Tables 2.1
Factors that influence pDEP versus nDEP. . . . . . . . . . . . . . . . . . . 25
2.2
Table displaying the time required for a 1 mm diameter bead to travel down a 25 mm channel for various bead-medium combinations, assuming a highfrequency electric field. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.3
Table displaying the time required for a 1 pum diameter bead to travel down a 25 prm channel for various bead-medium combinations, assuming a highfrequency electric field. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
11
12
Chapter 1 Introduction Litz wire is a bundle of thin individual wire strands that are braided together in a prescribed pattern [1]. These patterns typically involve several levels of braiding and twisting, which are designed to enhance the current carrying capacity and to limit losses seen at frequencies below the MHz range [1]. Figure 1-1 illustrates an example of a litz bundle comprised of nine wire strands. Although litz bundles would have a huge impact at higher radio frequencies, these bundles have not been pursued at those frequencies because the technology to make them at the appropriate scale is not currently available [5]. The Charles Stark Draper Laboratory and a Harvard University research team are now collaborating to develop "NanoLitz" wires.
1.1
Nano-Litz Wire Bundles
The team envisions NanoLitz to be a 3D braided wire bundle that leverages nano-scale features constructed in a micron-to-millimeter scale component. The overarching goal is to achieve ultra-low loss radio-frequency (RF) performance [5]. With the technology that is currently available, typical RF inductors have a quality factor Q < 10. However, with access to NanoLitz technology, engineers would be able to produce inductors with quality factors approaching
Q
= 1000 at 1-10 GHz [5]. The quality factor is a dimensionless
number that represents the energy being stored in a circuit compared to the energy that is 13
Figure 1-1: Example of a litz bundle comprised of nine wire strands (image excerpted from [5]). thermally dissipated:
QOL L Q =w 0
(1.1)
RDC'
where wo is the frequency, L is the inductance and RDC is the equivalent resistance [4]. For an inductor, as the frequency of a given system increases, the equivalent resistance of the system also increases due to the skin effect [4]. The skin effect is the inclination of current to distribute more densely at the outer surface, or "skin", of a conductor as frequency increases [2]. The higher the frequency, the smaller the skin depth, which causes the effective cross-section to decrease [2].This leads to a decrease in the
Q factor,
and thus
a decrease in the overall efficiency of the system [4]. NanoLitz would enable a reduction in the losses caused by the skin effect. These low loss components would provide better filters to address spectral crowding and jamming, as well as improved power handling for thermally robust portable and miniature systems [5]. The NanoLitz team has proposed to fabricate wires using a nano-wire scaffold for copper with silica insulation. The team has anticipated two main production challenges in creating the NanoLitz wires: (1) the current approaches to conducting wire fabrication are not scaleable to the 0.6-2pm diameter size needed for radio-frequencies ranging from 1 GHz to 10 GHz, and (2) the current approaches to wire braiding leverage macro-scale machines that impose tension and bending forces that are incompatible with braiding nanoto-micro-scale wires [5]. To address the second production challenge, the NanoLitz team plans on exploring 14
two technologies to braid the custom nano-wires. The first method is a "Self-Assembly" approach that relies on the specific binding properties of DNA to enable controlled wire braiding [5]. The second method is a "Directed Assembly" approach where the wire ends will be attached to beads that will then be manipulated in such a way that will enable controlled wire braiding [5]. The purpose of this thesis is to explore the directed assembly method that was proposed by the NanoLitz team at a macro scale. From this exploration at a larger scale, a recommendation would then be made to the NanoLitz team to frame their efforts as they enter the first phase of the fabrication of 1-10 GHz range litz bundles.
1.2
Goals
In order to properly explore options for the directed assembly method, three main goals were identified: 1. Explore bead manipulation options that can enable wire-braiding at a micro scale. 2. Perform calculations to determine what settings are required for each option to produce the required force to perform wire-braiding. 3. Create a macro-scale demo of one of the options that illustrates controlled wire braiding. The NanoLitz team proposes to develop novel assembly technologies that can be scaled to the application of low loss RF conductors. The program goals for NanoLitz will be to braid ten's of threads of approximately one prm diameter wires that are approximately one cm in length. The team would like to focus on fundamental technology development rather than engineering of fully scaled up manufacturing. The demo that will be covered in this thesis will serve as an intuitive design tool that the NanoLitz team engineers will utilize to be able to visualize the 3D geometry of a possible platform option, as well as visualize the braiding of three wires. This will allow the design engineers to adapt the platform to manipulate ten's of threads of wires and smaller beads. This demo will serve useful as it is hard to capture the braiding mechanics in a CAD tool. 15
1.3
Requirements
The basic platform configuration that is considered in this thesis involves a series of radially symmetric channels. The concept behind the basic platform design is that each bead will be attached to the end of an individual wire. A collection of wires will be fixed together at one end at a prescribed height above the channel platform. This setup is shown in figure 1-2.
/
7
yxx'
(2)
(1)
K
(3)
(4)
Figure 1-2: Overall setup concept - independent of proposed platform geometries.
The two bead manipulation methods that are explored in this thesis are dielectrophoretic manipulation and driven fluid flow. For both of these bead manipulation options, the platform is designed such that a constant fluid level can be maintained in the channels. The beads will be manipulated by an externally applied force that allows for the travel of each bead to be electronically controlled. Outlined below are the three main requirements that were identified to make wire braiding possible. 16
1.3.1
Wire Stiffness
In order to braid a set of wires, each wire must be deflected to a certain amount that varies as the braid grows. To understand the force required to overcome the wire stiffness and bend the wire, a wire made of certain length L, diameter D, and modulus of elasticity E can be modeled as a cantilevered beam [10]. For small deflections, a relationship between the deflection of the wire and the applied force F can be represented based on Bernoulli-Euler beam theory [10]: 3EI
F= 3
=
2EI 2
00max
(1.2)
where I is the moment of inertia of the beam.
-
---
----------------------
max
a
--------------------------
F Figure 1-3: Cantilevered beam undergoing a small deflection (image excerpted from [10]).
For large deflections however, like the ones required to braid a wire, a deeper analysis
must be performed on a vertical cantilevered beam. In reference [10], a model was developed to simulate a beam undergoing a large deflection. In this analysis, the bending force that is required is defined as: 2
a
Fbend =
EI
2
,
(1.3)
where a is a parameter defined based on the bending angle and is described in more depth in [10]. Based on this model, the force required to bend copper wires made of length L = 10cm and diameters D =1mm and D = lyt in the 2 pN range and 100 pN range respectively. 17
through a 90' turn are estimated to be
1.3.2
Viscous Force
In addition to overcoming the wire stiffness, the chosen applied force must also overcome the viscous force of the fluid that is within the platform. When a spherical particle that is submerged in a fluid medium begins to move with a certain velocity, it experiences this viscous force. In this thesis, the viscous force is explored in two different regimes: typical laminar flow and Stokes' flow. For an open channel flow like the one described in figure 1-4, the laminar flow regime applies when Re < 500 and the Stokes' flow regime refers specifically to flows with Re < 0.1 [8] [16]. The Reynolds number, Re, is defined as Re - u,
(1.4)
where u is average velocity of the fluid traveling through the fluid, R is the hydraulic radius, and v is the kinematic viscosity of the fluid [6]. The hydraulic radius is defined as follows: A
R=
Pw'
(1.5)
where A, the cross-sectional area and Pw, the wetted perimeter, are defined as [6]: A=WD
(1.6)
Pw = W + 2D.
(1.7)
Frce surface
/n IL)
Figure 1-4: Cross-section of an open rectangular channel (image excerpted from [6]). 18
As can be inferred from equation 1.8, laminar flow occurs when the following condition is met: Ulaminar
1
___
C
!1
m
0
0225
U'
~
16.67
48
Figure A-3: Solidworks drawing of the outer ring of the structure.
-
0
m
z
z
N)
N)
w
C
5
4 4
3 3
2 2
6 6
5
A --
-245 I
AB
*240.24 0
Q0 0 LOr
*
5 I
n
C
CN
0O (Y)
UNLESS OTHERWISE SPECIFIED: DIMENSIONS ARE IN MILUIMETERS SURFACE FINISH: TOLERANCES: LINEAR: ANGULAR: NAME
DEBUR AND BREAK SHARP EDGES
FINISH:
SIGNATURE
DATE
I_
_
DO NOT SCALE DRAWING
REVISION
TITLE:
IDRAWN CHK'D
'-
.
U- LO
MFG GQA
____
MATERIAL:
WEIGHT:
DW
""'Bottom Support ^A SCALE:1:3
SHEET I OF I
*
9.76
10
I>
-M
CDi
-U
CD
0
1~
17
Li..
T-0i
0
M
0
0
0
62.44
200
600
to
50
Figure A-5: Solidworks drawing of the platform sections.
0
M52
0.
~5.08
----I
M
VY
3
2
56
4
00
3
2
B
40
*
B
0
*0
4.76
0o
0
0 '40 CN
to
0 c
c
10 DEBUR AND BREAK SHARF EDGES
FINISH: UNLESS OTHERWISE SPECIIED: DIMENSIONS ARE IN MILUIMEERS SURFACE FINISH: TOLERANCES: UINEAR: FANGULAR: NM INTR
SIGNATURE
NAME
DO NOT SCALE DRAWING
REVISION
TITLE:
DATE
DRAWN CHKD
Dj
APPVD
2
Base Plate
MATERIAL:
IGQA
1
-t
!WBGHT:
SCALE:1:3
SHEET I OF
1
Figure A-7: Image of the overall structure.
52
Appendix B Valve Arduino Code
53
const int valvel
const int valve2 const
int
valve3
13; 12; 11;
void setup() { // initialize digital pin 13 as an output. //white pi nMode(valvel, OUTPUT); //green pinMode(valve2, OUTPUT); //purple pinMode(valve3, OUTPUT);
} void loopo
{
//Valves are always open, so by turning output to high, it closes valve // close valve 2 // wait for 5 seconds delay(5000); // open valve 2 digitolWrite(valve2, LOW); // wait for 3 second //delay(3000);
dgiitalWrite(valve2, HIGH);
// close valve 1 digitalWrite(valvel, HIGH); // wait for 5 seconds delay(5000); // open valve 1 digltalWrite(valvel, LOW); // wait for 3 second //delay(3000); // close valve 3 digitalWrite(valve3, HIGH); // wait for 5 seconds delay(5000); // open valve 3 digitalWrite(valve3, LOW); // wait for 3 second //delay(3000); I
Figure B-1: Arduino code for gate release to enable braiding.
54
Bibliography [1] M. Bartoli, N. Noferi, A. Reatti, and M.K. Kazimierczuk. Modeling Litz-wire winding losses in high-frequency power inductors. In Power Electronics Specialists Conference, 1996. PESC '96 Record., 27th Annual IEEE, volume 2, pages 1690-1696 vol.2, Jun 1996. [2] M.V.K. Chari and Z.J. Csendes. Finite element analysis of the skin effect in current carrying conductors. Magnetics, IEEE Transactionson, 13(5):1125-1127, Sep 1977. [3] Stuart Churchill. Viscous Flow: The PracticalUse of Theory (Fluid Flow). Springer Wien New York, 2011. [4] David Cory and Manos Chaniotakis. Frequency Response: Resonance, Bandwidth, Q Factor. MIT OCW 6.071, 2006. [5] Amy Duwel. Nano-Litz: Braided nano-wires for high performance RF components. November 2014. [6] Shreeram Inamdar. Open Channel Flow. April 2012. [7] Thomas B. Jones. Electromechanicsof Particles. Cambridge University Press, 1995. [8] Mohamed Kharboutly, Micha8l Gauthier, and Nicolas Chaillet. Modeling the Trajectory of a Microparticle in a Dielectrophoresis Device. Journal Of Applied Physics, 2009. [9] H Morgan, N Green, M Hughes, W Monaghan, and T Tan. Large-area travellingwave dielectrophoresis particle separator. journal of micromechanics and microengineering. Journalof Micromechanicasand Microengineering,7, June 1997. [10] Joshua C. Nation. Fabrication of Chip-Scale Radio Frequency Inductors. Master of Science in Mechanical Engineering, Massachusetts Institute of Technology, Department of Mechanical Engineering, Jun 2014. [11] Adrian Neculae, Claudia G. Biris, Madalin Bunoiu, and Mihail Lungu. Numerical Analysis of Nanoparticle Behavior in a Microfluidic Channel Under Dielectrophoresis. 2012. [12] N. Phansiri and B. Techaumnat. Study on the electromechanics of a conducting particle under nonuniform electric field. Dielectrics and Electrical Insulation, IEEE Transactionson, 20(2):488-495, April 2013. 55
[13] Ant6nio Ramos. Electrokinetics And Electrohydrodynamics In Microsystems. Springer Wien New York, 2011. [14] Jong Ming Sung. Dielectrophoresis and Optoelectronic Tweezers for Nanomanipulation. Stanford Physics 210, 2007. [15] Marc A. Unger, Hou-Pu Chou, Todd Thorsen, Axel Scherer, and Stephen R. Quake. Monolithic Microfabricated Valves and Pumps by Multilayer Soft Lithography. Science, (5463):113, 2000. [16] Frank M. White. Fluid Mechanics. McGraw-Hill, 4 edition, Dec 1998.
56
NSTITLITE MASSACHUSETTS OF rECHNOLOLGY
by
JUN 2 4 2015
Alexxis Isaac and Makai Cartman
LIBRARIES
Submitted to the Department of Mechanical Engineering in partial fulfillment of the requirements for the degree of Bachelor of Science in Mechanical Engineering at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY June 2015 Massachusetts Institute of Technology 2015. All rights reserved.
Signature redacted Signature redacted .
Author'.
Department of Mechanical Engineering May 14, 2015
Signature redacted .. .. ... ..
.
Certified by ..................
Cullen R. Buie
Assistant Professor of Mechanical Engineering Thesis Supervisor
Signature redacted Accepted by ......................................................... Anette Hosoi Undergraduate Officer, Professor of Mechanical Engineering
2
Bead Manipulation to Enable Electrically Controlled Wire Braiding by Alexxis Isaac and Makai Cartman Submitted to the Department of Mechanical Engineering on May 14, 2015, in partial fulfillment of the requirements for the degree of Bachelor of Science in Mechanical Engineering
Abstract Litz wire bundles are highly effective at enhancing the current carrying capacity and limiting the losses of electronic devices up to MHz frequencies due to the pattern in which the individual wires are braided in the bundle. However, the technology to fabricate Litz wire bundles at higher radio frequencies has not been developed due to current manufacturing limitations. Litz wire bundles developed to accommodate higher radio frequencies would have a tremendous impact for electronic devices because these bundles would allow for inductors to be manufactured with increased quality factors from the current range of less than 10 to a possible range of up to 1000 at frequencies of 1-10GHz. This would allow for less spectral crowding, jamming, improved power handling, and more efficient systems. In this thesis, through collaboration with The Charles Stark Draper Laboratory, dielectrophoretic and driven fluid flow bead manipulation methods were explored for the purpose of demonstrating the plausibility of controlled litz wire braiding at a nano-to-micro scale. Results from this thesis show that both dielectrophoresis and driven fluid flow are viable methods for bead manipulation and should be further developed to enable fabrication of "NanoLitz" wires. Thesis Supervisor: Cullen R. Buie Title: Assistant Professor of Mechanical Engineering
3
4
Acknowledgments We would like to thank our advisor, Prof. Cullen R. Buie, for his support in our completion of this thesis - especially at a time when we needed him most. We have both been lucky enough to have you as a professor during our time here at MIT and we appreciate the time that you took out of your schedule then and now to accommodate for our needs. We are also especially grateful to our mentor, Amy Duwel, for being a constant source of advice for us, both academically and personally, over the time that we have been blessed enough to know her. You have done so much for us since we first interned at The Charles Stark Draper Laboratory with you and we are so thankful for all of your generosity. Lastly, we would like to acknowledge Alisha Schor for all of her support in our understanding of the material and fabrication of the demo. You created an open space for us where we felt comfortable approaching you with questions and we are very grateful for the time that you sacrificed to help us reach our goal.
5
6
Contents
1
Introduction 1.1
Nano-Litz Wire Bundles
1.2
Goals
1.3
Requirements
1.4 2
. . . . . . . . . . . . . . . . . . . . . . . . . . .
13
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
15
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
16
1.3.1
Wire Stiffness . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
17
1.3.2
Viscous Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
18
1.3.3
Electric Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
Thesis Layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
Dielectrophoretic Bead Manipulation 2.1
2.2
2.3
Physics of Dielectrophoresis
2.4
23
. . . . . . . . . . . . . . . . . . . . . . . . . 23
2.1.1
Dielectrophoretic Force
2.1.2
Positive DEP vs. Negative DEP . . . . . . . . . . . . . . . . . . . 24
. . . . . . . . . . . . . . . . . . . . . . . 24
Channel Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2.2.1
Spoke Electrode Configuration . . . . . . . . . . . . . . . . . . . . 26
2.2.2
Point Electrode Configuration
Force and Dynamic Model . . . . . . . . . . . . . . . . . . . . . . 29
Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 2.4.1
DEP for Nano-wire Braiding . . . . . . . . . . . . . . . . . . . . . 30 33
Bead Manipulation via Fluid Flow 3.1
. . . . . . . . . . . . . . . . . . . . 27
Numerical Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.3.1
3
13
Fluid Flow Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 7
3.2
3.3
3.4
Platform Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 3.2.1
Initial Platform Prototype
3.2.2
Gate System
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.2.3
Final Design
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 3.3.1
Platform Fabrication . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.3.2
Experimentation
. . . . . . . . . . . . . . . . . . . . . . . . . . . 39
Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 3.4.1
4
. . . . . . . . . . . . . . . . . . . . . . 34
Driven Flow for Nano-Wire Braiding
Conclusions and Future Work 4.1
4.2
. . . . . . . . . . . . . . . . 41 43
Summary of Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 4.1.1
DEP Manipulation . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.1.2
Driven Flow Manipulation . . . . . . . . . . . . . . . . . . . . . . 43
Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
A CAD of Platform Design
45
B Valve Arduino Code
53
8
List of Figures 1-1
Example of a litz bundle comprised of nine wire strands (image excerpted 14
1-2 Overall setup concept - independent of proposed platform geometries. . .
16
.
.
from [5]). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Cantilevered beam undergoing a small deflection (image excerpted from [10]).
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
.
1-3
1-4
Cross-section of an open rectangular channel (image excerpted from [6]).
1-5
CD
18
versus Reynolds number for a smooth, spherical sphere (image ex.
cerpted from [3]). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-6
17
19
Force diagram illustrating the relationship between overall force and the .
viscous and bending forces. . . . . . . . . . . . . . . . . . . . . . . . . .
20
2-1
Particle polarity for pDEP vs. nDEP (image excerpted from [14]).
. . . 25
2-2
Spoke electrode geometry integrated into a six-channel system.....
. . . 26
2-3
Point electrode geometry integrated into a six-channel system.....
27
2-4
Point electrode geometry integrated into a six-channel system (image ex. .
cerpted from [9]). . . . . . . . . . . . . . . . . . . . . . . . . . . .
28
Machined version of the initial prototype.
. . . . . . . . . . . . . .
. . . 35
3-2
Schematic representation of the balloon gating system. . . . . . . .
. . . 36
3-3
Final platform design. . . . . . . . . . . . . . . . . . . . . . . . . .
. . . 36
3-4
Final channel geometry. . . . . . . . . . . . . . . . . . . . . . . . .
. . . 37
3-5
Each type of acrylic part used and the overall platform assembly. . .
. . . 38
3-6
Schematic of the electrical circuit. . . . . . . . . . . . . . . . . . .
. . . 39
3-7
Balloon gating system integrated into the platform channels. . . . .
. . . 40
.
.
.
.
.
.
.
3-1
9
3-8
In-lab experimental setup.
. . . . . . . . . . . . . . . . . . . . . . . . . . 41
3-9
Soft lithography layering process. (image excerpted from [15]).
A-1
Solidworks drawing of the top wall, where the braid wires are joined.
. . . . . . 42 . . . 46
A-2 Solidworks drawing of the side walls, which hold up the overall structure and the top w all. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 A-3 Solidworks drawing of the outer ring of the structure. . . . . . . . . . . . . 48 A-4 Solidworks drawing of the outer ring of the structure. . . . . . . . . . . . . 49 A-5 Solidworks drawing of the platform sections. A-6 Solidworks drawing of the base plate. A-7 Image of the overall structure.
. . . . . . . . . . . . . . . . 50
. . . . . . . . . . . . . . . . . . . . 51
. . . . . . . . . . . . . . . . . . . . . . . . 52
B-1 Arduino code for gate release to enable braiding.
10
. . . . . . . . . . . . . . 54
List of Tables 2.1
Factors that influence pDEP versus nDEP. . . . . . . . . . . . . . . . . . . 25
2.2
Table displaying the time required for a 1 mm diameter bead to travel down a 25 mm channel for various bead-medium combinations, assuming a highfrequency electric field. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.3
Table displaying the time required for a 1 pum diameter bead to travel down a 25 prm channel for various bead-medium combinations, assuming a highfrequency electric field. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
11
12
Chapter 1 Introduction Litz wire is a bundle of thin individual wire strands that are braided together in a prescribed pattern [1]. These patterns typically involve several levels of braiding and twisting, which are designed to enhance the current carrying capacity and to limit losses seen at frequencies below the MHz range [1]. Figure 1-1 illustrates an example of a litz bundle comprised of nine wire strands. Although litz bundles would have a huge impact at higher radio frequencies, these bundles have not been pursued at those frequencies because the technology to make them at the appropriate scale is not currently available [5]. The Charles Stark Draper Laboratory and a Harvard University research team are now collaborating to develop "NanoLitz" wires.
1.1
Nano-Litz Wire Bundles
The team envisions NanoLitz to be a 3D braided wire bundle that leverages nano-scale features constructed in a micron-to-millimeter scale component. The overarching goal is to achieve ultra-low loss radio-frequency (RF) performance [5]. With the technology that is currently available, typical RF inductors have a quality factor Q < 10. However, with access to NanoLitz technology, engineers would be able to produce inductors with quality factors approaching
Q
= 1000 at 1-10 GHz [5]. The quality factor is a dimensionless
number that represents the energy being stored in a circuit compared to the energy that is 13
Figure 1-1: Example of a litz bundle comprised of nine wire strands (image excerpted from [5]). thermally dissipated:
QOL L Q =w 0
(1.1)
RDC'
where wo is the frequency, L is the inductance and RDC is the equivalent resistance [4]. For an inductor, as the frequency of a given system increases, the equivalent resistance of the system also increases due to the skin effect [4]. The skin effect is the inclination of current to distribute more densely at the outer surface, or "skin", of a conductor as frequency increases [2]. The higher the frequency, the smaller the skin depth, which causes the effective cross-section to decrease [2].This leads to a decrease in the
Q factor,
and thus
a decrease in the overall efficiency of the system [4]. NanoLitz would enable a reduction in the losses caused by the skin effect. These low loss components would provide better filters to address spectral crowding and jamming, as well as improved power handling for thermally robust portable and miniature systems [5]. The NanoLitz team has proposed to fabricate wires using a nano-wire scaffold for copper with silica insulation. The team has anticipated two main production challenges in creating the NanoLitz wires: (1) the current approaches to conducting wire fabrication are not scaleable to the 0.6-2pm diameter size needed for radio-frequencies ranging from 1 GHz to 10 GHz, and (2) the current approaches to wire braiding leverage macro-scale machines that impose tension and bending forces that are incompatible with braiding nanoto-micro-scale wires [5]. To address the second production challenge, the NanoLitz team plans on exploring 14
two technologies to braid the custom nano-wires. The first method is a "Self-Assembly" approach that relies on the specific binding properties of DNA to enable controlled wire braiding [5]. The second method is a "Directed Assembly" approach where the wire ends will be attached to beads that will then be manipulated in such a way that will enable controlled wire braiding [5]. The purpose of this thesis is to explore the directed assembly method that was proposed by the NanoLitz team at a macro scale. From this exploration at a larger scale, a recommendation would then be made to the NanoLitz team to frame their efforts as they enter the first phase of the fabrication of 1-10 GHz range litz bundles.
1.2
Goals
In order to properly explore options for the directed assembly method, three main goals were identified: 1. Explore bead manipulation options that can enable wire-braiding at a micro scale. 2. Perform calculations to determine what settings are required for each option to produce the required force to perform wire-braiding. 3. Create a macro-scale demo of one of the options that illustrates controlled wire braiding. The NanoLitz team proposes to develop novel assembly technologies that can be scaled to the application of low loss RF conductors. The program goals for NanoLitz will be to braid ten's of threads of approximately one prm diameter wires that are approximately one cm in length. The team would like to focus on fundamental technology development rather than engineering of fully scaled up manufacturing. The demo that will be covered in this thesis will serve as an intuitive design tool that the NanoLitz team engineers will utilize to be able to visualize the 3D geometry of a possible platform option, as well as visualize the braiding of three wires. This will allow the design engineers to adapt the platform to manipulate ten's of threads of wires and smaller beads. This demo will serve useful as it is hard to capture the braiding mechanics in a CAD tool. 15
1.3
Requirements
The basic platform configuration that is considered in this thesis involves a series of radially symmetric channels. The concept behind the basic platform design is that each bead will be attached to the end of an individual wire. A collection of wires will be fixed together at one end at a prescribed height above the channel platform. This setup is shown in figure 1-2.
/
7
yxx'
(2)
(1)
K
(3)
(4)
Figure 1-2: Overall setup concept - independent of proposed platform geometries.
The two bead manipulation methods that are explored in this thesis are dielectrophoretic manipulation and driven fluid flow. For both of these bead manipulation options, the platform is designed such that a constant fluid level can be maintained in the channels. The beads will be manipulated by an externally applied force that allows for the travel of each bead to be electronically controlled. Outlined below are the three main requirements that were identified to make wire braiding possible. 16
1.3.1
Wire Stiffness
In order to braid a set of wires, each wire must be deflected to a certain amount that varies as the braid grows. To understand the force required to overcome the wire stiffness and bend the wire, a wire made of certain length L, diameter D, and modulus of elasticity E can be modeled as a cantilevered beam [10]. For small deflections, a relationship between the deflection of the wire and the applied force F can be represented based on Bernoulli-Euler beam theory [10]: 3EI
F= 3
=
2EI 2
00max
(1.2)
where I is the moment of inertia of the beam.
-
---
----------------------
max
a
--------------------------
F Figure 1-3: Cantilevered beam undergoing a small deflection (image excerpted from [10]).
For large deflections however, like the ones required to braid a wire, a deeper analysis
must be performed on a vertical cantilevered beam. In reference [10], a model was developed to simulate a beam undergoing a large deflection. In this analysis, the bending force that is required is defined as: 2
a
Fbend =
EI
2
,
(1.3)
where a is a parameter defined based on the bending angle and is described in more depth in [10]. Based on this model, the force required to bend copper wires made of length L = 10cm and diameters D =1mm and D = lyt in the 2 pN range and 100 pN range respectively. 17
through a 90' turn are estimated to be
1.3.2
Viscous Force
In addition to overcoming the wire stiffness, the chosen applied force must also overcome the viscous force of the fluid that is within the platform. When a spherical particle that is submerged in a fluid medium begins to move with a certain velocity, it experiences this viscous force. In this thesis, the viscous force is explored in two different regimes: typical laminar flow and Stokes' flow. For an open channel flow like the one described in figure 1-4, the laminar flow regime applies when Re < 500 and the Stokes' flow regime refers specifically to flows with Re < 0.1 [8] [16]. The Reynolds number, Re, is defined as Re - u,
(1.4)
where u is average velocity of the fluid traveling through the fluid, R is the hydraulic radius, and v is the kinematic viscosity of the fluid [6]. The hydraulic radius is defined as follows: A
R=
Pw'
(1.5)
where A, the cross-sectional area and Pw, the wetted perimeter, are defined as [6]: A=WD
(1.6)
Pw = W + 2D.
(1.7)
Frce surface
/n IL)
Figure 1-4: Cross-section of an open rectangular channel (image excerpted from [6]). 18
As can be inferred from equation 1.8, laminar flow occurs when the following condition is met: Ulaminar
1
___
C
!1
m
0
0225
U'
~
16.67
48
Figure A-3: Solidworks drawing of the outer ring of the structure.
-
0
m
z
z
N)
N)
w
C
5
4 4
3 3
2 2
6 6
5
A --
-245 I
AB
*240.24 0
Q0 0 LOr
*
5 I
n
C
CN
0O (Y)
UNLESS OTHERWISE SPECIFIED: DIMENSIONS ARE IN MILUIMETERS SURFACE FINISH: TOLERANCES: LINEAR: ANGULAR: NAME
DEBUR AND BREAK SHARP EDGES
FINISH:
SIGNATURE
DATE
I_
_
DO NOT SCALE DRAWING
REVISION
TITLE:
IDRAWN CHK'D
'-
.
U- LO
MFG GQA
____
MATERIAL:
WEIGHT:
DW
""'Bottom Support ^A SCALE:1:3
SHEET I OF I
*
9.76
10
I>
-M
CDi
-U
CD
0
1~
17
Li..
T-0i
0
M
0
0
0
62.44
200
600
to
50
Figure A-5: Solidworks drawing of the platform sections.
0
M52
0.
~5.08
----I
M
VY
3
2
56
4
00
3
2
B
40
*
B
0
*0
4.76
0o
0
0 '40 CN
to
0 c
c
10 DEBUR AND BREAK SHARF EDGES
FINISH: UNLESS OTHERWISE SPECIIED: DIMENSIONS ARE IN MILUIMEERS SURFACE FINISH: TOLERANCES: UINEAR: FANGULAR: NM INTR
SIGNATURE
NAME
DO NOT SCALE DRAWING
REVISION
TITLE:
DATE
DRAWN CHKD
Dj
APPVD
2
Base Plate
MATERIAL:
IGQA
1
-t
!WBGHT:
SCALE:1:3
SHEET I OF
1
Figure A-7: Image of the overall structure.
52
Appendix B Valve Arduino Code
53
const int valvel
const int valve2 const
int
valve3
13; 12; 11;
void setup() { // initialize digital pin 13 as an output. //white pi nMode(valvel, OUTPUT); //green pinMode(valve2, OUTPUT); //purple pinMode(valve3, OUTPUT);
} void loopo
{
//Valves are always open, so by turning output to high, it closes valve // close valve 2 // wait for 5 seconds delay(5000); // open valve 2 digitolWrite(valve2, LOW); // wait for 3 second //delay(3000);
dgiitalWrite(valve2, HIGH);
// close valve 1 digitalWrite(valvel, HIGH); // wait for 5 seconds delay(5000); // open valve 1 digltalWrite(valvel, LOW); // wait for 3 second //delay(3000); // close valve 3 digitalWrite(valve3, HIGH); // wait for 5 seconds delay(5000); // open valve 3 digitalWrite(valve3, LOW); // wait for 3 second //delay(3000); I
Figure B-1: Arduino code for gate release to enable braiding.
54
Bibliography [1] M. Bartoli, N. Noferi, A. Reatti, and M.K. Kazimierczuk. Modeling Litz-wire winding losses in high-frequency power inductors. In Power Electronics Specialists Conference, 1996. PESC '96 Record., 27th Annual IEEE, volume 2, pages 1690-1696 vol.2, Jun 1996. [2] M.V.K. Chari and Z.J. Csendes. Finite element analysis of the skin effect in current carrying conductors. Magnetics, IEEE Transactionson, 13(5):1125-1127, Sep 1977. [3] Stuart Churchill. Viscous Flow: The PracticalUse of Theory (Fluid Flow). Springer Wien New York, 2011. [4] David Cory and Manos Chaniotakis. Frequency Response: Resonance, Bandwidth, Q Factor. MIT OCW 6.071, 2006. [5] Amy Duwel. Nano-Litz: Braided nano-wires for high performance RF components. November 2014. [6] Shreeram Inamdar. Open Channel Flow. April 2012. [7] Thomas B. Jones. Electromechanicsof Particles. Cambridge University Press, 1995. [8] Mohamed Kharboutly, Micha8l Gauthier, and Nicolas Chaillet. Modeling the Trajectory of a Microparticle in a Dielectrophoresis Device. Journal Of Applied Physics, 2009. [9] H Morgan, N Green, M Hughes, W Monaghan, and T Tan. Large-area travellingwave dielectrophoresis particle separator. journal of micromechanics and microengineering. Journalof Micromechanicasand Microengineering,7, June 1997. [10] Joshua C. Nation. Fabrication of Chip-Scale Radio Frequency Inductors. Master of Science in Mechanical Engineering, Massachusetts Institute of Technology, Department of Mechanical Engineering, Jun 2014. [11] Adrian Neculae, Claudia G. Biris, Madalin Bunoiu, and Mihail Lungu. Numerical Analysis of Nanoparticle Behavior in a Microfluidic Channel Under Dielectrophoresis. 2012. [12] N. Phansiri and B. Techaumnat. Study on the electromechanics of a conducting particle under nonuniform electric field. Dielectrics and Electrical Insulation, IEEE Transactionson, 20(2):488-495, April 2013. 55
[13] Ant6nio Ramos. Electrokinetics And Electrohydrodynamics In Microsystems. Springer Wien New York, 2011. [14] Jong Ming Sung. Dielectrophoresis and Optoelectronic Tweezers for Nanomanipulation. Stanford Physics 210, 2007. [15] Marc A. Unger, Hou-Pu Chou, Todd Thorsen, Axel Scherer, and Stephen R. Quake. Monolithic Microfabricated Valves and Pumps by Multilayer Soft Lithography. Science, (5463):113, 2000. [16] Frank M. White. Fluid Mechanics. McGraw-Hill, 4 edition, Dec 1998.
56
